Music Theory Through Improvisation: A New Approach to Musicianship Training

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Music Theory Through Improvisation: A New Approach to Musicianship Training

Music Theory Through Improvisation Music Theory Through Improvisation presents a unique approach to basic theory and mus

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Music Theory Through Improvisation Music Theory Through Improvisation presents a unique approach to basic theory and musical training, examining the study of traditional theory through the art of improvisation. The book follows the same general progression of diatonic to non-diatonic harmony in conventional approaches, but integrates improvisation, composition, keyboard harmony, analysis, and rhythm. Geared toward the diverse interests and abilities of today’s student, Music Theory Through Improvisation places the study of harmony within improvisation and composition in stylistically diverse formats, including jazz and popular music. Keyboard realization, for students with little or no keyboard training, is the primary mode of assimilation of harmonic materials. FEATURES • • • •

Based on a user friendly system of improvisation study Combines Jazz, Popular, Classical, and other musical sources Enhances understanding of the creative process and the inner workings of music Includes an Audio CD of play-along tracks for improvisation and a companion website with resources for students and instructors,

Edward Sarath is Professor of Music in the Department of Jazz and Improvisation Studies at the School of Music, Theatre, and Dance at University of Michigan. He is the president and founder of the International Society for Improvised Music.

Music Theory Through Improvisation A New Approach to Musicianship Training

EDWARD SARATH University of Michigan

First published 2010 by Routledge 270 Madison Ave, New York, NY 10016 Simultaneously published in the UK by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to © 2010 Taylor & Francis All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Sarath, Ed. Music theory through improvisation : a new approach to musicianship training / Edward Sarath. p. cm. 1. Music theory. 2. Jazz–Instruction and study. 3. Improvisation (Music) I. Title. MT6.S2547 2010 781–dc22 2009009413 ISBN 0-203-87347-5 Master e-book ISBN

ISBN 10: 0–415–80453–1 (hbk) ISBN 10: 0–415–99725–9 (pbk) ISBN 10: 0–203–87347–5 (ebk) ISBN 13: 978–0–415–80453–0 (hbk) ISBN 13: 978–0–415–99725–6 (pbk) ISBN 13: 978–0–203–87347–2 (ebk)


Preface Acknowledgments Chapter 1

Improvisation Across Boundaries: A Trans-stylistic Approach Getting Started 2 Non-syntactic Catalysts 4 Tension and Release, Variety and Unity, Motion and Stability 5 Melody 7 Ostinato, Motive, Sequence 7 Antecedent-consequent Structure 9 Melodic Contour 9 Pitch-based Melodic Improvising 10 Pulse-based Improvising 11 Form-based Improvising 12 Graphic Formal Analysis 13 The Inner Dimensions of Improvisation 13 Silence 17 Solo Pieces 17 Free or Open Collective Improvising 19 Clarity of Ideas 20 Transparency, Laying Out, and Soloing 21 Endings 21 Culminating Exercises 23 Concluding Thoughts: Template for Artistic Development 24 Listening Resources 24 Further Reading 27

Chapter 2

Music Fundamentals Staff, Clefs, Scales 29 Key Signatures 31 Major Scale 31 Minor Scale 33

xi xvii 1




Intervals 34 Modes 38 Pentatonic Scales 40 Aural Transposition 41 Melodic Cells 42 Aural Transposition with Pentatonic Scales 45 Chapter 3

Modality and Rhythm I: Time Feels Importance of Aural Immersion 48 Core Elements of Time Feels 49 Further Aural Immersion Strategies 50 Modal Etude 1 52 Two-player Improvisation Practice Frameworks 56 Rhythmic Templates for Time-feel Grooves and Melodic Improvising 58 Listening Resources: Time-feel-based Music with African and African-American Roots 61 Suggested Recordings 62 Further Reading 64


Chapter 4

Modality and Rhythm II: Small Group Framework Call and Response 66 Strategies for Generating New Ideas 68 Mode-rhythmic Formats 76 Minor Blues 77 Indian Rhythmic Practices 80 Small Group Ensemble Performance and Project Format 82


Chapter 5

Basic Tonal Materials: Triads and Seventh Chords Triads 85 Seventh Chords 87 Two Roman Numeral Systems 89 Inversions 90 Close Position and Open Position or Spread Voicings 92 Keyboard Realization 95 Fortification Exercises: Aural and Analytical 97 Modes 98 Modemaster Drills 98


Chapter 6

Harmonic Functions Tonic–Subdominant–Dominant Functions 103 The Dominant Seventh Chord 104 Cadence 105 Keyboard Application 107 Improvising on the II–V–I Progression 109 Integrating Diverse Forms of Musical Knowledge 111 Chord-scale Analysis 111




II–V–I in Minor 113 Writing and Analysis Exercises 116 Voice Leading 117 Idiomatic Progressions 121 Turnarounds 123 Free-tonicization Strategies Level I 124 Chapter 7

Swing: Global Rhythmic Gateway Elements of Swing 129 Swing Articulation 130 Blues 131 Transcription Format 133 Scale and Chord Exercises for Cultivating the Swing Concept 135


Chapter 8

Melodic Line Construction and Harmonization Composing Melodic Lines on Chord Changes 138 Diatonic Target Notes 140 Problems with the Root of the Major Seventh Chord in the Melody 141 Melodic Analysis 142 Guide Tones 143 Written Application 145 Incorporating Guide Tones in Melodic Lines 147 Two Approaches to Composing Melodies on Chord Changes 150 Harmonizing Melodic Lines 151 Top–down Harmonization at the Keyboard 151 Harmonic Rhythm 155 Small Group Application 156


Chapter 9

Chord Inversion Present and Past Chord Inversion in Jazz 158 Non-harmonic Tones 161 Analysis of Bach Chorales 163 Pedal Point and Inversion 166


Chapter 10 Non-diatonic Harmony I: Applied Chords Secondary Dominant Chords 169 Secondary II–V7 Sequences 171 Secondary Dominant Chords of Non-diatonic Target Chord/Key Areas 172 Delayed Resolution of Secondary Dominant Chords 173 Secondary or Applied Leading Tone Chords 174 Passing Diminished Seventh Chords 175 Substitute Dominant Chords 177 Improvising on Chord Sequences with Applied Dominant and Leading Tone Chords 180 Free-tonicization Strategies Level II 183




Chapter 11 Non-diatonic Harmony II: Modal Mixture Modal Mixture on Diatonic and Non-diatonic Roots 186 Passing and Structural Functions in Modal Mixture Harmonies 187 Improvising on Modal Mixture Progressions 191 Composing 192 Analysis Exercises 193 The Neapolitan Sixth Chord 195 Free-tonicization Level III 196 Modal Mixture As an Entry Point into Modal Composition Techniques 197 Creative Synthesis 199


Chapter 12 Figured Bass Realization at the Keyboard Basic Principles 201 Triads 202 Seventh Chords 203 Accidentals 204 Voice Leading and Doubling Considerations 205 Four-part Chorale Writing 210 Figured Bass Lines Applied to Jazz Chord Changes 211


Chapter 13 Extended Chords General Principles of Chord Extensions 213 Types of Chord Extensions 215 Replacement Tones and Chord Superimposition 216 Extended II–V7–I Voicings 217 Smooth Voice Leading 218 Multiple Configurations of Extended Voicings: A and B Voicing Patterns 221 Extended II–V–I Voicings in Minor 225 Extended Substitute Dominant Chords 229 Further Reading 232


233 Chapter 14 Altered Extensions The Altered Dominant Chord 233 Chord Superimposition Strategy: Build a Maj7(b5) on the Third to Yield V7(#9,b13) 235 Extended and Altered Substitute Dominant Chords 237 Further Keyboard Work 240 Substitute Dominant Chords as Augmented Sixth Chords 245 Improvising on Altered Harmonies 248 Integrating Scales into your Melodic-Harmonic Palette Through Improvising and Composing 251 Improvising with Altered Scales 251 Composing Lines with the Scales 252 Reharmonization 252 Rhythm Changes 254



Chapter 15 Diverse Approaches to Analysis Tonicization and Modulation Revisited 257 Tadd Dameron’s “Lady Bird” 259 Jerome Kern’s “All the Things You Are” 261 John Coltrane’s “Moment’s Notice” 262 Chopin, Prelude No. 4 267 Schubert, Waltz 269


Chapter 16 Fine-tuning and Expanding the Jazz Palette Rhythmic Layers for Melodic Clarity 273 Registral, Density, and Contour Variety 275 Intervallic Variety 276 Motivic and Multi-motivic Development 278 Integrating Strategies 279 Expanding the Harmonic Palette 280 Cross-stylistic Melding 285 Final Composition Project 290 Final Creative Synthesis 290 Concluding Thoughts 291


Appendix 1 Introduction to Species Counterpoint Overview of Species Principles 294 Creating Contrapuntal Lines: General Principles Pertaining to Writing Species Melodies 296 First Species 1:1 299 Second Species 2:1 300 Third Species 4:1 301 Improvising with More Florid Lines 303 Fourth and Fifth Species 304 Fourth Species: Suspensions 304 Fifth Species: Integration of the Previous Four Species 306


Appendix 2 Overtone Series and Equal Temperament


Appendix 3 Rhythmic Exercises


Appendix 4 Jazz Etudes


Appendix 5 Additional Keyboard Exercises Seminal Keyboard Projects 334 Advanced Guide Tone Exercise 334 Advanced Two-hand, Non-tertial Open Voicings 335


Appendix 6 Instrument Ranges, Transposition, and Score Excerpts




Appendix 7 Aural Transposition Triads 351 Seventh Chords 352 Pentatonic Scales 353 Idiomatic Lines 354 Repertory 355


Appendix 8 Sample Syllabus


Appendix 9 CD and Web Audio Tracks





Music Theory Through Improvisation is a hands-on, creativity-based approach to music theory and improvisation training designed for classical musicians with little or no background in improvisation. It is also designed for jazz musicians who are interested in new approaches to improvisation, music theory, and forging connections with the broader musical world. The book may serve both purposes as a primary or secondary text in a variety of educational formats, ranging from coursework in jazz improvisation and jazz theory, contemporary improvisation and music technology, as well as music theory coursework that seeks to integrate improvisation in the learning process. MTI has evolved in the latter capacity over the past 15 years in conjunction with a musicianship course at the University of Michigan School of Music, Theatre, and Dance that fulfills two terms of core musicianship requirements for classical and jazz students. Conventional musicianship training has long been largely focused on interpretive performance and analysis of European classical repertory. While the richness of this tradition is beyond dispute, the diversity of today’s musical world calls for a much-expanded skill set that includes engagement with diverse musical traditions and robust creative processes— improvisation foremost among them—and that bridges the divide that has long separated musical study from the musical world. Music Theory Through Improvisation (MTI), one of the very first musicianship textbooks of its kind, bridges this divide through the combination of a unique breadth of creative processes and carefully selected content that derives from wide-ranging sources. While jazz factors prominently among these sources, the aim is not jazz-specific training but skills that open up connections to the broader musical landscape.

Features • Based in a “user-friendly” system of improvisation study that is specifically designed for classical musicians with little or no experience in this age-old musical practice. The system is also effective in expanding the boundaries of experienced style-specific improvisers (e.g. in jazz, baroque, or other improvisatory genres). • Integrates improvisation, composition, performance, keyboard realization, writing, analysis, rhythmic training, and multiple approaches to aural skills.



• Integrates jazz, popular, European classical, and other musical sources. • Harmonic materials follow the same general trajectory as most conventional approaches, moving from diatonic to non-diatonic chords and functions (e.g. secondary dominants, modulation, modal mixture, extended and altered harmonies). • Keyboard realization system—designed for non-keyboard principals and keyboard principals alike—juxtaposes jazz, pop, and European classical harmonic models. Students learn to play jazz/pop as well as baroque “chord symbols,” and all writing extends from keyboard realization practice. • Rhythmic training derives from Indian, Arabic, African, African-American, and European classical sources. • Grounded in a cross-cultural aesthetic that enables musicians to understand and appreciate differences between musical traditions as well as identify connecting threads. • Introductory exposure to concepts in music cognition that enhance understanding of the creative process and the inner workings of music.

Why Music Theory Through Improvisation is Needed The breadth and eclecticism of the contemporary musical world presents both untold opportunities for musicians as well as challenges in its sheer magnitude. Indeed, the musical pulse of our times lies as much in the intersections between genres as in the genres themselves, at which point musicians and music schools must face the daunting task of identifying and gaining the skills needed to engage in this cross-cultural melding. A shift is needed in musicianship training from the conventional, content-based approach—which in the realm of music theory focuses on analysis and written work with European classical repertory—to a process-rich model in which carefully selected content is integrated with hands-on, creative engagement. This is where improvisation excels, particularly when framed within a process-content spectrum that is designed with the contemporary musical world in mind. Let us take a closer look at how MTI embodies these principles. In addition to improvisation, MTI’s broad process spectrum also includes keyboard realization, which is a central means for developing command of harmonic materials in this system, and rhythmic training, writing, and analysis. MTI’s content scope draws from jazz, European classical, and other sources. However, whereas conventional theory texts as well as jazz theory texts have been designed around a priori-style assumptions— e.g. conventional text presuming European classical as a default style source, jazz theory books presuming the same with jazz—MTI was created by stepping back from style boundaries and responding to two fundamental questions. First, what skills do today’s musicians need? Second, what are the richest, most integrative, and practical sources for those skills? Students need training in improvisation, composition, and performance; they need to develop fluency with a range of tonal, modal, post-tonal materials, formal structures, and contemporary time-feels as well as other rhythmic practices; and they need to be able to



transcend category, in other words, to situate particular genres within the broader musical landscape. While it is clear that no one genre is capable of providing this complete range of skills, it is also clear that jazz—due to its process-breadth and integrative capacities, where improvising, composing, performing, harmony, rhythm, and melody are integrated— must be cited as a particularly fertile resource. As noted above, this is not due to the idea of jazz as a destination for all musicians, but rather to the quest for a foundational platform from which openings to a wide diversity of areas may be forged. MTI approaches jazz not as an end-goal but as an integrative, creative point of departure that will not only enable students to thrive in subsequent coursework—whether this involves European classical music, further jazz study, world music, technology, or music education—but will also help them navigate their individual pathways through the musical world. These principles are exemplified in MTI’s units on contemporary improvisation, figured bass realization, species counterpoint, and rhythmic training that draws from Indian, African, and Arabic traditions. While there is no denying that MTI represents a new paradigm of musicianship training, it is also important to recognize the ways in which it intersects with, if not bolsters, conventional areas of study. This was an important issue in the MTI review process, both in the proposal stages and after the manuscript was completed, and hits at the core of educational reform debates. MTI, due to its broader orientation, does not venture into European classical repertory in as detailed a way as is found in conventional musicianship books. However, MTI not only follows the general trajectory of diatonic (chord structure and function) to non-diatonic harmony (applied chords, modal mixture, altered and extended chords) that underlies conventional theory courses; the approach may enable levels of assimilation that may not be likely in conventional approaches. This is due to MTI’s process-based application. Consider, for example, the kind of assimilation that is possible when, as is central in MTI, students learn secondary dominant chords by realizing them in multiple keys at the keyboard, improvising with chord progressions containing them, and composing with these structures in addition to more conventional written and analytical strategies. Or consider MTI’s approach to augmented sixth chords through the lens of altered jazz harmonies, again which are realized at the keyboard in multiple keys, and are approached through improvisation and composition in addition to conventional modalities of writing and analysis. Hands-on, creative engagement enables the development of a new level of fluency with theoretical materials that allows musicians to traverse wide-ranging style boundaries.

Music Theory Through Improvisation for the Undergraduate MTI may be used as a primary text for two or more terms in the undergraduate musicianship core. At the University of Michigan School of Music, Theatre, and Dance it is primarily aimed toward classical musicians with little or no experience in improvisation. Students have the option of electing the alternative track to fulfill two terms of their core musicianship requirements. Mounting appeals for more diverse musicianship models suggest that this class may be a precursor to further curricular innovations.



Moreover, the book has also been beneficial for jazz musicians and other musicians with experience in improvisation that has been confined to a given style; the diverse strategies of MTI will both help expand the creative horizons of style-specific improvisers as well as fine-tune their aural and theoretical skills. Jazz musicians, for instance, benefit considerably from the trans-stylistic improvising approaches, work in species counterpoint, stylistically diverse approaches to keyboard, and multi-ethnic rhythmic training that are included in the book. MTI’s hands-on and efficient approach to core training also makes it an ideal resource for music technology students.

Using Music Theory Through Improvisation in the Classroom MTI’s broad scope enables wide-ranging possibilities for classroom application. While different instructors will necessarily adapt MTI to fit their particular situations, the following approach has been used successfully in classes ranging from 16 to 40 students and is offered as a guide that may be of use at many institutions: • Students are grouped in small ensembles of three to six members that remain intact for all or most of the semester and serve as formats for improvisation, composition, rhythmic training, and aural transposition. The groups may consist of virtually any combination of instrumental types—e.g. bassoon, voice, cello, guitar, and trombone— and among the compelling aspects of the approach are the creative results that stem from unusual instrumentations. • Each class meeting begins with one or two small groups presenting their work to the rest of the class. In a class of 30 students that meets twice per week, six quintets could be formed, two of which would begin each class session, enabling each group to play every fourth class. • Discussion and feedback follow the small group performances. Engaging in theoretical knowledge provides an all-important balance between creative application and analysis. The theoretical portion of the class session may be used for written work, ear-training, analysis, exams, etc. • Special projects, such as transcriptions—where each student plays his or her transcription for the class—or written exams that require the entire class period, present exceptions to the general format of class sessions. • Individual proficiency exams are conducted outside of regular class time to monitor keyboard work. These exams may be done in short appointments lasting five minutes per student and may be scheduled at appropriate intervals throughout a semester. Four proficiency exam sessions per term, held over the course of two semesters, should be sufficient to cover the Seminal Keyboard Projects sequence presented in the book.



Teaching Resources 1 Over 300 hands-on, creative exercises integrated into the body of the text. 2 Accompanying CD provides background tracks for improvisation, correlated to the text. 3 Listening lists with specific examples corresponding to specific exercises. 4 Sample syllabus for two-semester sequence in the Appendix. 5 Website includes: • Listening tracks corresponding to selected examples. • Additional syllabi for shorter and longer sequences. • Chapter-by-chapter outlines that provide a sense of how the various parts of the book fit together as a whole. • Suggestions for instructors, including advice for skills assessment. Music examples that correspond to the play-along CD are indicated by the CD icon. Listening examples on the website are indicated by the website icon. To access the website, log on to:

Toward a New Era of Musicianship Imagine the kind of vitality and programming that might be possible in a symphony orchestra which largely comprises contemporary improvisers-composers-performers, where the music of Brahms and Beethoven is juxtaposed with new works that cross genres and engage musicians in new ways. Imagine a music school or department in which the conventional specializations that are currently the norm (e.g. in performance, jazz, theory, history, technology) unite in entirely new curricular pathways that transcend category and exemplify the creative horizons of musical innovators past and present. This kind of scenario is not only possible; it is likely the most apt description of the music school of the future. MTI is a resource to help expand, enliven, and transform core musical training in order to promote movement in this direction. Ed Sarath January 2009


Conceding that it will be impossible to identify everyone who has played a role in the evolution of this book, I will make an attempt to cite some of the most important contributors. Thanks to Geri Allen, Judith Becker, Andrew Bishop, Steve Bizub, Gabe Bolkosky, Paul Boylan, Roger Braun, Mathew Buchman, Rui Carvalho, Colleen Conway, Jason Corey, Robert Culver, John Daniel, Michael Dessen, Katherine Doversberger, David Elliott, James Froseth, Kyra Gaunt, Michael Gould, David Greenhoe, Karri Harris, Michael Herbst, Katt Hernandez, Karlton Hester, Maud Hickey, Robert Hurst, Fritz Kaenzig, Christine Kapusky, Christopher Kendall, Richard Kim, Andy Kirschner, Gregg Koyle, Ralph Lewis, Joe Lukasik, Andrew Mead, Marie McCarthy, Lester Monts, Janne Murto, Michael Nickens, Josh Palay, Jari Perkiomaki, Guthrie Ramsey, John Rapson, Bennett Reimer, Ellen Rowe, Steve Rush, Alex Ruthman, George Shirley, Mary Simoni, Donald Sinta, Charles Young, Betty Anne Younker, Sarah Weaver, Jackie Wiggins, Dennis Wilson, and Karen Wolff for the various kinds of support they have provided for the project through the years. Many thanks to Lenore Pogonowski for planting the seeds over 30 years ago. My deep gratitude goes to Mark Kirschenmann who has taught much of the material with me for a number of years. Many thanks to Constance Ditzel, music editor at Routledge, for her pioneering spirit, to Denny Tek for preparing the book for production, and to Maggie Lindsey-Jones, Ann King, Ruth Jeavons, and Emma Wood for their great work in the production process. Finally, I am deeply indebted to my wife Joan Harris for her painstaking feedback and help in preparing the manuscript and materials. Permission to use the following material: EXAMPLE 1.3 TAKE THE ‘A’ TRAIN Music and lyrics by Billy Strayhorn and The Delta Rhythm Boys. ©1941 (Renewed) Billy Strayhorn Songs, Inc. (ASCAP) and FSMGI (IMRO). All rights controlled and administered by State One Songs America (ASCAP). All rights reserved. Used by permission of Alfred Publishing Co., Inc. (Renewed) by Music Sales Corporation (ASCAP) and Tempo Music, Inc. (ASCAP). All rights for Tempo Music Inc. administered by Music Sales Corporation (ASCAP). International copyright secured. All rights reserved. Used by permission.



EXAMPLE 9.1 MY FUNNY VALENTINE Controlled by WB Music Corp. and Williamson Music Co. All rights reserved. Used by permission of Alfred Publishing Co., Inc. from Babes In Arms. Words by Lorenz Hart, Music by Richard Rodgers. Copyright 1937 (renewed) by Chappell & Co. Rights for the extended renewal term in the US controlled by Williamson Music and WB Music Corp. o/b/o the Estate of Lorenz Hart. This arrangement copyright 2008 by Williamson Music and WB Music Corp. o/b/o the Estate of Lorenz Hart. International copyright secured. All rights reserved. EXAMPLE 14.4 INVITATION Music by Bronislau Kaper. Lyrics by Paul Francis Webster © 1944, 1955 (copyrights renewed) Metro-Goldwyn-Mayer Inc. All rights controlled by EMI Robbins Catalog Inc. (Publishing) and Alfred Publishing Co., Inc. (Print). All rights reserved. Used by permission of Alfred Publishing Co., Inc. © Webster Music. Used by permission. EXAMPLE15.1 LADYBIRD Music by Tad Dameron © 1947 (renewed) by Music Sales Corporation (ASCAP). This arrangement copyright 2008 by Music Sales Corporation (ASCAP). All rights for the British Reversionary Territories administered by Redwood Music Ltd. Reprinted by permission. Copyright 1947 Consolidated Music Publishing (renewed). Redwood Music Ltd. for the Commonwealth of Nations (including Hong Kong, Canada, and Australia), Eire, South Africa, and Spain—all rights reserved. Used by permission. All rights reserved. EXAMPLE FIGURE 15.2 ALL THE THINGS YOU ARE From Very Warm For May. Lyrics by Oscar Hammerstein II. Music by Jerome Kern. Copyright 1939 Universal-Polygram International Publishng, Inc. Copyright renewed. This arrangement copyright 2008 Universal-Polygram International Publishing, Inc. All rights reserved. Used by permission. Used by Permission of Music Sales Limited. All Rights Reserved. International Copyright Secured. EXAMPLE A6.9 FINGERS Music by Thad Jones. Copyright 1969 D’Accord Music. © Publishers’ Licensing Corporation, PO Box 5807, Englewood, NJ 07631, USA. Copyright renewed 1997. Used by permission.

chapter 1

Improvisation Across Boundaries: A Trans-stylistic Approach

In this chapter, we: • Improvise with a trans-stylistic approach. • Create with basic elements such as density, dynamics, duration, tessitura, ostinato, motive, sequence, pulse, form, and silence. • Examine basic concepts such as tension and repose and non-syntactic elements. • Consider new perspectives on listening and the inner dimensions of the creative process. • Set the stage for systematic acquisition of music theory skills.

Improvisation has been central to most of the world’s music traditions and has begun to assume even greater prominence in today’s cross-cultural musical melding. In response to this emergent eclecticism, as well as for pedagogical reasons, Music Theory Through Improvisation begins with a “trans-stylistic” system of improvisation practice. Trans-stylistic simply means that instead of specifying style elements in advance—such as jazz chord changes or Baroque figured bass lines or Hindustani raga-tala cycles—we allow style elements to manifest as a byproduct of the creative process. This not only helps foster in our classrooms the very syncretism that prevails in the overall musical world, it also lays important groundwork for the acquisition of musicianship skills. A central feature of the trans-stylistic approach is its “user-friendly” entryway for musicians who are new to improvisation. The very thought of making music apart from the printed page can be intimidating for many musicians, and this challenge may be exacerbated when style-specific constraints are imposed at the outset. By contrast, the trans-stylistic approach seeks first to elicit a creative flow that extends from each musician’s unique background in order that they can gain a glimpse of the expressive power of improvisation early on in their journeys. Everyone has an inner reservoir of influences and imagery that is shaped by the totality of their musical exposure and life experience. When we tap into


Improvisation Across Boundaries

this reservoir and begin to experience music as a means for personalized, creative expression, we establish a new and more meaningful relationship with music and the quest for musicianship skills. Music theory is a common example of a knowledge area from which many musicians feel disconnected due to the lack of an outlet for creative application. The trans-stylistic approach plants the seeds for this connection between theory and practice, craft and creativity, and skills and artistry, to flourish. The trans-stylistic approach also provides tools for expanding the horizons of experienced, style-specific improvisers. This occurs through the use of “non-syntactic” catalysts, which are introduced in this opening chapter, that expose musicians to new ways of generating and organizing ideas. Having transcended familiar style terrain, musicians can now return to it with a newfound appreciation and understanding. Here it should be emphasized that the aim of the trans-stylistic approach is not to replace style-specific engagement but to lay groundwork that enables musicians to move freely between both worlds. While the music of many of today’s leading innovators cuts across wide-ranging style boundaries, rigorous immersion in style-specific training has in most cases been central to their development. At a single stroke, the trans-stylistic approach lays groundwork for beginning and experienced improvisers to engage directly in the style-specific and crossstylistic synthesis that will enable them to forge their unique pathways through the vast possibilities of the contemporary musical landscape.

Getting Started The following exercises may be used in a variety of formats—from private lessons, to classroom formats, and some may even, with a little creative adaptation, be applied to largeensemble rehearsal settings involving 30 or more musicians. They are intended to be done using the principal instrument or voice, unless otherwise indicated. The exercises need not necessarily be done in the sequence given, although the very first exercises are particularly geared to new improvisers. While the formats generally proceed from minimal constraints to gradually more involved parameters, they should not be thought of as mere stepping stones along a linear course of growth. Rather, they are intended as stimulating vehicles that can yield compelling results at all stages of musical development. I often return to these very first exercises with even my most advanced students as they have the capacity to elicit an infinite range of musical responses. Reminder: The exercises in this chapter are to be done using the principal instrument or voice, unless otherwise indicated.

Long tone exercise Sit in a circle if possible. Select a scale that everyone knows. It could be anything from a C major scale to something more exotic, such as an octatonic scale. Each musician is to

Improvisation Across Boundaries


play only long tones, selecting notes only from the designated scale. Listen carefully to the collective sonority as you enter and try to hear in advance how your tone will fit in; it is permissible, upon entering with a tone that you feel clashes excessively with the sonority of the moment, to shift to another tone. Generally, this will be resolved by playing a tone a half or whole step above or below the first note attempted. The duration of the tones should be determined by what is comfortable on one’s instrument. You may rest between entrances. • Variation A: Do the long tone exercise without designating a scale. Musicians can thus play any pitch as they add to the collective sonority. As in the above exercise, attentive listening is essential. • Variation B: Have individuals take turns improvising short solos, involving more florid passages (faster notes), atop the long tone texture. Soloists should make every effort to stand out atop the collective texture. Ensemble must make every effort to play softly enough so that soloists stand out.

Exercise 1a

The above exercise and its variations provide an inviting beginning format for musicians who are intimated by the idea of making music apart from the printed page. They also call for heightened listening from new and advanced improvisers alike. The following questions will stimulate reflection and dialogue regarding creative decision-making that these exercises involved: Were there times when you felt the need to change your note or your volume, or had to decide whether or not to play? What were the criteria by which these decisions were made? Were there moments when you felt that the piece really worked? Others that were less compelling? Why? The following exercises provide more creative latitude. Wheel of duets Sit in a circle if possible. Each student pairs with the student directly across from him or her in the circle. Each pair improvises a short duet—perhaps 30–60 seconds—with no parameters (e.g. key area, style) delineated in advance. The importance is listening as intently as possible to what is happening. The pieces can follow one another without pause (applause is allowed, though!) unless the instructor wishes to break the sequence in order to comment.

Exercise 1b

After one full cycle (one rotation of the wheel) of duets, discuss the results. What was particularly interesting? What were some of the limitations? Might some tendencies be identified—such as limited dynamic range, lack of clarity of ideas, all pieces ending up sounding the same? How might these problems be rectified?


Improvisation Across Boundaries

Play another cycle or partial cycle of duets with the intention of addressing the ideas that have been expressed in the feedback session, or trying out new possibilities. Perhaps simply striving to make each piece as contrasting as possible from the one before it may yield significant results.

Non-syntactic Catalysts The theorist Leonard Meyer identified two categories of basic musical elements. Syntactic parameters include harmony, melody, and rhythm. Non-syntactic parameters include dynamics (volume), density (amount of note activity—from highly sparse to highly dense— in a given passage), tessitura (high or low range), duration, timbre, and silence. Now that we have initiated a creative flow we can begin to refine our playing through the use of nonsyntactic parameters as improvisatory catalysts. This will help us improve the clarity and variety in our ideas. Later in this chapter we will begin to explore the syntactic domain, which will assume center stage beginning in Chapter 2. In the meantime, it will be helpful to observe the syntactic elements that spontaneously emerge as by-products of our improvisations with non-syntactic catalysts. Dynamics Improvise a short piece—20–30 seconds—that includes the loudest sound you can make comfortably and musically, without reaching a decibel level that is uncomfortable or harmful (e.g. in the case of trumpet players or electric guitarists) to anyone present. Then do the same with your softest extreme: play a note or short phrase at your softest volume. At first, there will be tendency to not broach the outer boundaries, and so it is important to be vigilant in actually reaching your extremes.

Exercise 1c

Density Density pertains to the amount of note activity in a given unit of time. Higher-density passages comprise faster note activity than sparse, lower density passages, where slower note activity and rests predominate. Play a short piece that juxtaposes high-density music with low-density music.

Exercise 1d

Do not be concerned if your high-density playing stretches the boundaries of your technique to the point where you may not feel in total control of what you are playing. The main point here is the effect and experience of high-density music and going beyond our

Improvisation Across Boundaries


ordinary boundaries. Often we stop short of the high-density texture we are capable of because it means risking the precision we work so ardently to develop. While these are admirable ideals, the purpose of this brief exercise is to move outside of our comfort zone. Hence a different kind of vigilance is called for; instead of the usual attention we might pay to issues such as tone quality and precision of execution, now our challenge is to temporarily let go to a degree we may not be accustomed to. Occasional forays of this kind can be highly beneficial to our creative as well as technical development. Registral variety The same exercise may be applied to registral or tessitura variety. Improvise brief passages that traverse the highest and then the lowest range of the instrument.

Exercise 1e Combinations of non-syntactic elements Play improvisations that combine the various parameters—e.g. density and dynamic variety; dynamic and registral variety; and dynamics, density, and registral variety.

Exercise 1f

Tension and Release, Variety and Unity, Motion and Stability The goal of the above and forthcoming exercises is to develop the tools to create interesting improvisations. An important factor in creating musical interest is the balance between two kinds of emotional and perceptual responses, described variously as repose and tension, unity and variety, and stability and motion. Too much familiarity breeds boredom, too much novelty has an alienating effect. Two common shortcomings in the above sorts of exercises are (1) when the improviser fails to venture far enough into the extremes specified by the exercise—e.g. very soft and very loud, very dense and very sparse, very low and very high— and thus the music may lack variety; and (2) when the improviser does broach his or her extremes but provides only the briefest glimpse of a given parameter—e.g. a single low or high tone in order to fulfill the requirement of tessitura variety—thus failing to adequately establish a given idea. In the second instance, a modicum of variety may be achieved but unity and coherence are compromised. Here it may be helpful to think of musical ideas as characters in a play; a character needs to be not only introduced but also developed. While a brief improvisation does not provide much time for this to happen, even an extra few seconds on a given idea can make a significant difference in terms of establishing that musical character. As you perform the improvisations in this chapter and throughout the book, maintain a sense of how your music not only fulfills the parameters specified in each format but also makes a compelling musical statement. How well are you balancing unity and variety, or


Improvisation Across Boundaries

repose and tension? Are you establishing your musical characters adequately? What kind of emotional response are you evoking? The next exercise, which may be done with any size ensemble, utilizes a two-movement format that will result in a longer improvisation which allows us to incorporate the concepts discussed above as well as introduce new ideas. Here the importance of listening as fully as possible cannot be emphasized strongly enough. The kind of listening that is required of improvisation calls for a total immersion— mental, emotional, physical, and transpersonal/transcendent—in the music being made. We will go into this further later. In short: strive to engage with the sounds happening around you with the utmost urgency of attention, or as the saying goes, “as if your life depended upon it.” This is not to overlook the playfulness that can be part of improvised music, but to ground that play in the most complete kind of engagement possible. Another point has to do with silence, which we will also discuss more in depth later. It is not necessary to play constantly. Find places to rest in order to let the music breathe and give space to ensemble members; you will appreciate it when they return the favor, and the music will inevitably reach new heights as a result. As ironic as it may sound, the ability to not play is as important as the ability to play in the development of improvisation skills. Two-movement improvisation Duration 2–3 minutes. First movement, no pulse. Second movement, introduce pulse. In movement one, strive to create interest through the use of variety in non-syntactic elements. In movement two, which is pulse-based, strive for variety in dynamics, register, and duration. Note: Movement one can come to a complete pause before movement two begins, or movement two can grow organically out of movement one.

Exercise 1g More Duets

Duets are an excellent way to begin improvisation classes and improvising ensemble rehearsals because they give each musician ample space and exposure, yet also deal with interactive concerns. Wheel of duets Students pair with a partner across the circle—with no parameters delineated in advance except for the stipulation that each duet contrasts as much as possible with the one that precedes it. Contrast may be created through different tempos, dynamic levels, density levels, etc.

Exercise 1h

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Flip-flop duets Player A states an idea and begins to develop it. Player B enters with material that is as contrasting as possible. Gradually, A begins to adopt some of B’s ideas, and B adopts A’s, until both partners have fully exchanged roles. This requires that both individuals pay close attention to the ideas generated by their partners.

Exercise 1i

Melody While harmonic practice tends to be the focus in conventional approaches to musicianship, harmony as we generally think of it in the West is absent in much of the world’s music. Such is not the case with melody, which is virtually as prominent as rhythm in musical traditions across the globe. Two principles of melodic construction will be introduced here that we will also revisit later in the book. One involves the development of basic melodic ideas over time. The second is melodic contour, or shape.

Ostinato, Motive, Sequence Music unfolds in time; in other words, one thing happens after another. The meaning inferred in a given piece or performance is significantly shaped by how the music is structured in time. The meaning inferred in a painting, on the other hand, is generally not nearly as time-dependent; we apprehend the work in its entirety and then attend to aspects more according to our inclinations rather than according to a temporal sequence that might be suggested in the image. Even paintings that may direct our attention sequentially from one image to another upon initial viewing leave us free to follow our own temporal pathways thereafter; not so in music. A central strategy in establishing a musical train of thought is the use of repetition in one form or another. When we repeat an idea, either exactly or with modifications, we assert its importance. Two approaches to repetition in the realm of melody are found in the ostinato and the motive. An ostinato is an idea that is repeated exactly several times (many ostinati are repeated extensively). Ostinato bass lines are perhaps the most common form of ostinato, although any line in any register played by any instrument can be an ostinato. A motive is a basic musical idea that is usually a measure or so in duration and which undergoes modification over time, either through alteration of its melodic shape or rhythm, or—as in what is called a sequence—by repeating the motive on different pitch levels. Example 1.1 shows an ostinato pattern; Example 1.2 shows the same pattern treated as a motive that is developed sequentially by being reiterated on new pitch levels (up a step with each new iteration). Notice that after three times, the initial motive, for the sake of variety, gives way to a new idea.


Improvisation Across Boundaries

EXAMPLE 1.1 Ostinato

EXAMPLE 1.2 Motive and sequence

The following exercises allow you to improvise with these devices. Ostinato duet Improvise freely with a partner, without pulse. After 15–30 seconds or so, one player establishes a pulse by creating an ostinato line. The second player then creates another ostinato that aligns with the first one (can be a contrasting or similar idea, but should not be an identical idea, and must be rooted in the same pulse) thus yielding a texture in which two ostinato patterns occur simultaneously.

Exercise 1j Ostinato ensemble exercise Proceed as in the above exercise, but now with a larger group. One by one, each member creates a different ostinato pattern that aligns with the basic pulse. This may be done with an ensemble of any size.

Exercise 1k Motivic flip-flop duet Player A establishes a motivic idea and develops it. Player B plays a contrasting motivic idea and develops it. Gradually A and B take segments of each other’s ideas and either meld them, or move on to entirely new material.

Exercise 1l

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Antecedent-consequent Structure Another melodic strategy that makes use of motives is the antecedent-consequent structure. An antecedent idea poses a melodic question, and a consequent idea offers a response (Example 1.3).

EXAMPLE 1.3 Billy Strayhorn, “Take the ‘A’ Train”

Solo format Improvise antecedent-consequent phrases. Strive for optimal clarity of ideas.

Exercise 1m

Melodic Contour A second facet of melodic construction has to do with the contour or shape of the melody. Parameters that impact upon shape include direction—whether a melodic line ascends or descends—and the size of the intervals between any two melodic notes. Variety along these two parameters—use of ascending and descending motion and the distribution of stepwise motion and larger intervals—can open up untold melodic possibilities. In the melodies below, the use of intervals such as fifths, sixths, and octaves creates interesting contours. The next melody makes use of large intervals while still maintaining a lyrical effect at a fairly rapid tempo. In the following melodies (Examples 1.4 and 1.5) leaps are generally followed by a change in direction, an effective melodic device that is found in much tonal or modal music. Example 1.6 demonstrates exceptions to this principle, and the more jagged atonal melodic contour that results, yielding yet another melodic strategy to add to our creative palette. In no way is this to suggest that successive intervalic leaps in the same direction are not found in tonal or modal music, nor that these prevail in atonal music, but simply to identify general principles that may serve as a helpful guide in developing our skills.



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EXAMPLE 1.4 Brahms, Symphony No. 1 in C minor, op. 68, theme from first movement

EXAMPLE 1.5 Ed Sarath, Shirodara


Solo format Improvise and explore different melodic contours (e.g. passages that move largely by stepwise motion but make use of occasional leaps; passages that predominantly make use of large intervals).

Exercise 1n

Pitch-based Melodic Improvising In Chapter 2 we will begin formal study of pitch-based improvising, utilizing various modes and pentatonic scales. As a prelude to that work, here we will explore pitch-based improvising in its most basic form, involving the use of a drone. A drone is a sustained pitch that underlies a musical passage or, as in Indian music, an entire piece. Our purpose at hand is to improvise melodies atop the drone and draw upon our basic instincts regarding melodic shape and coherence prior to systematically studying specific melodic principles and scalar and chordal structures. An excellent listening example from the list at the end of the chapter is found in Zakir Hussain’s Making Music.

Improvisation Across Boundaries


Drone improvisation Designate a pitch to serve as the drone, and one or more ensemble members to play the drone. Ideally, all ensemble members will take turns playing the drone, atop which all ensemble members take turns improvising melodically. A key or scale can be selected (the drone note would be the tonic or fundamental note; A is the tonic note in an A minor scale), or ensemble members can use key areas or scales of their choice when they solo. Strive to use registral variety and density variety in your melodic improvising, as well as motivic development. • Variation: Choose a key area or scale and have ensemble members who are not soloing improvise sustained note backgrounds behind each soloist. • Variation: After the drone has sounded for a while, terminate the drone and have ensemble members create pulse via one or more ostinato patterns within that key area.

Exercise 1o

Pulse-based Improvising The correlate in rhythmic improvising to the drone in pitch-based improvising is the use of a basic pulse or beat. The ability to sustain a steady pulse in your improvising is an essential skill for all improvisers given the prevalence of pulse and rhythmic time feels—or “grooves,” as in jazz, rock, funk, hip hop, blues—in much of the world’s music. In these introductory exercises, it is unnecessary to designate meter or a particular kind of time feel. It is simply necessary to establish a pulse and then improvise in whatever style you are comfortable. What is essential, however, is that the pulse is clearly upheld in your improvised lines. In other words, if someone were to hear only a single improvised line without hearing the establishment of a pulse prior to the piece or any instrument that might be playing the pulse as a background, that pulse should be clearly evident in your improvising. Several strategies might be pointed out regarding the note values you play. You can improvise with the basic rhythmic unit that defines the pulse. To create more interest, you can also divide that note value by two, and in turn divide that by two—and so on—as your technical capacities allow. Thinking of this in terms of notated rhythmic values: if we assign a quarter note value to the basic pulse, we would be improvising with eighth notes and possibly sixteenth and thirty-second notes atop the pulse. We can also extend this thinking in the opposite direction to give us longer durations, where we double the length of notes, improvising with quarter notes, half notes, whole notes, etc. These subdivisions and expanded durations may be thought of as rhythm layers, a concept that we will return to when we move into improvisation in time feels. Rhythmic layers may be thought of in terms of duple relationships (2:1, 4:1, etc.) and triplet relationships (3:1, 6:1, etc).


Improvisation Across Boundaries

Solo format Establish a pulse and improvise lines that embody the pulse, moving freely between the various rhythmic layers using duple subdivisions (e.g. eighth notes, sixteenth notes) and composite note values (half notes, whole notes), always maintaining a solid rhythmic foundation in your playing. • Variation: Do the same thing with triplet subdivisions and composite note values. • Variation: Play these exercises in duets and larger ensembles.

Exercise 1p

Form-based Improvising Musical form pertains to the overarching structure of a piece, whether composed or improvised. A wide array of approaches to musical form are found within and throughout the many musical traditions of the world and reflect the different conceptions of time, language, and other kinds of sensibilities that are unique to different cultures. While we have become quite accustomed in the West to teleological, or goal-driven formal structures, in which ideas are introduced, developed, and lead to some climactic point, after which the initial idea might return to yield a kind of formal symmetry, much of the world’s music is not teleological in nature but rather involves cyclical structures that obscure the sense of linear (past-presentfuture) temporality and promote a more non-linear, present-based sense of time. Jazz happens to be an interesting blend of teleological and non-teleological conceptions. The following are several formal frameworks that can help guide our improvisatory work. ABA form involves the statement of an initial idea A, followed by a contrasting idea B, and the return of the initial idea. By contrast is what is sometimes called through-composed form, which might be represented as ABCDE, etc., where new material is continually spun out with no significant use of recurring themes; this presents an entirely different and equally valid approach to formal design. Arch form involves a kind of retracing of formal sections so that the first and last correspond with each other, the second and second-to-last correspond with one another, the third and third-to-last similarly correspond to each other, and so on depending on the length of the piece; this is analyzed as ABCDCBA. These are a few of the many possibilities that call upon the improviser to invoke different kinds of concept in terms of the development of materials at hand. Form-based improvisation Select formal structures from those described above and improvise pieces that conform to them. Make sure that each section contrasts sufficiently with the one before in order that clear and solid landmarks uphold the sense of formal structure.

Exercise 1q

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Graphic Formal Analysis The above frameworks represent but a slice of what is possible in terms of musical form and most schools offer upper-level coursework that will promote further understanding in this area, usually from the standpoint of composed-notated musical form. Application of these formal designs to improvisation is a largely untapped area and has much to offer the contemporary improviser. However, this is in no way to invalidate formally open improvisatory approaches, in which no formal or other constraints are specified in advance. Rather, engagement with formal designs can expand the palettes of improvisers by either providing them with frameworks that may be delineated in advance, or helping cultivate strategies that may be invoked spontaneously as the music unfolds. A preliminary kind of formal analysis that can be beneficial even to individuals with no formal musical training is “graphic analysis.” This involves listening to a piece of music and sketching with pencil and paper—using whatever graphic imagery you might choose—the overall trajectory or shape of the music as you perceive it. For instance, fast sections may be represented with highly active images, sparse sections with simpler markings, etc. You can even include brief narrative descriptions—such as “the music gets particularly intense (or subtle, or both) at this point”—to help convey what you are hearing and feeling. The primary intention of the exercise is to gain exposure to some of the wide-ranging possibilities regarding how music is structured over time so that you can draw upon these possibilities when you create. The exercise can also help you develop the capacity for a deeper and more focused engagement as a music listener; the more you perceive, the more you gain from every musical encounter. Analyses Choose three recorded samples of music from traditions or styles that are as contrasting as possible and do graphic analyses of them.

Exercise 1r

The Inner Dimensions of Improvisation So far our focus has been on exterior aspects of the improvisation process—ways of generating and organizing musical ideas. Now let us explore what might be termed the inner dimensions of improvisation, which takes us to the realm of consciousness or transcendence. Improvisers commonly talk about peak creative moments—also called “flow,” “the zone,” or being “in the moment”—that are characterized by enhanced fluidity of performance, presence, mental clarity, freedom from conditioning, well-being, mind– body coordination, group interaction, and other attributes of heightened consciousness. Whereas ordinary consciousness is prone to conditioned patterns where individuals resort to pattern responses, heightened consciousness enables new levels of freedom and spontaneity, which are naturally high priorities for improvisers. While for many individuals


Improvisation Across Boundaries

these episodes occur only on an occasional basis, even small glimpses of these states can be highly meaningful and inspiring in terms of the possibilities inherent in human creative development. Many improvisers have pursued disciplines such as meditation in order to help cultivate these capacities. The following are further strategies. One approach involves a more engaged kind of listening, where hearing becomes as much an emotional, physical, and transpersonal/transcendent activity as it is aural. It is one thing to register the various sounds happening around us; it is quite another to experience them as deeply connected with our own consciousness, as if we were creating these sounds ourselves. In doing the following exercises, it is important to emphasize that expanded listening and experiences of heightened consciousness are not so much a matter of exerting intensive effort in hopes of involving a new experience but rather a process of letting go and simply allowing oneself to relax into a more complete immersion in the present moment. It may be helpful to think of the capacity for expanded awareness and engagement in sound as a matter of unlocking inherent possibilities that lie dormant within us as opposed to learning to experience something that is foreign. The sounds around you While walking or sitting outside, whether in the woods, by the seashore, or in a city park, allow yourself to become quiet and fully engaged in the present moment. Listen to the full array of sounds around you. Take an inventory of all the sounds that you rarely notice and appreciate them as parts of the infinite sonic palette that exists. Imagine each of these sounds as parts of a piece of music. Let yourself relax into the sonic tapestry around you. One thing that may help is to use your breathing as a guide; with each exhalation feel yourself letting go and becoming more immersed in your surroundings. As you do this, observe your inner state; you may notice that your awareness expands, your clarity of perception increases, and a heightened sense of inner calm and well-being ensues. Again, this is not a matter of forcing expanded experience, but rather simply allowing this expansion to unfold of its own accord.

Exercise 1s Feel the sounds Proceed as above, but now add a new component: feel the sounds around you as facets of your own consciousness, as if they are flowing through you, or that you are actually creating the sounds.

Exercise 1t

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Internalize sounds Apply the above approach when you are listening to music, either live or recorded, where you experience the music as if you are the one creating it. This is an excellent practice to use in improvisation sessions during moments in which you are not playing; the more you can engage with the sounds around you as if you were the one playing them, the more you will be able to interact and contribute when the time comes for you to play.

Exercise 1u

Another way of cultivating the capacity for heightened listening and heightened consciousness is through the lens of the present—in other words, by exploring the different kinds of present experience that are possible. Musical moments may be experienced as parts of a linear flow, in which the meaning of any given event is largely dependent upon its relationship to what precedes and follows it, or as nonlinear entities that are relatively autonomous from their temporal surroundings. While linear or nonlinear conception is usually a matter of degree and at least somewhat dependent upon the musical context, we can cultivate our capacities for these kinds of perception as both musical listeners and performers. The ability to shift modes of present awareness enlivens our capacity to be in the moment and invoke heightened consciousness. One approach to this shifting of present awareness from a linear to nonlinear orientation is through directing our attention to “implication–realization” cycles. Implication– realization theory originated with the work of Leonard Meyer and was subsequently developed by him and his student Eugene Narmour. Originally oriented toward the perception of melody, from the standpoint of the listener, basic principles may be extrapolated from the theory that apply to broader musical parameters as well as the experience of the creative musician. Music unfolds in time; one thing follows another. In musical contexts whose meaning is dependent upon the sequence of ideas, as in the use of motivic development, each idea that sounds, or is realized, may be perceived as related to what has preceded it and also as a catalyst for implied successors—those ideas that one expects might follow. Put another way: musical ideas (realizations) trigger expectations (implications) about what is to come next. When expectations/implications are fulfilled, a sense of unity is promoted. When expectations/implications are thwarted, a sense of surprise and variety is enlivened. The effectiveness of the music is dependent upon the balance between these two poles; excessive fulfillment of expectations breeds predictability and boredom, thus requiring some element of surprise, via expectations that are thwarted. By the same token, excessive thwarting of expectations breeds alienation. We can heighten our engagement in the moment by observing our response to implication–realization cycles. The following exercises have us do this by focusing in two different directions. One involves what might be called “anticipatory hearing,” where we perceive each moment as a generator of future possibilities. Another involves the attempt


Improvisation Across Boundaries

to perceive moments as autonomous, self-contained moments that stand on their own independently of what precedes and follows them. Anticipatory hearing In an improvised music rehearsal or concert in which you are not playing but listening to others, focus on experiencing each moment as a catalyst for future events. In other words, when an idea sounds (or is realized), sense what might follow (is implied). As you do this, observe whether or not your expectations are fulfilled and what response is thereby created.

Exercise 1v

While it is not possible to attend to every single moment in a piece in the manner indicated, listening with this intention will likely provide a clear glimpse of a newfound level of present engagement that may be invoked when you improvise. From this linear musical perspective, the present is the source from which the future springs and, by attending to what might unfold, we penetrate more deeply to the heart of the present moment. Now let us attempt to experience heightened present engagement from a nonlinear angle. Again, it will not be possible to experience every single moment in this way, and because nonlinear hearing is more challenging and context-dependent, even a few glimpses of this experience will be productive. It should be emphasized that music in which non-syntactic elements (e.g. density, dynamics, timbre, tessitura) rather than syntactic elements (particularly harmony) are prominent is more conducive to nonlinear perception. Nonlinear hearing In an improvised music rehearsal or concert in which you are not playing but listening to others, focus on experiencing each moment as an autonomous entity, whose meaning is independent of what precedes and follows it.

Exercise 1w

While it is recommended that the exercises be done in improvised music situations where the music is being heard for the first time, the different kinds of perception are also possible in non-improvised music and you are encouraged to try out these exercises in different contexts.

Improvisation Across Boundaries


Silence Another way of invoking heightened awareness is the use of silence in your improvising. While it is only natural in our ardent pursuit of musical skills to focus largely on making sounds and understanding the various ways they are melded together, let us not forget that music consists of both sounds and silence. In fact, instead of thinking in terms of sound as the basic fabric of music, consider thinking of silence as the basic fabric and sounds as temporary interruptions in the silence. While it may be hard to find much music in which sounds are subordinate, in terms of length of time, to silence, an awareness of sound as a kind of a foreground phenomenon against a backdrop of silence can help get us out of middle-zone conception; it is yet one more way of expanding our boundaries and liberating us from day-to-day, conditioned modes of conception. In the following “silence study,” two points are essential. One involves how silence is framed: silence needs to be prepared, executed, and resolved. In order to prepare silence, a second point is important, which is the creation of variety within one or more of the basic non-syntactic elements: dynamics, density, or register. Ultra-soft, ultra-loud, ultra-dense, ultra-sparse passages can help create a sense of expectation. When followed by silence, this expectation fills the space and continues to propel the music forward even though no sounds are being made. When prepared effectively, the silence can extend for some time, and then it is up to the musician to decide how it might be resolved. Resolution of the silence can be similar to how it is prepared (e.g. ultra-soft and low tones into and ultra-soft and low tones out of silence), or it can contrast radically (ultra-soft and low in, ultra-high and loud and high density out), creating an entirely different effect. Silence study This exercise is done in a solo format. Play an improvisation of one to two minutes that incorporates at least one, and ideally several, prominent stretches of silence as part of the musical fabric. The silence needs to be more than merely the length of time to take a breath on a wind instrument. One of the criteria for the effective use of silence is the sense that the silent moment is self-contained and complete as opposed to eliciting a feeling of discomfort, as if the musical flow has been abruptly interrupted. Effective use of silence is experienced as part of the musical flow.

Exercise 1x

Solo Pieces The following is a series of formats for solo, unaccompanied improvisation. Solo improvising challenges us to access a wider range of strategies to sustain interest. Solo improvising can be not only tremendously rewarding, it can help us cultivate skills that are invaluable in collective formats (which, for most musicians, will comprise the bulk of their improvising).


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Two-part solo piece Improvise a piece that consists of two sections. Section A will have no pulse; section B will be pulse-based. In section A strive to use as much variety as possible along the parameters of dynamics, duration, density, and register. In other words, explore the extremes of these parameters (very soft, very loud; very dense, very sparse, etc.) Use silence as part of the musical fabric; silence can be more than just a pause to take a breath, it can stand on its own as a self-contained part of the musical flow. Section B involves the establishment of a clear pulse. Seek to utilize dynamics and registral variety. You are encouraged to explore different layers of the pulse (e.g. 2:1 relationships, 4:1, etc.) as well as motivic development.

Exercise 1y Scale-based solo piece Solo piece using designated scales/modes (e.g. pentatonics, octatonics, phrygian, etc.). Proceed, as in the above two-section exercise (no-pulse/pulse; non-syntactic variety), but this time select a scale with which you will improvise.

Exercise 1z

The next solo pieces take motivic development to a new level. Instead of developing a single motive, they involve developing two or contrasting motives by moving back and forth between them. Key to these exercises is that each idea is crystal clear, and that the ideas are clearly contrasting with one another. Here it may be helpful to think of the contrasting motives as different characters on a stage in a theater piece. When character A enters, we immediately gain a sense of who he or she is, and that character B is a completely different personality. Clear ideas engage us and generate a sense of expectation about what is to follow. The clearer the ideas, the more likely they will be retained in short-term memory, which is required of the following piece. Multi-motivic development solo piece Establish a motive A and allow it to develop briefly. Then introduce a contrasting motive B and allow it to develop briefly. Then return to A and develop it further, and similarly return to B and develop it further. Continue alternating the two motives. Eventually, you may let the two motives merge. This may be done with and without pulse. • Variation: Establish and develop three or more contrasting motives (e.g. A, B, C).

Exercise 1aa

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Multi-motivic development using designated scales/modes Proceed as in the above multi-motivic development exercise, but select a scale or mode that you are familiar with in which this multi-motivic development will occur.

Exercise 1bb Unaccompanied time feels Set up a rhythmic groove on your instrument by repeating some basic idea, and then improvise around the idea, retaining enough of its basic character to sustain its role as a rhythmic anchor. Eventually your improvisatory excursions may become longer, but they should reiterate some fragment of the initial idea often enough to sustain continuity and the sense that you are playing on this particular groove. For those who play single-line melodic instruments, this may be challenging given the rarity of this kind of opportunity. Recommendation: strive for variety in register and dynamics in framing this anchor, in addition to a crystal-clear sense of pulse. • Variation: when you establish the initial idea to start the groove, leave an equal amount of silence between iterations of the idea. In other words, if the idea is two bars, then that should be followed by two bars of silence (during which, nonetheless, a solid pulse should be felt). Then, after a few iterations of the basic idea, gradually begin to fill in the spaces. Can be done with and without designated scales/modes.

Exercise 1cc

Free or Open Collective Improvising Most of the above exercises, while not specifying style constraints in advance, have delineated at least one and often multiple improvisatory parameters. These constraints will become more involved as we move further through the book. As a complement to these approaches, it is not only highly valuable to engage in completely free or open improvisation formats—with nothing specified in advance—but these approaches can also yield highly magical and powerful results. At this point, improvisers need to call upon their utmost capacities in listening and creative engagement, because now there is nothing to fall back on. The larger the free improvising ensemble, moreover, the more important these issues become. Free or open improvising can be a great way to process many of the concepts covered as well as to unearth entirely new ideas. In addition to the above considerations, two key issues bear emphasis in this kind of music-making: clarity of ideas and endings.


Improvisation Across Boundaries

Clarity of Ideas Strive for statements that are as clear as possible, whether they are simple or complex ideas. How do we define clarity? One criterion is the degree to which the idea stands on its own as a compelling statement that commands our attention. Another is its capacity to suggest forward motion. In other words, clear ideas are more likely to generate a sense of what may come next—which may often involve some reiteration of the idea—than unclear ideas, from which future development is nebulous. In going into some strategies for ensuring clarity of ideas, it is important not to become enmeshed in value judgments when we improvise. Improvisation should be a process of mindful and joyful play; we are engaged in the moment, we attend as fully as possible—mentally, aurally, emotionally, physically—to what is happening around us, and we embrace what transpires and the opportunity to contribute to the flow in whatever ways we can (which include playing or not playing). Moreover, any idea that might be deemed less clear may, through simple strategies, be transformed into a highly compelling musical statement. Let us first consider some approaches that may enhance clarity. First, it is important to emphasize that clear ideas need not be complicated or virtuosic. A single, short staccato note surrounded by silence can be a crystal-clear idea, as can be a long tone that is held for five or ten seconds or more. At the same time, so can a highdensity flurry consisting of streams of notes, perhaps akin to the “sheets of sound” that were associated with the jazz saxophonist John Coltrane later in his career. Clear ideas are like characters on a stage; when they enter, you know immediately that this is a new character, a new entity with its own personality, history, and future potential. One strategy for promoting a sense of clarity is to create ideas that utilize the extremes of some of the basic non-syntactic elements—such as dynamics, density, duration, and register—considered earlier. In other words, instead of playing ideas that are not very soft or loud (dynamics), whose note activity is not very fast or slow (density), whose notes are not very long or very short (duration), and which are not very low or high (register), try creating ideas that extend beyond these “middle zone” parameters. In no way is this to suggest that the interesting and crystal-clear ideas that use these parameters are not possible. Rather, the process of consciously stepping outside of these parameters may require us to engage more fully—to be more present—in the creation of ideas, and this can carry over to situations in which we may create ideas that, say, utilize mid-range dynamics or register. Another helpful strategy may be to combine non-syntactic extremes that may be less commonly combined, such as extremely soft flurries, or loud, short notes, or high, soft tones separated by long stretches of silence. When an idea is introduced that is not as clear as it might be, one strategy may be, instead of jumping in with a perhaps nebulous sense of direction, to simply wait and see if the first player or players may achieve greater clarity on their own. Another is to play something entirely contrasting to the first idea, which may compel the musician who plays it to shape it into a more accessible form. A third idea is to try to find some kernel or core ingredient in the idea and exaggerate it in an attempt to “press the issue.” In essence, making sense of unclear musical ideas is not entirely different than what happens in verbal interactions when the point of the dialogue is obscured. At some point, one of the parties will likely ask,

Improvisation Across Boundaries


“What are we talking about?” The same thing can happen in improvisation; the only difference is how this question is posed.

Transparency, Laying Out, and Soloing Two of the most important aspects of collective improvisation are the capacities to lay out— to not play for possibly extended periods of time—and to play transparently, as these allow the ideas of others to move to the forefront. A third necessity is the ability to move to the forefront when the music calls for it. One of the signs of mature improvisers is the ability to move fluidly between these roles. The ability to listen intently and not play is much like being a good listener in a conversation; sometimes in the course of human interaction the most valuable contribution is made by simply listening in a heartfelt way to what our partner or colleague is saying. The same holds for music. To play transparently, promoting related goals, means to play ideas that support but do not overshadow what else is happening. This may happen by playing softly, interjecting silence between one’s notes, or playing timbres that add interest but do not predominate. Drum-set players, when playing in ensembles that also include strings and woodwinds, must pay special attention to playing transparently because even relatively soft cymbal sounds can easily assume prominence. The same holds for when the music moves into rhythmic grooves; drummers in eclectic instrumentation formats need to find new ways to play grooves that are transparent enough to allow all instruments to be heard. Having established the importance of these kinds of musical sensitivity, it is equally important for improvisers to step up and assume a solo role from time to time. Sometimes a single player can take the whole ensemble to an entirely new plateau. When all of the musicians in an ensemble are able to sustain a level of engagement that permits them to move between these roles—silent listener, transparent supporter, or soloist—truly exciting and magical results are possible.

Endings Endings are one of the most challenging yet important, and in fact exciting, aspects of improvised music, particularly in open improvisation. Few things distance audiences from the music more than excessively long pieces, and endings can be among the most compelling moments of an improvisation because, unlike in composed music, when at least the musicians are aware of the approach of the ending, now no one knows. The ability to create compelling endings in collective improvisation is clearly an art. A few principles will help cultivate this ability. First, the ability to create effective endings is based most fundamentally in the ability to engage in the music on a moment-by-moment basis. It is from this vantage point that the improviser is able to spontaneously decide—feel, intuit, reason—that this particular instant may be the last in a given piece. Creating endings, therefore, is not so much a matter of playing an idea that is particularly suited to be the very last idea, but rather simply being


Improvisation Across Boundaries

able to choose not to play anything further and letting the most recent event stand as the ending. The more one is able to engage in a moment-to-moment manner, the greater the freedom to make this kind of musical decision. A second principle extends from the first, which is that the kind of awareness that allows compelling endings is no different than the kind of awareness that leads to compelling beginnings or interactions at any point in a piece. From this standpoint, musicians ought to be able to end pieces even after a few seconds. This, in fact, is a kind of litmus test for the ability to create effective endings. Playing very short improvisations—which is challenging the larger the group—is a good way to cultivate this awareness. Try collective improvisations with the stipulation that they will last for only 30–45 seconds. Then try even shorter pieces that are to end after perhaps 10 seconds. In these attempts, it is important to proceed as if the piece might follow a more conventional course of development—lasting four to eight minutes or more—and at the same time maintain the intention of finding an endpoint at any given moment early on. This, in fact, is an excellent head-set to maintain at all times— the capacity to either continue or to end—as it indicates a heightened sense of being in the moment. It is also helpful to be aware of three possible kinds of endings. Most common is the gradual decrescendo and fade, where you sense early on in this closing passage that the end is near and it is just a matter of time before the last note sounds. A second type of ending is more common in composed notated music, where a gradual crescendo and buildup in intensity eventuates in a final chord or gesture in which everyone cuts off together. Since this final event requires some kind of cue, improvisations do not often end this way. Instead, when improvisations reach such peaks in intensity at points far enough into the piece where they could serve as endings, the culminating chord or event—rather than being sharply cut off as in an orchestral work—tends to decay into something more resembling the first type of ending. However, this is not to rule out this possible ending in improvised music, and there is nothing wrong with a policy whereby ensemble members can give a visual cue for a cut-off to make this effect possible. A third type of ending is perhaps the most interesting of all of the options, involving sudden endings that present themselves spontaneously and are instantaneously seized by the musicians. In such instances, unlike the above two scenarios, neither musicians nor listeners have any idea in advance that the ending is imminent; it comes out of the blue. These “found” endings can be highly effective in the way they take everyone by surprise. In fact, these endings are often only realized as endings after the fact. A typical scenario is as follows: some passage is followed by an instant of silence, which is initially conceived as a space that connects prior sounds with sounds yet to be made. Then—and all this happens within the briefest instant of time—it may occur to one or more of the musician(s) that this could possibly be the end of the piece. But until group consensus is attained, the question still remains—is the piece continuing or not? Only after the silence remains uninterrupted for a sufficiently longer moment—again, we are talking about a few seconds at most—will the collective decision for the piece to be over be officially made. At this point the ending—in terms of the final notes sounding—is realized only in retrospect. Whereas endings following gradual fades or buildups are anticipated prior to the fact, found endings are experienced retroactively—“Oh, that was the end!”—much to the delight of players and listeners alike.

Improvisation Across Boundaries


This is not to suggest that found endings are more desirable than the other two types of endings and that improvisers should strive to end all of their pieces this way. Rather, improvisers should be open to the phenomenon of found endings so that they may be seized when they present themselves, a capacity which, to reiterate, is based in a keen momentto-moment awareness and freedom. But different improvisatory moments will call for different kinds of endings, and improvisers need to be conversant with all possibilities. An excellent way of developing this important capacity is to play short improvisations, with the length delineated in advance. Tracks 2 and 3 on the website provide two examples of relatively short improvisations and the following exercise has you play even shorter pieces.


Collective improvisation In an ensemble format, create several improvisations of the following durations: 45 seconds; 10 seconds; 90 seconds; 5 seconds; 2 minutes.

Exercise 1dd

The extremely short improvisations are particularly valuable because they force us to invoke a degree of moment-to-moment concept we may not ordinarily experience. Our task is then to sustain this awareness over the course of improvisations of any length.

Culminating Exercises Small group improvisation (three to six players) Map out a multi-movement form that includes as many of the above elements as possible (e.g. non-syntactic variety; pitch-based, pulse-based, and form-based improvising; silence and listening; solo passages, etc.) using a notational system of your choosing (graphic score, narrative sketch, etc.). Try to find a balance between pre-ordained structure and spontaneity. Perform in class.

Exercise 1ee Free collective improvisation Divide the class into several randomly chosen groups (e.g. count off 1, 2, 3, 4—and the 1s form a group, 2s, etc.) that are to improvise with nothing planned in advance. Emphasize the importance of clarity of ideas, listening, laying out when needed, assuming prominence when needed, etc.

Exercise 1ff


Improvisation Across Boundaries

Concluding Thoughts: Template for Artistic Development Artistic development may be thought of in terms of input and output phases, both of which are important and complementary aspects of a program of study. Input involves focused skill acquisition and study, output involves creative expression. Since most of the musicians who will be working with this book have engaged in considerable input activity but have had limited output experience, our focus so far has been on initiating output activity in this opening chapter through stylistically open improvisatory exercises. By tapping into the inner reservoir of musical and extra-musical experiences that each of us has acquired, we have elicited a creative flow which prepares us for the subsequent input activity that is to follow. This is not to suggest that input and output phases need to occur separately. Indeed, they work hand in hand, as will be seen in forthcoming chapters. In that most of the input and output activity to follow will be style-specific, you are highly encouraged to continue working with the stylistically open formats provided in this chapter as they will serve as stimulating catalysts for creative application of the skills you will gain. Interspersing one or more of the above exercises between forthcoming chapters or sections of chapters may be one way of accomplishing this.

Listening Resources Improvisation enables us to tap into the totality of our musical experiences and forge unique expressions that transcend category. The musical pulse of our times lies as much, if arguably not more, in the intersections between genres as in the discrete musical categories that tend to prevail in academic and commercial music sectors. From this standpoint, it is important to listen to as wide a variety of music as possible—whether this music is improvised or not— and to compile a personal library of sources that you find inspiring. This, of course, is a lifelong endeavor and one which will not only help provide you with much creative vitality in your music-making but also bring you great personal fulfillment. The following is a very encapsulated list of artists and recordings that may help you get started. It is intended to provide a kind of snapshot of the diverse range of music that falls under the heading “improvised music,” which has emerged as a kind of default way of describing the increasing volume of music that defies categorization and within which improvisation is a common thread. The list includes artists such as John Coltrane, Alice Coltrane, Miles Davis, and the group Weather Report, who have stretched the boundaries of the jazz idiom; artists such as Roscoe Mitchell, Cecil Taylor, and Nicole Mitchell from the Association for the Advancement of Creative Musicians, which from the 1960s has served as a forum through which a largely African-American innovative voice has been able to evolve, galvanize and make significant contributions to the contemporary musical world; artists such as John McLaughlin and Zakir Hussain and groups such as Oregon and Eastern Bloc which have drawn from Indian, Arabic, and other world cultures; musicians such as Robert Dick and Ursel Schlicht who come from largely European contemporary classical musical backgrounds; improvisers Tetuzi

Improvisation Across Boundaries


Akiyama and Yumiko Tanaka from Japan, and Yan Jun and Wang Yong from China, providing a small representation of the growing improvised music scene in the Far East; and artists such as Evan Parker, John Surman, Joelle Leandre, and Wojieeck Konikiewicz from different parts of the thriving European improvised music scene. It must be emphasized that any attempt at such a list immediately calls attention to the vast numbers of artists and even greater volume of recordings that are also important yet due to space limitations could not be included. Hopefully this list will help those for whom much of this music is new embark on a quest that knows no bounds. And while this list purposefully focuses on music with strong improvisatory aspects that tends to transcend conventional categories, a virtual kaleidoscope of great style-specific music from all over the world is also available, including European classical music and its offshoots, from which the contemporary improviser may gain immeasurably. It should also be noted that at the end of Chapter 3 a list of jazz and related sources with strong rhythmic time-feel components (some examples of which are found in the list at hand) will be provided. Art Ensemble of Chicago Rarum VI-Art Ensemble of Chicago Selected Recordings (ECM 2002) Peter Brötzman, with Han Bennink and Fred Van Hove FMP 130 (Unheard Music Series, Atavistic 2003) Marilyn Crispell Vignettes (ECM 2008) Alice Coltrane Translinear Light (Verve Music Group 2004) John Coltrane A Love Supreme (Verve Music Group 1964) Miles Davis Filles de Kilimanjaro (Columbia 1968) Robert Dick and Ursel Schlicht Photosphere (Nemu/Be1Two 2005) Zakir Hussain Making Music (ECM 1987) In Performance (Live) (Electra Entertainment 1980) Joëlle Léandre Joëlle Léandre Project (Leo Records 2004) Nicole Mitchell/Black Earth Ensemble Vision Quest (Dreamtime Records 2008) Roscoe Mitchell, with George Lewis and Muhal Richard Abrams Streaming (Pi Recordings 2006) Oregon In Performance (Live) (Electra Entertainment 1980)


Improvisation Across Boundaries

Evan Parker Eleventh Hour (ECM 2005) John Surman The Spaces in Between (ECM 2007) Cecil Taylor Unit Structures (Blue Note 1987, original released 1966) Weather Report Heavy Weather (Sony 1977) Yumiko Tanaka, with Ivar Grydeland Continental Crust (Sofa 2005) The following is a more general list of prominent artists in contemporary improvised music whose work you are encouraged to learn about as you further expand your listening library. Artists and Ensembles

Geri Allen, Susan Allen, AMM, Ray Anderson, Art Ensemble of Chicago, Vijay Ayer, Derek Bailey, Hans Bennick, Karl Berger, Tim Berne, Carla Bley, Jane Ira Bloom, Jerome Bourdelain, Joanne Brackeen, Anthony Braxton, Peter Brotzman, Earle Brown, Steve Coleman, Nels Cline, Anat Cohen, Ornette Coleman, Alice Coltrane, John Coltrane, Marilyn Crispell, Robert Dick, Pierre Dorge, Dave Douglas, Mark Dresser, Eastern Bloc, Marty Erlich, Douglas Ewart, Michael Formanek, Gerry Hemmingway, Liang Heping, Dave Holland, Zakir Hussain, Kazuo Imaj, Toshiimaru Kakamura, François Janneau, Joseph Jarman, Keith Jarrett, Mathias Kaul, Mazen Kerbaj, Jin Hi Kim, Wojciech Konikiewicz, Oliver Lake, Yusef Lateef, Joelle Leandre, George Lewis, David Liebman, London Improvisers Orchestra, Lionel Loueke, Rudresh Mahanthappa, John McLaughlin, Myra Melford, Pat Metheny, Nicole Mitchell, Roscoe Mitchell, Musica Viva, Stephen Nachmanovitch, Miles Okazaki, Pauline Oliveras, Oregon, Ivo Papasov, Evan Parker, Claudio Parodi, Anto Pett, Edwin Provost, Sun Ra, Leo Smith, Michael Jeffrey Stevens, John Surman, Cecil Taylor, Walter Thompson, Henry Threadgill, Ursel Schlicht, Ralph Towner, Cuong Vu, Dan Weiss, Christian Wolff, Liu Yuan, and Carlos Zingaro. Musicians who play instruments such as flute, oboe, bassoon, French horn, cello, viola, and to a somewhat lesser extent violin, are often hard-pressed to find improvisers on their instruments that might serve as role models. The following is a brief list that may be helpful in this regard. Contemporary Improvisers on Largely “Classical Instruments” (Instruments not Commonly Associated with Improvisation)

Violin: Julie Lyon-Lieberman, India Cooke, LaDonna Smith, Mark O’Connor, Leroy Jenkins, Billy Bang, Stephen Nachmanovitch. Viola: Judith Insell, Jeremy Kittel. Cello: David Darling, Gil Selinger, Deidre Murray. Bassoon: Michael Rabinowitz, James Johson, Daniel Smith, Ray Pizzi, Paul Hanson. Oboe: Kyle Bruckman, Brenda Schuman-Post,

Improvisation Across Boundaries


Paul McCandless, Joseph Celli. Flute: James Newton, Ali Ryerson, Robert Dick. Voice: Thomas Buckner, Bobby McFerrin, Ursula Dudziak, Ella Fitzgerald, Sarah Vaughn, Norma Winstone, Betty Carter. French Horn: Jim Rattigan, Tom Varner, Adam Unsworth, Jeffrey Agrell.

Further Reading Jonathan Kramer, The Time of Music. New York: Schirmer, 1988. Geroge Lewis, A Power Stronger than Itself: History of the AACM and American Experimental Music. Chicago: University of Chicago, 2008. Stephen Nachmanovitch, Free Play: The Power of Improvisation in Life and the Arts. Los Angeles: Tarcher, 1990. Eugene Narmour, The Analysis and Cognition of Basic Melodic Structures. Chicago: University of Chicago, 1990. Pauline Oliveros, Deep Listening: A Composer’s Sound Practice. New York: iUniverse, 2005. Ed Sarath, “A New Look at Improvisation.” Journal of Music Theory 40.1:1–38, 1996. Kenny Werner, Effortless Mastery. New Albany, IN: Jamey Aebersold, 1996.

SUMMARY QUESTIONS 1 What is meant by the term trans-stylistic and how does it differ from conventional approaches to improvisation study (e.g. as found in jazz improvisation coursework)? 2 True or false? The ultimate aim of the trans-stylistic approach is to replace stylespecific improvisation study, which is no longer necessary due to the eclecticism in today’s world. 3 What are the two categories of basic elements or parameters delineated by Leonard Meyer? Give examples of each category. 4 Define these terms: • Dynamics • Density • Duration • Registral variety or tessitura • Motive • Ostinato • Motivic sequence • Drone 4 Provide some of the characteristics of heightened consciousness or “flow.” 5 Name two important considerations for effectively using silence in your improvising. 6 List three possible types of endings in improvised music. 7 List three kinds of formal structures.

chapter 2

Music Fundamentals

In this chapter, we: • Cover clefs, key signatures, scales, intervals, modes, and melodic cells. • Do written and improvisation exercises that will aid mastering these elements. • Begin work with aural transposition.

The initial improvising experiences in Chapter 1 likely gave rise to some compelling moments, perhaps providing glimpses, even if fleeting, of the infinite creative scope that is possible through improvisation. These initial experiences also likely shed light on the need for further technical, aural, and theoretical skill development if substantive progress as an improviser is to occur whether in trans-stylistic or style-specific formats. As we move in a style-specific direction, with the intention not of forsaking trans-stylistic engagement but rather of integrating it within a broader scope, the syntactic parameters of harmony, melody, and rhythm begin to assume central focus. Whereas we broached syntactic elements peripherally in Chapter 1, in this chapter we begin a formal, systematic study of this domain. We begin with the basic components of Western tonal and modal music: key signatures, scales, intervals, and modes. If you already have a solid grounding in these aspects, you may either use the opening of this chapter as a quick review or skip directly to whatever areas might be new or in need of strengthening. Of utmost importance is that you establish as part of your regular practice routine work in aural transposition, which entails taking basic melodic patterns derived from various scales and working them out by ear in all 12 keys. This is an excellent means for developing technical facility on your instrument and also builds ear-to-hand coordination, so that you can play what you hear, which is naturally essential for improvisers.

Music Fundamentals


Staff, Clefs, Scales Let us begin with the basic elements of Western musical notation. Musical sounds, or notes, are notated on what is called the staff, which consists of five lines. Notes are placed either on the lines or in the spaces between the lines. Higher pitches fall higher on the staff; lower notes fall lower. The staff may be extended through the use of ledger lines to represent notes that are higher or lower than the highest or lowest lines or spaces of the staff. To the far left of the staff is placed a clef, which indicates which notes correspond to which lines and spaces. Examples 2.1 to 2.4 give four staffs, each with a different clef, with the note middle C indicated on each.





Middle C is a common reference point and will be discussed further below. The note C is among the basic series of pitches in Western music that are designated by the seven letters: A, B, C, D, E, F, and G. Each of these seven notes can be lowered, as indicated by a flat symbol (b), or raised, as indicated by a sharp symbol (#), to yield a total of 12 tones that comprise Western pitch practice. For instance, in addition to A is Ab and A#; in addition to B is Bb and B#, etc. At first glance, this would appear to yield 21 tones. However, some of the derivatives cancel each other out—e.g. since A# is the same sound as Bb, one need include either one or the other, not both—and thus while one might be able to theoretically spell 21 different notes, the practical reality is a total of 12 tones. These tones may be used in different registers or octaves. An octave is an eight-note expanse that is measurable by building a scale on any tone and proceeding upward or downward—according to the alphabetic sequence—until one arrives at that same tone either in a higher or a lower position. In other words, a scale built on A eventually comes to the end of the alphabetic sequence whereby A recurs; this note actually sounds like the initial A, just a higher version of the pitch. Thus, when we specify a middle C, we are talking about the version of the tone C that appears in a particular position relative to lower and higher versions of that tone. Example 2.5 illustrates middle C by placing it within a series of several octaves in which other C notes are identified. Example 2.6 illustrates a C major scale beginning on middle C and ending on the C an octave above it.


Music Fundamentals



Example 2.7 illustrates a chromatic scale built on middle C going to the C an octave above, in both ascending and descending forms. The scale includes all 12 tones, and uses sharps in the ascending form and flats in the descending form. The note C raised to C# is the same pitch as D lowered to Db; the note D raised to D# is the same pitch as the note E lowered to Eb. In this way, any note can be spelled enharmonically; that is, with the letter name of the note above or below it but with necessary accidentals. Notice that in certain cases, notes in the ascending form are not followed by the same note with a sharp but simply by the next note, as in E to F and B to C. The counterpart to this is found at the same spots in the descending form, where C proceeds directly to B without an intervening Cb and F proceeds to E without an intervening Fb. The reason for this is that there are natural half-steps between these notes, and the use of those accidentals would, in fact, make the modified note the same pitch as the one that follows it. In other words, Cb is the same pitch as (and thus may be spelled enharmonically as) B, Fb as E, E# as F, and B# as C. It is important to be aware of these natural half-steps, where no intermediary notes may be located, and the use of enharmonic spellings by which one pitch may be notated with different letter names.


Music Fundamentals


Key Signatures Just as the lines and spaces of the staff, with the aid of a clef, delineate what particular note sounds at a given point in time, the use of a key signature delineates what key area the music is centered in. A key area is defined by a tonic note—or main tone—and the notes of a scale generated from that tonic note. Later we will see that chords—simultaneously sounding groups of notes—are generated from the scale. As there are 12 chromatic tones, there are 12 keys and corresponding key signatures.

EXAMPLE 2.8 Key signatures

The top line proceeds from the key of C major, with no sharps and flats, through the sharp keys; beginning with G major, with one sharp, and through D, A, E, B, F#, and C#. This sequence follows what is called the cycle of fifths, and as we proceed through the cycle we add one more sharp with each successive key. Note also that the name of the key is one half-step above the farthest sharp to the right. The bottom line lists the flat keys, and proceeds through the cycle, this time with descending fifths, beginning with F major with one flat, and on through Bb, Eb, Ab, Db, Gb, and Cb. Note that, with the exception of F major, the second last flat from the right is the name of the key. You will find the ability to recite the sequences of sharp and flat keys quickly to be a very useful skill, as it will come into play in the determination of interval sizes and qualities, chord structures, and chord functions.

Major Scale Example 2.9 illustrates the C major scale in the four different clefs introduced above: treble, bass, alto, and tenor. All scales begin on middle “C,” except for the one written in bass clef, which begins an octave below and ends on middle C. While many musicians may rarely encounter alto and tenor clef, basic knowledge of them is essential to abilities such as score reading, or composing with these and other instruments that utilize the clefs, and thus should be considered important to overall musicianship. The counterpoint exercises that are included in Appendix I also make use of these clefs and so it is important to develop a basic familiarity with them.


Music Fundamentals


Major scale written exercise Write out the following major scales in the clefs provided. You can either write the key signatures or apply accidentals before each note.

Exercise 2a

Music Fundamentals



Minor Scale There are three kinds of minor scale: natural, harmonic, and melodic, as illustrated in Example 2.11. Notice that the D natural minor scale contains the same notes as the F major scale, but begins on the note D. From this vantage point, we can think of the harmonic minor as natural minor with a raised seventh degree. Melodic minor consists of ascending and descending forms; ascending may be thought of as a major scale with a lowered third and descending as identical to natural minor.



Music Fundamentals

More scales Write out these scales using the clefs indicated:

Exercise 2b and EXAMPLE 2.12

Intervals An interval is the space between two notes. When two notes sound simultaneously, and to a lesser extent consecutively, the size of the space between the notes produces a specific sound color. A wide range of intervalic sizes is possible, each having a different flavor, and thus the various intervalic types are labeled by size. It will be particularly essential to be fluent with these types when it comes to working with chords—triads, seventh chords, and extended chords—since the quality of these structures will be determined by their respective intervalic make-up.

Music Fundamentals


When we label intervals according to size, we take into account two aspects. One is the basic or general size of the interval, indicated simply by a number, and the second is the quality of a given intervalic size. The quality may be thought of as a kind of fine-tuning of the general size. The basic size of the interval is easily determined by counting up from the lowest of the two notes—with the lowest note as “1”—to the higher note. Example 2.13 illustrates in the key of F:


However, proper identification of intervals requires also that we indicate the quality of each intervalic size. In other words, it is not enough to identify an interval as a third, fourth, or fifth, as indicated above (Example 2.13); there are different types of seconds, thirds, etc. which may be thought of as gradations or, as noted above, finely tuned measurements, of the general size. Here, then, it is necessary to understand how the different general sizes are qualified to indicate larger or smaller gradations. The following two categories of gradations correspond to the general sizes: • Seconds, thirds, sixths, and sevenths can be major, minor, diminished, or augmented. • Unisons, fourths, fifths, and octaves can be perfect, diminished or augmented. At this point the question becomes: How do we know which qualifier to apply? How can we distinguish between a major, minor, diminished, or augmented third? Here a simple strategy comes into play. The strategy begins with the question: Is the top note in the major key (or major scale) of the bottom note? If the answer is yes, and the interval is a second, third, sixth, or seventh, then the quality of the interval is major (e.g. major second, major third, major sixth, major seventh). If the interval is a unison, fourth, fifth, or octave, then the quality of the interval is perfect (e.g. perfect fourth, perfect fifth, perfect octave). If the answer is no—if the top note is not in the major key or scale of the bottom note— we must determine whether the top note is higher or lower than the diatonic note in question. Here we proceed as follows. If the interval is a second, third, sixth, or seventh, and the top note is a half-step below that which would be diatonic to the key, then it is minor in quality. Therefore, instead of a major sixth, we would have a minor sixth. If the interval is a half-step lower than the note that would make it a minor interval, it is diminished (e.g. diminished sixth). In the opposite direction, if the interval is a half-step higher than that which would make it a major interval, it is augmented. If the interval is a unison, fourth, fifth, or octave, and the top note is a half-step lower than what it would be in the major scale, it is diminished. If the interval is a half-step higher


Music Fundamentals

than it would be in the major scale, it is augmented. Unisons, fourths, fifths, and octaves cannot be major or minor. Seconds, thirds, sixths, and sevenths cannot be perfect. Example 2.14 provides a progressive illustration of a variety of different intervals, beginning with the very small and moving up to the major thirteenth interval. The intervals are shown in both melodic formats, where the top note follows the bottom, and harmonic formats, where both notes sound at the same time. Note that when you play through the intervals, some will sound exactly the same as the preceding interval listed, even though the names are different (e.g. an augmented second sounds the same at the keyboard as a minor third). In certain performance formats, fine performers on non-keyboard instruments which allow for subtle nuances of pitch to be played may actually make a slight difference between D# and Eb if the D# follows a D natural and leads to E in a chromatically ascending passage. Hence, composers will write D# in such cases instead of Eb, and in analyzing repertory we thus need to recognize the D#, if it sounds against or follows a C, as an augmented second above the C, not a minor third above.


Inversions of Intervals

Any interval can be inverted, so that the note that was on top is on the bottom. An interesting principle provides an easy way to know the inversion of any given interval: the interval and its inversion totals nine. For instance, fifths invert to fourths (5+4=9), sixths to

Music Fundamentals


thirds (6+3=9), seconds to sevenths (2+7=9). In addition, major intervals invert to minor intervals—the inversion of a major sixth is a minor third—and perfect intervals invert to perfect intervals (a perfect fifth inverts to a perfect fourth). Interval identification Identify these intervals, using these abbreviations: Perfect=P, Major=M, Minor=m, Augmented=A, Diminished=d. Be able to name their inversions.

Exercise 2c and EXAMPLE 2.15 More intervals Identify the intervals between each successive note in the following sequence; e.g the interval between the first and second note, second and third, and so on. Remember to count up from the lower of the two notes, regardless of which one comes first in the sequence.

Exercise 2d and EXAMPLE 2.16 Aural practice With a partner, sing a pitch and specify the interval to be sung by your partner above or below that note. Switch roles.

Exercise 2e Choose an interval Choose an interval and improvise, vocally or on your principal instrument, passages that make prominent (not necessarily exclusive) use of that interval.

Exercise 2f


Music Fundamentals

Modes In addition to major and minor scales are another category of diatonic or stepwise scales that span an octave. These are the seven modes, all of which may be derived from the major scale, as shown in Example 2.17. The modes of Western music find parallels in music throughout the world (e.g. Indian ragas, Arabic maqam) and offer interesting scalar and melodic options for improvisers and composers. Entire pieces, or sections of pieces, may be based on a single mode or combinations of modes. Facility with modes is of great value to jazz improvisers, who commonly equate particular modes with particular chords in order to guide their melodic decision-making processes. Example 2.17 lists the seven diatonic modes and correlates them, using Roman numerals, with each scale degree of the major scale. We will take up Roman numerals as an analytical tool in more depth later when we move into chord structures and functions. Here they help us correlate the modes with the different degrees of the major scale: the Ionian mode is built on I of major, Dorian on II, Phrygian on III, Lydian on IV, Mixolydian on V, Aeolian on VI, and Locrian on VII.


Another way of understanding the modes is by analyzing their different uses of whole and half-step intervals. Ionian=W-W–H-W-W-W-H Dorian=W-H-W-W-W-H-W Phrygian=H-W-W-W-H-W-W Lydian=W-W-W-H-W-W-H Mixolydian=W-W-H-W-W-H-W Aeolian=W-H-W-W-H-W-W Locrian=H-W-W-H-W-W-W It is not necessary to attain absolute fluency with the modes at this moment, although this should be our ultimate aim. What is necessary here is to have a basic understanding and a method for determining the notes of any given mode—whether this be relating the modes to the degrees of the major scale or thinking of them in terms of their whole- and half-step intervals—when it is encountered. The following exercises will help to this end,

Music Fundamentals


and Chapter 5 provides exercises that in a single stroke fortify knowledge of both chords and modes. The following exercise is an excellent way of learning on your instrument five of the seven modes, which here form a sequence that we will later correlate with chords on each of the scale degrees listed. The chord sequence is discernible from playing the scales/modes without any kind of harmonic accompaniment, showing the close link between melody and harmony. Melody contains harmony; harmony contains or at least can strongly suggest melody. Put another way: scales or modes are horizontal or melodic configurations of pitch areas, and chords are vertical or harmonic configurations of pitch areas. When we later improvise on pitch structures such as jazz chord changes, the more fluent we are with scales/modes and chords, the more freely we will be able to move back and forth between horizontal and vertical kinds of conceptions in the creative process. Scale pattern in all keys Learn the following pattern in all keys on your principal instrument. This is a preliminary form of aural transposition, where we take a pattern—in this case a scale or mode—that is given in one key and work it out in other keys by ear. This particular pattern works well moving around the cycle of fifths (e.g. first in F as given, then to B , E , A , etc.). You can also move chromatically through the keys (F, G , G, etc.).


Exercise 2g and EXAMPLE 2.18

Modes (1) Write the names of the following modes atop the staff.

b b b


Music Fundamentals

Exercise 2h and EXAMPLE 2.19

Modes (2) Write out the following modes.

Exercise 2i and EXAMPLE 2.20

Pentatonic Scales Pentatonic scales are found in a wide range of music throughout the world. The major pentatonic scale is easily understood as comprising tones 1, 2, 3, 5, and 6 of the major scale. The minor pentatonic scale consists of the exact same tones, except that scale degree 6 (or the fifth note of the major pentatonic) serves as the root. In this way, the relationship between major and minor pentatonic scales is very similar to that between major and natural minor scales—the natural minor scale is built on the sixth degree of the major scale, and the minor pentatonic scale is also built on scale degree 6 (which is the fifth note of the

Music Fundamentals


pentatonic). Example 2.21 shows the C major pentatonic scale and the related A minor pentatonic scale.


Pentatonic scales Write out these pentatonic scales: A major, B minor, C minor, F# major, F# minor, A major, E minor, F minor.


Exercise 2j

Aural Transposition Let us now begin to get these modes under our fingers so that we can use them when we improvise. It is one thing to be able to identify or write a scale, or even play it up and down; it is another to be able to spontaneously generate a variety of melodic shapes using the notes of the scale. A central practice for developing these skills is aural transposition. Aural transposition entails taking a pattern and transposing it by ear to other pitch levels within a given key or scale, and to other keys and scales. It is likely evident that this is an allimportant part of the improviser’s daily practice routine. Aural transposition is a challenging yet highly fruitful practice that will enhance not only your improvising skills, but also your all-around technical facility on your instrument. It is important to recognize that aural transposition poses different challenges for different instrumental types. For singers, once a pattern is learned in a single key, it is immediately replicable in all keys—hence singers should take it upon themselves to work on a greater volume of patterns. String players—violin, viola, cello, bass, and guitar—are somewhat more challenged as they may in certain instances have to re-finger a given pattern to play it in other keys. Pianists and wind and brass players are the most challenged in that they have minimal carry-over in terms of technical execution from one key to the next. As will be recommended below, what is most important is to work on patterns whose level of difficulty—and here it is important to select an appropriate tempo—is adequately challenging but not overwhelming for your particular instrument and skill level. We will apply aural transposition to three basic types of scales we have covered: major and minor scales, modes, and pentatonic scales. Let us now take up useful melodic permutations derived from the major scale and which may be applied to all diatonic (seven-tone stepwise) scales once we have them under our fingers. These are called melodic cells.


Music Fundamentals

Melodic Cells In Chapter 1 we considered the motive as a basic kind of melodic gesture. Let us now examine smaller-scale melodic relationships that may be found within these gestures that will help us fine-tune our melodic decision-making processes as improvisers. Here we come to the principle of melodic cells, groups of three to five notes that possess an internal clarity and coherence. Becoming fluent in even a small group of these cells will provide tools which you can use to create elaborate melodic fabrics; this will be of particular value when it comes to time-feel-based improvising. While melodic cells may comprise any configuration of intervals or rhythmic values, we will identify a basic set of cells that utilize intervals of seconds and thirds, and all of whose notes consist of the same note value—which we will define here as eighth notes. The clarity inherent in the melodic cell is due to the interplay, even if on a small scale, of passing and target notes. Passing notes, as the name suggests, function in a more movement-driven capacity as they connect one note to another. There is some resemblance here to the non-harmonic passing tones to be considered later, although whereas in that instance the classification was primarily due to the dissonant nature of the tones, here the classification is due the role of the tone in upholding a melodic shape. Target notes are landing points, even if only temporary, and are often defined as such simply by their length (they tend to be longer than the other notes in a phrase) or placement (they tend to come at the end of a phrase). This is evident in Example 2.22, where the four eighth notes establish clear motion that sets up a temporary moment of repose on the quarter note F. Notice here too how the two eighth notes preceding the target note E actually frame the target note through a kind of anticipatory “gap” whereby a melodic sequence skips over a note it appears to be heading toward, only to then approach the note from the opposite direction. Thus, when the F arrives, the ear recalls the note (and series of notes) that preceded it and groups the entire cell into a coherent pattern. When we have a number of these cells under our fingers (and in our ears), we can spontaneously mix and meld them to create an infinite variety of coherent melodic possibilities.


Example 2.23 provides samples of common melodic cells. It is followed by aural transposition exercises through which one can begin to internalize these shapes. The exercises presented below expand several of these cells into patterns that move up and down the major scale and are to be used for aural transposition. Learn to sing each pattern in one key before learning it in multiple keys on your instrument. The voice is an ideal link between ear and hand. By deferring to the voice when you run into difficulties in realizing a given pattern on your instrument, you will strengthen this link as well as your overall aural and expressive capacities. As with all aural transposition exercises, you are

Music Fundamentals



encouraged to take the basic pattern beyond the range given in order to further expand your technical skills on your instrument. A further point bears emphasis at this juncture. As you work on aural transposition exercises and begin to get these basic shapes under your fingers, you may find yourself inclined to launch into extended improvisations with them. This is a primary indicator that you are beginning to internalize these shapes and you are highly encouraged to follow your instincts when these moments arise. You are also encouraged to freely meld the different shapes and harness the interplay of coherence and unpredictability that is inherent in the creative use of these shapes. As you listen to master improvisers, appreciate the feeling of play—the joyful exuberance that stems from the spontaneous spinning out of compelling melodic lines—that is possible in improvised music. When these waves of play arise in your own practice, do not hesitate to ride them, just as the surfer does who waits hours for the big wave at the ocean front; important progress may be made during these seemingly unbridled episodes as they allow you to spontaneously integrate material you have been diligently practicing. And of course it is important to take care that the time spent on these flights of fancy is kept in balance with the all-important focused practicing of these patterns in all keys. Aural transposition Work out these patterns in multiple keys by ear. Proceed around the cycle of fifths (e.g. first play the pattern in C, then F, then B , etc.) or move chromatically (e.g. C, D , D, E , etc.).


2k (cell 1 from above)

2l (cell 2 from above)




Music Fundamentals

2m (cell 3 from above)

Exercises 2k–2m and Examples 2.24–2.26

You can create further aural transposition exercises from the melodic cells. A few more are provided here, however, since they warrant commentary. Exercise 2n, based on melodic cell 7, is of particular value for contemporary improvisers due to its inherent rhythmic properties. The cell contains naturally occurring accents on offbeats that produce a kind of two-against-three rhythmic relationship. We will see in the subsequent chapters that this relationship is central in time-feel-based improvising. Continue the aural transposition with the following exercises. Aural transposition

Exercise 2n and Example 2.27

Exercise 2o provides two kinds of sequences that may be derived from melodic cell 8. Appreciate the resemblance between the second of these and exercise 2n. Aural transposition (cell 8)

• Variation

Exercise 2o and Examples 2.28–2.29

Exercise 2p presents four different sequential possibilities that may be derived from the same melodic cell.

Music Fundamentals


Aural transposition (melodic cell 9 from above)

Variations 1 and 2 alternate ascending and descending forms of the cell. Variation 3 provides another form in which this cell is commonly found. • Variation 1

• Variation 2

• Variation 3

Exercise 2p and Examples 2.30–2.33

Aural Transposition with Pentatonic Scales The following exercises present several aural transposition patterns based on minor pentatonic scales. The patterns are given in one or two keys; your task is to play them by ear in all keys around the cycle of fifths. It is not necessary to master these in all keys before proceeding with the remainder of the chapter. However, try to at least be able to play them in a few keys to get a glimpse of what aural transposition entails and its benefits. The first of these patterns involves a phrase that is to be repeated prior to being transposed to the next pitch level. As you listen to the recorded version of this, please take careful note of the articulation used—particularly the connectedness of the notes and strong rhythmic definition—and attempt to match it. One further suggestion: with all your aural transposition work, take some time to improvise with the shapes that you are transposing aurally. This will help integrate them as organic facets of your evolving melodic voice.


Music Fundamentals

Aural transposition Play these patterns by ear in all 12 keys around the cycle of fifths. 2q



Exercises 2q–2s and Examples 2.34–2.36

As you have undoubtedly found, learning these patterns in all keys by ear is challenging and will not happen overnight. As mentioned above, you need not master every single pattern in all keys before moving forward in the book; this could easily take weeks if not much longer. Rather, it will suffice to select one pattern to begin working out in all keys, and just play through the other patterns for now, perhaps working them out in only a few keys with the intention of trying to make use of these melodic shapes in your improvising. It is recommended that you keep a practice log, checking off each pattern once you get it in all keys, so that you can monitor your progress. Do not be discouraged if aural transposition seems unduly challenging at first. This is arguably the most intensive form of technical practice you will encounter, as it requires high degrees of coordination between ear and hand. Needless to say, this kind of skill is also absolutely essential for improvisers and the yield from this kind of work is more than worth the effort; you will likely begin to see results in your technical facility fairly soon after embarking on an aural transposition program. You will also find it to be a powerful means for even developing sight-reading skills, which is ultimately an aural activity, as well as the ability to master technically difficult passages in written music more quickly. Aural

Music Fundamentals


transposition is the ultimate “daily vitamin” when it comes to developing virtuosity on your instrument. More important than the pace at which you are able to learn these patterns in multiple keys is that you establish aural transposition as part of your regular practice routine. Appendix 7 provides additional patterns once you have mastered those presented here and elsewhere in the book. It is ideal to work regularly on several different kinds of aural transposition patterns—e.g. melodic cells that utilize small intervals, triadic and seventh chord patterns and their many permutations that involve larger intervals, idiomatic phrases such as II-V-I patterns to be encountered later, and your favorite melodies. You are also encouraged to create your own patterns for aural transposition.

SUMMARY QUESTIONS 1 Name the four kinds of clefs. 2 Name the three types of minor scales. 3 Which size intervals (numeral size) can and cannot be major and minor? Which size intervals can and cannot be perfect? 4 Any interval can be diminished or augmented. True or false? 5 Name the seven diatonic modes and correlate them with the different degrees of the major scale. 6 Which modes begin with half-step intervals? 7 What is the difference between Ionian, Lydian, and Mixolydian modes? 8 What is the difference between Dorian and Aeolian modes? 9 Name the notes of a D major pentatonic scale. 10 Name the notes of a B minor pentatonic scale.

chapter 3

Modality and Rhythm I: Time Feels

In this chapter, we: • • • • • •

Begin to improvise in contemporary modal and rhythmic frameworks. Examine what musicians commonly call time feels or grooves. Learn about the importance of eighth note lines in time-feel improvising. Work with rhythmic templates to aid our melodic improvising. Work with the Dorian modes and constituent pentatonic scales. Embark on a program of listening to master time-feel improvisers.

Improvising musicians commonly talk about “time feels,” or “grooves,” when it comes to the rhythmic dimensions of contemporary music. Time feels are rhythmic frameworks that are usually cyclical—some basic pattern is repeated, even if undergoing significant elaboration and transformation in the process—and are usually connected with a pitch framework (e.g. jazz chord changes, modes). With roots that can be traced back centuries in African music, with sprouts beginning to bloom in the late nineteenth century through largely AfricanAmerican culture and practices, followed by a full blossoming in the twentieth century, time feels—exemplified in jazz, blues, funk, hip-hop, Afro-Cuban, Afro-Brazilian, to myriad multi-ethnic hybrids—have become pervasive in the musical world and warrant an important place in musicianship training. While a wide variety of time feels exists, common principles may be identified that help musicians begin to develop a basic fluency with this important musical language structure and engage with many of the diverse musical streams that are merging in our times.

The Importance of Aural Immersion As we approach the topic of time feels, an important point cannot be emphasized strongly enough. This has to do with the central role aural immersion plays in the learning process. In this regard, mastery of time feels is very similar to learning a spoken language, where

Modality and Rhythm I


extensive aural exposure and emulation are central. We learn to speak before we learn to read and even gain a fair command of syntax prior to formal study of grammar, which happens well after we learn to read. For musicians with largely or exclusively European classical backgrounds, rhythmic time feels may be considered foreign musical languages, whose inflections, nuances, and pronunciation principles need to be mastered aurally. Moreover, whereas one can become grammatically fluent in a foreign spoken language with less than perfect pronunciation skills, pronunciation is everything in music; it is core to the meaning, the expression, and the impact of the music. While we can attain fluency in a second language even while speaking that language with our native accent, music played with a “foreign accent” will likely sound out of place. A prominent case of this is in attempts at swing by Euroclassical musicians (those who specialize in European classical music) with limited grounding in this time-feel conception. The swing time feel is one of two major time-feel categories that exists and will be taken up in Chapter 7. Here we will begin with mainly “even-eighth note” time feels, which are less foreign to musicians from Euroclassical, pop, folk, rock, and many other backgrounds. Let us start by initiating a program of focused listening. Building a listening list The artists and genres listed at the end of this chapter will provide a good start for you to build your own library. As explained in Chapter 1, this kind of listening involves much more than having music on in the background while you engage in some other task. Rather, it involves deep aural, physical, and emotional immersion in the sounds, where you sense the music permeating every fiber of your mental, physical, emotional, and transpersonal being. Experience the music as if you were creating it yourself. Do not hesitate to let yourself physically move to the music. Moreover, do not hesitate, should you feel so inspired, to pick up your instrument and play along. You are learning a new language: the greater the number of parameters of engagement—whether aural, creative, physical, or analytical—the greater the assimilation.

Exercise 3a

Core Elements of Time Feels Co-existence of Legato Phrasing and Strong Rhythmic Integrity in Melodic Lines

Notice as you compile your listening library two core features of time-feel-based articulation and phrasing. One has to do with melodic lines in which legato, connected phrasing, and strong rhythmic integrity co-exist. This requires a different kind of articulation than is found in European classical music, and this articulation will vary from one instrument to another. For instance, where Euroclassical brass players will commonly attack a note with the syllable “tah,” time-feel brass players will more commonly use the syllable “dah” for an effect more conducive to the legato phrasing desired. And in contrast to the “ta-ka”


Modality and Rhythm I

articulation characteristic of Euroclassical double-tonguing for rapid tongued (as opposed to slurred) passages, time-feel brass players utilize a combination of “da” and “la”— trombonists call it the “doodle” tongue—to execute rapid lines with crystal-clear rhythmic definition while still retaining the legato effect. As you listen to time-feel performers on your instrument as well as other instruments, sense what sort of articulation they are employing and try to match it. Remember that the vast majority of these musicians learned the articulation by emulating others and may be hard-pressed to describe exactly what it is. Therefore, it is much more important to emulate the sound than to define how it is attained. 2:1 and 4:1 Rhythmic Ratios

A second aspect of the time feel, closely related to the first, is the prominence of the 2:1 or 4:1 rhythmic relationship between melodic line and basic pulse; in other words, eighth and sixteenth note lines, depending upon how the basic pulse is defined. What is important is the effect of the melody moving in multiples of two against the underlying beat—an effect to be encountered in Appendix I in second (2:1) and third (4:1) species counterpoint. When jazz musicians talk about the importance of “getting your eighth notes happening,” they are referring exactly to this principle. Listen to the important role 2:1 and 4:1 lines play in the improvised melodies from your recordings. It is not that other rhythmic values are prohibited, but these particular rhythmic values are essential in bringing out the character of the time feel. Once this is established, all rhythmic values are possible. As you begin to implement these concepts in your improvising, you will find that they go hand in hand; in order to play compelling 2:1/4:1 lines, you will need to master the articulation that enables the co-existence of legato and rhythmic definition described above.

Further Aural Immersion Strategies Live performances and DVDs In addition to listening to recordings, you are also encouraged to attend live performances and watch DVDs. Much can be gained from watching, as this is another important sensory input, a channel through which information about a language can flow. Observe how time-feel improvisers move and how their movement relates to their phrasing and articulation.

Exercise 3b

You may notice that time-feel improvisers move differently than European classical performers. Different musical languages not only involve different sounds but also different kinds of bodily engagement. It is not that one is better than another, any more than English is superior to French or Hindi. It is simply that different kinds of music flow through the

Modality and Rhythm I


psychophysiology in different ways. Time feels must therefore be internalized in the entire body as much as in the ears and mind. Find an exemplar As you begin to compile a list of sources for aural (and possibly visual) immersion, you will naturally come upon one or more artists whom you find particularly exciting. You are encouraged to emulate their style when you improvise—as if you are taking them on as a mentor. Now your improvisatory development will be driven by an entirely new impetus. Be prepared to share with classmates what it is about your exemplar that you find particularly compelling and how you are attempting to emulate his/her work.

Exercise 3c

The next step in our aural immersion process is called transcription, where we copy note for note the lines, shapes, patterns, and phrasing of master time-feel improvisers in order to learn exactly what they are playing. Transcription As you encounter a variety of time-feel improvisers, you will inevitably come upon one or more whom you find particularly compelling. Choose one as your first exemplar—a master artist whom you admire. Begin to select your favorite phrases and copy them note for note, inflection for inflection. Be able to play them exactly as your exemplar. Later we will transcribe entire solos in this manner; for now, short passages (e.g. 2–4 measures) will suffice. Record these phrases in a notebook. Create aural transposition exercises with them..

Exercise 3b

Transcription is not unlike the practice of aspiring visual artists when they visit art museums and copy the work of master painters. While the term “transcription” suggests capturing the music being copied in notation, important aspects of time feels cannot be notated. Thus, while the act of notating music from an aural source is a highly valuable activity in itself for students, the bulk of the benefit from transcription is simply the emulation of master artists. At first, it may appear that this intensive emulative activity is contrary to the goal of evolving an individual, creative voice as an artist. Here several points may be made, the first of which has to do with intention. We emulate master artists not so much with the goal of reproducing note for note what they play when we create, but rather to assimilate important kinds of idiomatic knowledge and skills that are embedded in the specific nuances and phrases they play. Internalization of these elements will enable us to speak the language in


Modality and Rhythm I

our own way. Hence, we emulate not with the ultimate goal of cloning other artists but in order to gain tools that allow our individuality to blossom. There are certain kinds of knowledge that are gained most effectively by emulating master practitioners as precisely as possible and one need not apologize for engaging in this practice, nor fear that it will impede creativity. Moreover, when situated within the broad spectrum of creative approaches that comprise this book, ample opportunity to expand one’s horizons are provided. A further valuable activity is to attend traditional African-American church services in which congregations become physically, emotionally, and spiritually engaged in the music. The African-American church was a primary forum for the evolution of time-feel-based music from the late nineteenth century to modern times and it is still possible to sense the deep meaning of the blues and spirituals from which this music developed. Therefore, in no way is this recommended activity an endorsement of a particular kind of religious or spiritual ideology, just as performances or study of Mozart’s Requiem, Beethoven’s Mass, or Bach’s Magnificat do not require that one subscribe to the strong religious roots of these works. Rather, it is simply to point to another way to connect first hand with the cultural roots of the musical practices we are working with and which factor prominently in today’s musical world.

Modal Etude 1



Listen to the recording of Modal Etude 1 on the website. The piece begins with an ostinato bass line, atop which a melody enters—this is the “head” or main theme. The head is followed by improvised solos atop the bass line, which outlines the same modal region as the head. Notice that the ostinato player departs from strict repetition of the ostinato pattern behind some of the improvised solos yet still maintains a solid foundation in outlining the pitch and rhythmic framework; this creates variety yet still upholds the supporting role of the rhythm section. The solos are followed by the out head, or return of the main theme. We will further analyze these aspects shortly. The following are transposed parts for Bb and Eb instruments, although players of these instruments are encouraged to learn to transpose at sight. Bb instruments (trumpet, clarinet) transpose up a whole step from concert pitch (tenor saxophone up a ninth), and Eb instruments (alto saxophone) up a major sixth (baritone saxophone up a thirteenth). Before we analyze the piece further, let us first gain first-hand aural and creative experience by improvising on the feel. Exercise 3e has you improvise with minimal theoretical knowledge, thus thrusting you into a situation where your ear is the guide.

Reminder: The exercises in this chapter are to be done using the principal instrument or voice, unless otherwise indicated.

Modality and Rhythm I

EXAMPLE 3.1 Ed Sarath, Modal Etude 1. © 2008 Ed Sarath



Modality and Rhythm I


EXAMPLE 3.2 Modal Etude 1 B part


EXAMPLE 3.3 Modal Etude 1 E part

Modal Etude 1 Proceed to the play-along track on the CD where, after the head, the rhythm section (bass, drums, and piano) plays the time feel as a background against which you are to improvise. Play the melody with the recording, and then improvise on the form. You might begin by playing more sparsely and finding notes that fit in before trying to play more florid, moving lines. You might also try improvising using phrases from the melody as points of departure.

Exercise 3e

Modality and Rhythm I


Let us now explore a few related theoretical ideas before attempting to improvise on the piece further. The first is that when even a few notes from a given scalar or modal structure sound, they imply a corresponding “pitch field” that provides a basis for improvisation. Scales are horizontal configurations of the notes of a pitch field; chords, to be taken up in Chapter 5, are vertical configurations of these notes. While ultimately we are not confined to improvising with only the notes from the scale or chord, it is important to gain aural and theoretical mastery of these tones as a basis for further exploration. The ostinato bass line in Modal Etude 1 implies a pitch field that includes not only the notes from which the bass line is constructed but several kinds of scales. One is the fivenote A minor pentatonic scale; we encountered major and minor pentatonic scales in Chapter 2. Two more scales are the A Aeolian (natural minor) and closely related A Dorian mode; the Dorian mode may be easily understood as a natural minor scale with a raised sixth degree. Thus A Aeolian contains an F natural and A Dorian contains an F#. While both Aeolian/natural minor and Dorian are compatible with the notes of the bass line, because the melody contains F#, this piece is in Dorian rather than Aeolian. The minor form of the pentatonic has emerged as more prominent in time-feel-based music and we will thus favor it in our work. Example 3.4 illustrates how the A minor pentatonic is contained within the A Dorian mode.


Here a useful principle bears emphasis: pentatonic scales and diatonic scales/modes may be used interchangeably when improvising. Improvisation using Dorian and pentatonic scales Return to Modal Etude 1 and improvise using the A Dorian and A minor pentatonic scales. Employ one, then the other, then move back and forth between them, noting how the sounds are both similar yet different. Notice that the stepwise structure of the Dorian mode makes possible smooth melodic motion, whereas the pentatonic scale, owing to its interval of a third, necessitates the use of skips in addition to stepwise motion.

Exercise 3f

Further connections between diatonic modes and constituent pentatonic scales might be noted here. In fact, within any diatonic scale or mode can be located three different pentatonic scales, as Example 3.5 illustrates in the context once again of the D Dorian


Modality and Rhythm I

mode. Accordingly, you could improvise on Modal Etude 1 by alternating not only between A minor pentatonic and A Dorian, but also include B minor pentatonic and E minor pentatonic in this mix.


Dorian and pentatonic written exercise Write out these Dorian modes and name the three constituent minor pentatonic scales within each of the modes: A, B , B, E , C, F, G.



Exercise 3g

Having worked with minor pentatonic aural transposition patterns, let us now proceed to aural transposition patterns on diatonic modes. This brings us to a set of core melodic cells that will greatly enhance your improvising facility.

Two-player Improvisation Practice Frameworks The following exercises enable you to integrate the material covered so far with a partner. They make use of minor pentatonic structures, diatonic modes, and invite the use of melodic cells. On these and many other two-person exercises in this book, you will both have the opportunity to play the role of both melodic improviser and keyboardist. If you have had little or no contact with the keyboard at this point, the following format will provide a unique entry point that is designed particularly for musicians like you. The first exercise involves simply playing a drone—thus has you strike a single note and sustain it— which is followed by options to explore slightly more involved keyboard strategies. No-pulse modal improvisation Select a modal area. Player A, at the keyboard, plays a drone on the root note, using the sustain pedal to let the pitch or interval ring. This piece is therefore not based in a pulse; it is “out of time.” Player B, either singing or on the principal instrument, improvises melodically atop the drone or open fifth, making use of both a minor pentatonic scale

Modality and Rhythm I


built on the tonic note of the mode, as well as either Dorian or Aeolian modes built on that root. B should strive to make use of melodic cells. Switch roles.

Exercise 3h Open fifths Proceed exactly as above, but this time instead of Player A playing just a single drone note at the keyboard, a perfect fifth above the drone or root note may be added, to yield what is called an open fifth interval.

Exercise 3i Open fifths and minor pentatonic scales Play through these intervals slowly and meditatively at the keyboard, allowing each sonority to resonate. In the right hand, play the notes of the minor pentatonic scale built on each of the roots (e.g. A minor pentatonic, C minor pentatonic, B minor pentatonic, F# minor pentatonic).


Exercise 3j and EXAMPLE 3.6 Open fifths and minor pentatonic scales Play open fifths on these notes at the keyboard in the left hand and allow the notes to sustain. Slowly and meditatively play the notes of the minor pentatonic scale built on each root in the right hand. Root tones: G, B, D, E, A , E , C#, G#.

b b

Exercise 3k Improvisation Proceed as in Exercise 3j, except now, after playing without pulse for a while, Player A should establish a pulse at the keyboard. Simply repeating the root note in some rhythmic pattern can do this; even a series of quarter-notes will suffice. Player A may opt to use one of the rhythmic templates shown in Example 3.7 (templates a and b would be ideal for this purpose). When the music becomes pulse-based, Player B, either singing or on the principal instrument, should attempt to improvise rhythmically. He or she is also encouraged to try the various rhythmic templates.

Exercise 3l


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Rhythmic Templates for Time-feel Grooves and Melodic Improvising The idea of the rhythmic template as a device for melodic improvising is as simple as it is for creating basic rhythmic grooves. However, whereas the keyboardist simply repeats a note or intervalic structure (and we will shortly expand this palette of possibilities), the melodic soloist, while adhering to the rhythmic pattern, varies his or her notes. At first, the melodic improviser may feel confined by this restriction. However, as with all kinds of disciplined work, narrowing the constraints may open up further creative possibilities once those constraints are removed. Therefore, while the challenge with this framework is that it restricts the melodic improviser’s rhythmic options, it also forces the improviser to seek other means for creating variety that will inevitably mean exploring melodic configurations within a given mode or scale that he or she may not have otherwise explored. Accordingly, the melodic improviser is encouraged to try using the full scope of intervallic possibilities imaginable when using these templates. The use of the templates also helps focus our hearing and awareness of what we are playing—helping to cultivate the ability to hear subsequent tones in advance—so that we are not just moving our fingers, but actually making choices from a more aurally and emotionally engaged vantage point. Example 3.7 provides some basic rhythmic templates that may be used in this way.


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These are just a few possibilities that are based in common rhythmic figures in time-feelbased improvised music. Feel free to add templates of your own creation to this collection. What is most important is that the template enhances melodic direction, and also that any given template, while specifying a rhythmic pattern, may be varied in a wide variety of ways. Example 3.8 illustrates ascending and descending melodic lines written with rhythmic template d.


Scales and rhythmic template Make a random list of scales and then improvise on the scales using different rhythmic templates from the set provided in Example 3.7 (you can also create your own and add to the set). For instance: G minor pentatonic/rhythmic template 2, A Dorian/rhythmic template 4, etc.

Exercise 3m

The following exercise provides the opportunity to further expand what we play at the keyboard. Whereas previously our keyboard accompaniment had been confined to playing single note drones or open fifths, now we will begin to create harmonic structures in the right hand that are derived from the minor pentatonic scale. However, the chords we will derive here will generally not be classifiable in terms of the conventional categories—e.g. major and minor triads and seventh chords—that we will work with extensively in Chapter 5. Therefore, those of you who are not conversant with such chords are in no way at a disadvantage. Rather, here we will use the structures that result when we simply play two or more notes of the minor pentatonic scale at the same time. We need not have an analytical understanding of these structures or be able to give them names; it will suffice to only play tones of the minor pentatonic scale. One of the interesting aspects of this scale is that any two or more of its notes may sound at the same time and produce a sonority that is consistent with the minor pentatonic sound. In other words, there are no wrong notes as long as the tones played are part of the scale. Moreover, a host of interesting chord types will result, most of which are more likely classified in the realm of quartal harmony—that in which fourths and fifths are prevalent—than the usual tertial structures built in thirds (although the minor seventh chord is one possible tertial structure that may be derived from the minor pentatonic). Again, we are not interested in the names of the structures we derive but rather the texture created. Example 3.9 shows some possibilities. This exercise provides an ideal prelude to the keyboard work that will be done later in the course and requires very little keyboard technique—one need only be able to plunk out the five tones of the minor pentatonic scale.


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Minor pentatonic duet Player A plays the keyboard, B some single-line melodic instrument (or voice). Select a minor pentatonic scale. Player A plays an open fifth at the keyboard in the left hand as above. Let the sound ring and resonate. Then, slowly and meditatively Player A begins to play different vertical configurations of the notes of the minor pentatonic scale in the right hand, exploring the different sonorities possible. Player A does not improvise melodically but rather simply by playing chord structures using the tones of the minor pentatonic. Once the atmosphere is established, Player B enters, improvising with the minor pentatonic scale, then related Aeolian or Dorian modes (choose one or the other, do not mix). B should strive to use variety of density and register, intervallic size, motivic development and sequences, and melodic cells. Player A then creates a rhythmic groove (again, rhythmic templates a and b are ideal) as a launching pad (he or she can vary from this later) while continuing to play vertical structures. B continues to improvise accordingly.

Exercise 3n Aural skills application This exercise proceeds similarly to 3n, except now, instead of specifying in advance the minor pentatonic to be used, Player A makes this choice on his or her own and Player B must find and improvise on the modal area by ear. After some time in one area (playing on one minor pentatonic scale and its related chords), Player A then moves to another, requiring Player B to once more adapt by ear. This random shifting from one area to another may be done in time or out of time. Swap roles.

Exercise 3o

The above is an excellent ear-training exercise for the person improvising (Player B), and also challenges Player A to be able to realize multiple minor pentatonic scales and related chord structures at the keyboard. We will return to this format throughout the book and apply it to the array of chords and chord progressions to be studied. Having to aurally apply

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knowledge gained theoretically (e.g. improvising without prior knowledge of the harmonies being used) provides yet another way of synthesizing this knowledge. This may be daunting at first and result in what seem to be blind stabs at a modal (or tonal) area with little success. Here is a recommended approach for the improviser. First, find a single tone that sounds resonant with the harmony being played. Second, slowly move up and down a step from that tone in an attempt to delineate a small cluster of tones a step apart—hence a portion of a scale—that works. Continue in this way until you have found all or most of a diatonic scale that fits with the harmony sounding (the keyboardist should not shift modal or tonal areas until the improviser has had some success finding tones that work). At this point the improviser can begin to play more florid lines, and explore larger intervals. While it may be tempting to plunge in and play highly active lines, if the tones do not resonate with the background, the benefits and musical results of this exercise will be negligible. Compose/improvise aeolian and dorian melodies Compose Aeolian and Dorian melodies using the principles specified above (motive and sequence, balance of leaps and steps). Have your partner play drone or open fifths at keyboard, or create and record your own backdrop. Play composed melody and then improvise, creating at times as florid and dense a melodic texture as possible, using melodic cells and minor pentatonic scales.

Exercise 3p Compose/improvise with minor pentatonic bass line Proceed exactly as in Exercise 3p, except now create a minor pentatonic bass line as a backdrop for your melody and improvisation. You may need to adjust your melody somewhat, or perhaps write a new one, in order to align with the bass line.

Exercise 3q

Listening Resources: Time-feel-based Music with African and African-American Roots The following is a very encapsulated list of recordings from jazz and its offshoots as well as other contemporary time-feel-based musical sources with African and African-American roots. In light of the sheer volume of recordings that are available from any one of these historically important artists, let alone their collective inventory, this list is intended as only a starting point for building your personal library of sources. One way to begin might be to sample and download specific tracks from various recordings, and then acquire entire recordings from artists whom you find particularly compelling. What is most important is to embark on a regular program of engaged listening in order to internalize this essential aspect of contemporary musical practice.


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In the case of artists whose music spans fundamentally different style periods, such as John Coltrane and Miles Davis, multiple recordings are included. The list includes music that is based in two general types of time feel—even eighth note and swing—which we have not yet differentiated from one another. Better to establish an aural foundation first and let the analytical study follow.

Suggested Recordings Cannonball Adderley Ultimate Cannonball Adderley (Verve 1999) Geri Allen The Gathering (Verve 1998) Louis Armstrong The Ultimate Collection (Verve 2000) Chet Baker, Stan Getz My Favourite Songs—The Last Great Concert (ENJA 1988) Art Blakey The Best of Art Blakey and the Jazz Messengers—The Blue Note Years (Blue Note 1988) Jane Ira Bloom Mental Weather (Outline 2007) Charlie Christian The Immortal Charlie Christian (Legacy International 2006) John Coltrane Blue Trane (Blue Note 2003) A Love Supreme (Deluxe Edition) (Verve 2002; original 1964) The Best of John Coltrane (Atlantic 2005) Chick Corea Inner Space (Atlantic 2005, original 1966) Play, with Bobby McFerrin (Blue Note 1992) Celia Cruz The Best of Celia Cruz (Sergeant Major 2007) Tadd Dameron The Complete Blue Note Recordings of Fats Navarro and Tadd Dameron (Blue Note 1995) Miles Davis Kind of Blue (Sony 1988, originally released 1959 Blue Note) Filles de Kilimanjaro (Sony 1996, originally released 1966) ESP (SONY, originally released 1965) On the Corner/New York Girl (Sony 1992)

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Pachito D’Rivera Reunion (Timba Records 2005) Duke Ellington and Ray Brown This One’s For Blanton (Pablo 1972) Bill Evans Affinity (Warner Bros 1979) Ella Fitzgerald Ella Fitzgerald and Billie Holiday (Unlimited Media Gmbh 2006) Best of Ella Fitzgerald (Verve 1994) Dizzy Gillespie Greatest Hits (BMG 1972) Guru Jazzmatazz, Vol. 4: The Hip Hop Jazz Messenger (Grand Records 2007) Herbie Hancock The Essential Herbie Hancock (SONY BMG 2006) Dave Holland Points of View (ECM 1998) Freddie Hubbard Ready for Freddie (2004 Blue Note/Capitol, originally released 1961) Red Clay (SONY 2002, originally released 1972) Thad Jones Thad Jones Legacy, Vanguard Jazz Orchestra (New World Records 1999) David Liebman The Elements: Water, with Billy Hart, Cecil McBee, and Pat Metheny (Arkadia 1999) Bobby McFerrin Play, with Chick Corea (Blue Note 1992) Pat Metheny and Lyle Mays As Falls Wichita, So Falls Wichita Falls (ECM 1981) Charles Mingus Ah Hum (Sony 1993, originally released 1959) Thelonious Monk The Best of Thelonious Monk (Fantasy 2004) Milton Nascimento Angelus (Warner Bros. 1994) Charlie Parker The Complete Savoy and Dial Takes (Savoy 2002)



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Hermeto Pascoal Ao Vivo (WEA International Inc. 2001) Max Roach Clifford Brown and Max Roach (UMG 2004, originally released 1954) Sonny Rollins Saxophone Collosus (1987 Fantasy, originally released 1956) Maria Schneider Evanescence (Enja 1994) Sarah Vaughn The Very Best of Sarah Vaughn (AML Records 2007) Chucho Valdez Bele bele en Habana (EMI 1998) Kenny Wheeler Deer Wan (ECM 1978) Lester Young Live at Birdland 1953 & 1956 (ESP Disk 2007)

Further Reading Leroi Jones (Amiri Baraka), Blues People: Negro Music in White America. New York: Harper Collins/Perennial, 1963. Jeff Pressing, “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception 19: 3: 285–310, 2002.

SUMMARY QUESTIONS 1 To what part of the world can the roots of much time-feel-based music be traced? 2 Because of the importance of establishing strong rhythmic integrity, sharp, staccato attacks are favored over connected, legato articulations in time-feel melodic lines. True or false? 3 What rhythm ratios are key in establishing time feel? 4 In time-feel improvising, we strive for both strong rhythmic definition (though not staccato) and legato connected lines. True or false?


5 Name the notes of these pentatonic scales: B major, F minor, D minor, E major, B minor, D major, B minor, F# minor.


6 Any Dorian mode contains how many pentatonic scales?

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7 Name the constituent pentatonic scales in these Dorian modes: E, B, F, A, F#, D, A .


8 When configuring the notes of the minor pentatonic scale vertically to form chord structures, only a few configurations uphold the minor pentatonic sonority and therefore may be used. True or false?

chapter 4

Modality and Rhythm II: Small Group Framework

In this chapter, we: • • • • • •

Work with Call and Response patterns. Utilize more advanced rhythmic templates as melodic catalysts. Improvise with Modal Etude #2 and a minor blues. Introduce a framework for small group performance projects. Begin to compose in modal and rhythmic frameworks. Begin rhythmic training using principles from Indian music.

We are now ready for more collaborative work, which can greatly enhance the learning process. We will begin with a Call and Response framework for ear-training practice and also as a way of helping us clarify our ideas, followed by additional rhythmic principles, and improvising with a minor blues progression. We will then delineate a framework for small group performance that may be used for much of the work in forthcoming chapters.

Call and Response We begin with a practice called Call and Response that is prevalent in African music and may be done with any number of individuals. The idea as we will apply it here is simple. One musician sings or plays a short phrase and the ensemble answers it collectively. This poses improvisatory challenges to the caller, whose task is to create clear, coherent musical statements that are readily discernible and reproducible by the ensemble. This is not to prohibit the caller from challenging the ensemble at times with more involved lines, but simply to assert the need for clarity. By clarity, I mean the level of immediately discernible coherence in an idea. After a single iteration, a clear idea stands on its own as a kind of

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self-contained, complete statement that listeners can readily identify and, if the idea is largely diatonic (our Call and Response work utilizes diatonic ideas), sing back with reasonable accuracy. In the case of ideas that are either largely textural in nature (e.g. high-density flurries, or pointillism) or employ significant chromaticism or intervalic leaps, listeners will be able to replicate the basic gestures when the ideas are clear. The fact that in the present framework the ideas will be in time—that is, they will be based in a pulse—will aid in ensuring clarity. The ensemble is challenged aurally by this practice as it must reproduce the idea as precisely as possible. Neither caller nor ensemble is to use notated music; the ideas are generated on the spot by the caller and immediately replicated by ear by the ensemble. We will begin with a variation of traditional Call and Response approaches that will aid in the clarity of ideas. This will involve the caller repeating the idea individually before the ensemble responds. This helps ensure clarity of line because, if the line is unclear, it will be difficult even for the caller to repeat it, let alone the ensemble. This simple practice, therefore, is yet another strategy to help us hear what we play instead of just letting our fingers lead without a solid aural foundation. Exercise 4a provides a format to develop this skill.

Reminder: The exercises in this chapter are to be done using the principal instrument or voice, unless otherwise indicated.

Call and response A caller creates a one-bar minor pentatonic phrase, repeats it, then the ensemble repeats the idea twice. Tempo: quarter note = 80. Caller then moves on to a new idea.


Exercise 4a and Example 4.1

An expanded version of this format provides further aural development as it involves transposing the initial idea by ear to a second key. While we are not concerned at the moment with connecting harmonic structures to our minor pentatonic phrases, we call the above exercise a “two-chord” Call and Response format because it implies two different harmonic areas. Two-chord call and response The caller proceeds exactly as indicated in Exercise 4a. However, after the ensemble responds, the caller then transposes the idea down a whole step, and the ensemble responds accordingly.



Modality and Rhythm II

Exercise 4b and Example 4.2

Strategies for Generating New Ideas Here are some strategies that will be helpful in generating a wide range of minor pentatonic ideas. These may be of use as well with other kinds of scales. 1 Change directions and intervallic size: play upward shapes, then downward shapes. Use smaller and larger intervals. 2 Change rhythms. Example 4.3 provides some rhythmic templates that may be helpful, and you can create your own. The following illustrations show melodic lines that are based on the templates. In Example 4.4, the melodic phrase developed from template a is repeated as it would be in the above Call and Response format. In Example 4.5, the same motive derived from template a is modified over time rather than repeated exactly; the rhythm is retained but the notes change. However, notice that after three iterations of the initial motive, the rhythm is also changed for the sake of variety. While adhering strictly to a single rhythmic template is an excellent drill, it is also valuable to take some time to vary the rhythms to achieve maximum musical interest. Minor pentatonic with rhythm template TRACK 8

Choose a minor pentatonic scale and a rhythmic template, and improvise different variations of the scale adhering to the rhythmic pattern. Then move through the other templates. An example is provided on the website.

Exercise 4c

The next exercise has you transpose your lines to other pitch levels moving around the cycle of fifths, at which point this creative activity also becomes an excellent eartraining drill.

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Cycle of fifths Transpose your minor pentatonic patterns up a fourth or down a fifth as you take it around the “cycle” by ear (e.g. C, F, B , E , etc.).

b b

Exercise 4d



After working with these approaches for a while, you will notice that your ability to consistently generate new ideas in Call and Response formats expands considerably. Of equal or greater importance will be the benefits to your improvising abilities that come from this work. Let us now turn to a small group performance format for improvising and composing with time feels and modes. Example 4.6 presents a modal composition created in this format, and which may be heard on the website. A play-along track is also provided on the accompanying CD.

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EXAMPLE 4.6 Ed Sarath, Modal Etude 2 © 2008 Ed Sarath

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The following are transposed parts for Bb and Eb instruments.




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Form an ensemble Practice with the play-along track 2 on the CD. Then form a small ensemble and play Modal Etude 2 according to the above format (e.g. head (main theme), improvised solos on solo form, tutti ensemble section, and out head). It is not necessary to form a group with the same instruments as the ensemble on the recording; you can adapt these etudes to virtually any instrumental combination. In addition, even if not everyone plays improvised solos on the recording, it is important that all members of your group have turns as improvising soloists.

Exercise 4e



Modality and Rhythm II

Mode-rhythmic Formats The modal etude above is created within the parameters of what are called in this book “mode-rhythmic” formats. These are frameworks that combine modal and rhythmic structures. The format may be used with virtually any combination of instruments and serves as a framework for developing a foundation in time-feel-based improvising and composing. The format consists of five basic parts. First is the creation of a minor pentatonic ostinato pattern (which can either be played as a bass line if a bass clef instrument is part of the group, or a treble clef line). You can create a two-chord or two-mode pattern by transposing it down a whole step (or up a minor third, or half-step). Second is the composition of a melody that is to be played above or below the ostinato pattern. This melody will be considered as the main theme, or what is referred to in jazz as the “head.” Third involves ensemble members taking turns improvising atop the ostinato pattern. Here is where everyone will have the opportunity to begin developing their 2:1 and 4:1 lines, using inflections, motivic development, and other devices that are important in timefeel-based music. Fourth involves the composition of a more florid, tutti-like ensemble line that the entire ensemble will play in unison (or octaves, as necessitated by the instrumentation). In Modal Etude 2, this is the section that comes after the solos. While the head will tend to be more symmetrical, lyrical, and most likely less active—in other words, the head is more likely to be a melody that one might hear and easily repeat while walking down the street—the tutti lines are meant to sound as if they are improvised, even if in fact they are composed and notated. The purpose of the tutti lines is to allow everyone, through the temporally discontinuous act of composition—where one can pause, reflect upon, and alter ideas—to attend more directly to melodic line construction that embodies the 2:1 and 4:1 rhythmic values that are important to time-feel-based improvisation. Accordingly, you are encouraged to write tutti lines that are virtuosic in nature; this will not only add an exciting ensemble component to the music, but it will also stretch your horizons. The interplay of composing active tutti lines and improvising with the intention of being able to spontaneously create compelling lines will promote optimal development. Fifth is the restatement of the main theme, which when recurring is called the out head. In summary, the performance format begins with the ostinato pattern, then the head (main theme) enters, which is followed by improvised solos by all ensemble members, then the tutti or soli section that is played by the ensemble in unison or octaves, and finally the out head. Creative variations are also possible. A non-pulse prelude may precede the opening ostinato. This can be effective in setting up the pulse. The tutti section may precede the improvised solos instead of following them. The ostinato need not be played by the same person as a backdrop for all of the improvised solos. Having different people play the background for different solos will provide variety. Generally, only one person need play ostinato during the solos unless a heavier effect is desired. It is not necessary for the ostinato to continue throughout the entire solo section. Some variation of the ostinato may be created that still upholds the pitch and rhythmic foundation.

Modality and Rhythm II


Mode-rhythmic framework Create a mode-rhythmic framework as described above and prepare it for classroom performance.

Exercise 4f

At this point in the course, all students should be part of a small ensemble of between three and six members that meets on an ongoing basis. An ensemble can consist of virtually any combination of instruments. While time-feel-based music typically involves some combination of rhythm section instruments (drums, bass, piano, or guitar) and single-line melody instruments (saxophone, trumpet, violin, flute), it is likely that many classes will not have enough rhythm section players to go around. While this is challenging, it also forces us to dig into our creative reservoirs and come to an important realization: every instrument (including voice) has the capacity to be strongly rhythmic. Moreover, interesting timbres can result when time feels are played with unconventional instrumentation, which poses exciting ramifications for musicians in chamber ensembles (e.g. string quartets and woodwind quintets) who seek to move between and synthesize European classical repertory and influences and African-influenced time-feel-based approaches. Finally, all ensemble members are encouraged to acquire one or more hand percussion instruments, such as eggshells, tambourine, hand drums, shakers, that enable them to contribute to the groove when not playing.

Minor Blues In addition to the two-chord vamp, another structure that serves our purposes well in addition to being prevalent in the musical world is the minor blues. The blues—which comes in a variety of forms (both major and minor)—has a long and rich history, evolving from field hollers, work songs, spirituals, and other primarily African-American practices. The basic structure of the blues, which commonly undergoes considerable variation, is generally thought of as consisting of three chords or harmonic structures—I, IV, and V7—that roughly conform to the framework outlined in Example 4.9. These Roman numerals, which we will go into extensively in subsequent chapters, designate the intervallic relationship of harmonic structures (in this case minor pentatonic scales) and the tonic or root tone of a given key. Thus, in the key of C, the root structure on I is C, on IV (up a fourth from C) is F, and on V is G. Here is a basic form of the blues.  I  I  I  I  IV  IV  I  I  V  IV 

I  I :

Example 4.9 applies a minor pentatonic bass line to the above structure. Thus, in bar five, the pattern moves up a fourth to uphold the function designated by IV (a fourth above I); the pattern moves up yet another step (hence, a fifth above I), to function as V. While blues can be in major or minor keys, here the minor pentatonic sonority established in the bass line and then upheld in the melody as well makes this a minor blues.


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When improvising on this progression, one can use the minor pentatonic scales of the bass line: D minor pentatonic on I; G minor pentatonic on IV; A minor pentatonic on V. Since these scales share many common tones, if one improvised on the entire progression with just the D minor pentatonic scale, the resultant note choices would be acceptable in terms of aligning with the bass line. Let us explore diatonic scale options for the sake of variety. It is advisable to look at the progression as a whole and, instead of thinking of using different scales or modes in each harmonic area, first see if there are scales that may work for large sections of the progression. Here D Aeolian stands out; it can basically be used over all the areas, even if the area of V upheld by the A minor pentatonic may more strongly suggest the use of B natural, which would contrast with the Bb of the D Aeolian. Other options are possible. For instance, D Dorian indeed provides that B natural. But D Dorian would have to give way to a new scale on harmonic function IV, where the G minor pentatonic scale includes a Bb. Nonetheless, the shift from D Dorian to G Dorian, which would be the most logical choice here, can be very effective. As you play on the next progression, try both of these options. Example 4.10 adds a melody atop the above bass line to provide a minor blues composition that you can play in your small ensemble. While the Roman numerals suggest specific chords that can be played by pianists or guitarists with each change in the bass line, interesting harmonic accompaniments may be created in this piece, regardless of one’s fluency with chords, by deriving vertical structures from the minor pentatonic scales indicated. As we saw in the previous chapter (review Example 3.9), virtually any configuration of the minor pentatonic scale yields structures that bring out the sound of the scale and will thus fit with a minor pentatonic bass line such as is found in this piece.

Modality and Rhythm II

Minor blues Practice with the play-along track on the CD. Then play the minor blues in your small group with all group members improvising several choruses (a chorus is one time through the form) on the form. Compose a tutti, quasi-improvised line on the progression to be played either before or after the improvised solos and prior to the out head.

Exercise 4g

EXAMPLE 4.10 Ed Sarath, Minor Blues © 2008 Ed Sarath



Modality and Rhythm II

Minor blues composition project Compose a minor blues progression, melody, and a tutti passage as specified in the above format. Prepare to perform in class with small group.

Exercise 4h Assorted time feels Use recordings from the listening resources listed at the ends of Chapters 1 and 2, as well as other time-feel music you encounter, as inspiration, and create as large and diverse a collection of time feels as possible. Create ways of notating them and if possible record them. The samples may be brief, even just 30–45 seconds in length.

Exercise 4i

Let us conclude this chapter with a further set of rhythmic activities that will greatly complement time-feel-based improvising.

Indian Rhythmic Practices The following rhythmic exercises apply principles from Indian music, in which some of the most sophisticated rhythmic practices in the world are found. The drills have you chant the syllables indicated, and clap the cross-rhythms which are indicated by accents above and below the syllables. While it must be emphasized that the exercises represent but a limited adaptation of certain Indian principles to Western formats, and thus barely scratch the surface in terms of any sort of substantive study of Indian rhythmic practices, they can be quite helpful in developing your sense of internal pulse, polyrhythmic skills, and the ability to work with metric cycles other than those based in four or three. You will also find that the syllables can be helpful when it comes to playing 2:1 and 4:1 improvised lines in timefeel formats. At the heart of the practice is a kind of solfege system used in Indian music, in which certain syllables are used to designate particular groupings of notes: Ta = 1 Ta ka = 2 (tah kah) Ta ki ta = 3 (tah kee tah) Ta ka di mi = 4 (ta ka dee mee) Ta di ki ni thom (or ta) = 5 (tah dee kee nee tah) Practice chanting the different patterns, repeating each pattern at length. Infinite possibilities emerge through the combination of these syllables. For instance, a beat cycle

Modality and Rhythm II


of seven can be achieved by combining 2+3+2 (Ta Ka  Ta Ki Ta  Ta Ka) or 4+3 (Ta Ka Di Mi  Ta Ki Ta) or 5+2 (Ta Di Ki Ni Ta  Ta Ka). A beat cycle of 13 can be achieved in many more ways: 4+5+4 (Ta Ka Di Mi  Ta Di Ki Ni Ta  Ta Ka Di Mi), or 5+5+3, or 4+3+5+2, etc. Beat cycle Create your own beat cycle and subdivisions and chant the corresponding syllables. Repeat the cycle at length so that it falls into a solid groove.

Exercise 4j

Below is an exercise that adds accents, to be clapped, atop a seven-beat chanted cycle. As you do these drills, let your body be relaxed and fluid rather than stiff. Recall the axiom stated above when it comes to rhythm: rhythm flows through the whole body. Do not be flat-footed when you practice these activities; stand on the balls of your feet, allowing yourself to be buoyant. And when you chant the syllables, do so with gusto! Seven-beat cycle (4 + 3) Repeat the cycle indefinitely, first just chanting the pattern before adding the clapped accents. Five lines of clapped accents are included, two above and three below the syllables. Repeat each accented line eight times before proceeding to the next line.


Exercise 4k

> > TA > >

> KA

> > DI > >


> > TA

KI >

> >

TA : >


Here is an illustration of how these syllables may be applied to contemporary Western formats. Example 4.11 shows the bass line used in the above minor blues, with the corresponding rhythmic syllables that delineate the phrasing of this bass line. Each syllable represents a sixteenth note. Thus, two syllables will sound on each eighth note in the bass line. While the tie between beats 2 and 3 of the measure is not respected in the chanted syllables, the syllables nonetheless nicely capture rhythmic phrasing and feel of the line, as the recorded selection indicates.



Modality and Rhythm II


Eighth-note solidification drill Take turns chanting the syllables while someone else plays or sings the bass line. Then improvise on the D minor pentatonic or D Aeolian modes using the syllables as a kind of rhythmic template. This is an excellent way to begin generating and sustaining eighthnote lines.

Exercise 4l Eighth-note solidification drill Here is another bass line with different rhythmic subdivisions to be approached as above.

Exercise 4m

Further rhythmic exercises are given in Appendix 3. The following section describes how to integrate rhythmic training into the small ensemble performance format that will be central to this class.

Small Group Ensemble Performance and Project Format A recommended strategy for this course is to have each class begin with small ensemble performances and projects. For instance, in a class of 30 students that meets twice a week, six quintets could be formed, and if two groups performed at the beginning of each class,

Modality and Rhythm II


every group and every student would have the opportunity to play every fourth class. Naturally, many other approaches are possible, and instructors are encouraged to come up with the format that is ideal for their particular situation. If this suggested approach is adopted, it can be further broken down so that each small group performance will consist of three parts. First, the ensemble begins with one of the Indian rhythmic drills (additional exercises are found in Appendix 3). Second, the ensemble performs an aural transposition drill, taking a short pattern (two to four bars) and playing it by ear in all keys. The instructor may specify the pattern, or students may create their own. It cannot be emphasized strongly enough that whatever pattern is used, it must be melodically clear and coherent. Weak patterns not only tend to be extraordinarily difficult to aurally transpose, but they ingrain poor melodic conception in the ears and fingers. Third, the ensemble presents a mode-rhythmic composition, as outlined above (be sure to include the five components), in which each group member improvises. Preparation for the performances is to be done outside of class. During class, the entire performance can be done in 10–15 minutes, including time for class feedback.


Self-assessment: assess your 2:1 and 4:1 lines in your improvising. Are you able to sustain compelling lines?


Record yourself, or reflect on how you sound. How authentic is your conception of time feel? Ask your friends to help evaluate your “time-feel chops.”


How is mastery of musical time feels similar to mastery of spoken language?


How does mastery of time feels differ from mastery of spoken language?


Who are some of your favorite improvisers when it comes to playing over time feels? What are some exemplary recordings or particular tracks?

chapter 5

Basic Tonal Materials: Triads and Seventh Chords

In this chapter, we: • Introduce triads and seventh chords in root position and inversions. • Begin a systematic approach to keyboard realization practice. • Fortify our command of chords and modes.

Up until this point our improvising has involved minimal pitch constraints, with the twomode framework in Modal Etude 2 being the most elaborate. Tonal music, involving chords and chord sequences that may move freely from one key area to the next, presents different kinds of challenges as well as creative opportunities for improvisers. This is in no way to suggest, however, that tonality is inherently more sophisticated or creative than modality, and that our primary interest in modal frameworks is as an entry point to tonality. Indeed, in some forms of what is characterized as modal jazz, highly elaborate structures are found that move freely and frequently between highly disparate modal areas. Moreover, contemporary jazz artists and others make interesting blends of tonal and modal approaches, hence calling for fluency with both kinds of pitch structures. Although beyond the scope of this book, an interesting point for historical reflection is the fact that whereas in European classical music tonality evolved out of modality, modality in jazz emerged only after a good half-century of tonal jazz. Accordingly, the use of modal formats prior to tonal formats in this book is consistent with our general proclivity to approach the past through the lens of the present. What do we mean by tonality? Whereas modal music, as it is conventionally defined, generally involves entire passages or pieces that are centered in a single scale or mode, tonal music is based in the use of chords and chord sequences that create movement within and between key areas. As we will see, different chords, according to their intervallic structures, uphold different functions in tonal music—hence the phrase “functional harmony” that is

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often used to describe tonal chord progressions. Some chords are stable, functioning more as target chords or arrival points. Here we can draw parallels to our prior consideration of melodic target notes. Other chords are less stable and, in suggesting movement or resolution to the next chord, uphold more of a passing function. And of course, context is paramount—a chord that functions as a target chord in one instance may serve more of a passing role in another. These and many other facets of tonality—which is unique to the West—appear in European classical music, jazz, popular music, folk music, and much music of the Caribbean and South America. A secondary dominant chord functions the same way in Bach as it does in Ellington. Before exploring harmonic functions in greater depth, which will be our focus in the next chapter, we first need to gain a grasp of the different kinds of chord structures that are available.

Triads Triads are three-note chords consisting of a root tone, a note an interval a third above the root, and a note a fifth above the root. We call these the root, third, and fifth of the chord. Example 5.1 illustrates four primary types of triads, which can be distinguished from one another according to their respective intervallic relationships.


Example 5.2 shows triads built on the seven steps of the C major scale, which is achieved by simply stacking notes in thirds atop each scale tone. Notes of triads fall either on all lines or all spaces, which is characteristic of all chords aligned in thirds. Three types of triads are found which are diatonic—that is, whose notes are derived from the key, requiring the use of no accidentals—to a major key: major, minor, and diminished. In every major key, therefore, the diatonic triad built on the tonic note, indicated by the Roman numeral I, will be a major triad. Similarly, the diatonic triad built on II will be minor, on III minor, on IV major, and so on. The chord symbols are listed above each triad (e.g. C, Dmin, Emin, etc.), indicating its root, and by an abbreviation, its quality (whether it is major, minor, diminished, or augmented). Minor is indicated by min, diminished by dim or just 0, and augmented by aug or +. In the case of major triads, no abbreviation is necessary; the letter name of the triad by itself will suffice to indicate that the quality is major. Notice the two systems of Roman numerals provided beneath the triads; we will discuss these shortly.


Basic Tonal Materials


Keyboard Fingerings for Triads

Example 5.3 shows how triads may be easily fingered at the keyboard. Play the chord with your right hand, placing your thumb on middle C. Middle C is the white key to the left of two black keys at the middle of the keyboard. Chords played in this central range of the keyboard provide the best sonority when accompanying bass and melody added by other instruments.

C Major Triad:





Keyboard exercise: triads Choose a major scale you are comfortable with, other than C major. Slowly play triads up and down the scale. Sense the different qualities of the different triads, and that some seem more stable while others seem to want to resolve.

Exercise 5a

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Triad spelling Spell (name the notes of) these triads (notice the use of different labels at times, such as aug and + for augmented): Fmin, Edim, A, C#min, Ddim, Gaug, G , C+, A min, F#, D, Bmin, D 0, E, D#min, A +, C#.





Exercise 5b Names of the notes Write the names of the notes on top of each of the following triads.

Exercise 5c and Example 5.4 Two-person drill Player A plays or sings a tone which is designated as the root of the triad and indicates the name of the root tone as well as the quality of a triad that is to be sung (e.g. he/she states “A major” and then sings or plays A). Player B not only sings the tones, but in so doing also names the notes (e.g. sings tones and names “A C# E”).

Exercise 5d

Seventh Chords Seventh chords are four-note structures attained by simply adding another tone a third above the fifth of the triad—or a seventh above the root. Hence seventh chords consist of a root, third, fifth, and seventh. We will later use this same procedure to create ninth, eleventh, and thirteenth chords. Example 5.5 illustrates the five basic types of seventh chords (additional types will be considered later) as well as the contemporary chord symbols that are used to indicate these chords. These are: major seventh, minor seventh, dominant seventh, half-diminished seventh, and fully diminished seventh chords. C half-diminished seventh is the same as Cmin7(b5) and in contemporary chord nomenclature is more commonly indicated as the second of these. It is important to know


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that they are synonymous however. Notice also the use of the circle with the slash through it as opposed to the unmodified circle of the fully diminished seventh chord. Example 5.6 illustrates the diatonic seventh chords of the major scale. Four of the five types of seventh chords shown above are seen. Which chord is absent?



Keyboard Fingerings for Seventh Chords





C Major 7th Chord:


Example 5.7 illustrates finger positions for seventh chords.





Basic Tonal Materials


Keyboard exercise: seventh chords Choose a major scale you are comfortable with, other than C major. Slowly play seventh chords up and down the scale. Sense the different qualities of the different chords, and that some seem more stable while others seem to want to resolve.

Exercise 5e Seventh chord spelling Spell (name the notes of) these triads: B min7, A07, Bmaj7, C#7, Dmaj7, G min7.



Exercise 5f Chord symbols Write the proper chord symbol above these seventh chords.

Exercise 5g and Example 5.8

Seventh chord singing Your partner plays a tone as the root of the seventh chord and indicates the name of the root tone as well as the quality of a triad that you are to sing. You sing the tones and the names of the notes.

Exercise 5h

Two Roman Numeral Systems As Examples 5.2 and 5.6 illustrate, two kinds of Roman numerals are used to designate the functions of the different triads and seventh chords. We will use the upper case Roman numerals when we analyze jazz and popular music, and the combination of upper and lower case when we analyze European classical music. The reason for the two different systems


Basic Tonal Materials

is to maintain consistency between Roman numerals and the two types of chord symbols used in the two traditions. Contemporary chord symbols as used in jazz and popular music consist of a letter name followed by the quality of the chord; in the case of major triads, the letter name itself will suffice. The counterpart to contemporary chord symbols in European classical music is the figured bass line, which consists of a bass line and Arabic numeral figures to indicate the inversion of the chord and any notes to sound above the bass note beyond those of the basic triad (generally nothing beyond the seventh is included). Musicians in the baroque era improvised atop figured bass lines much as today’s jazz and pop musicians improvise with contemporary chord symbols. We will therefore align our use of Roman numerals, respectively, with these two chord symbol systems. When we analyze jazz and popular music, the Roman numerals we use to designate chord function and quality will be upper case and, as with the chord symbols themselves, followed by the quality of the chord and the extension included. When we analyze European classical music, we will use a combination of upper and lower case. Major quality chords will take upper case; all others will take lower case. While at first it may seem rather unwieldy to learn two systems, this will ultimately not prove too difficult when our analytical work is integrated with our improvisatory work and the respective chord symbols utilized. Moving back and forth between the systems will aid in our understanding and appreciation of the common ground and distinctions between these two rich tonal traditions. As we will see in Chapter 12, the use of figures is ideal for indicating inversions of chords, which is a predominant aspect of European classical harmony. While chord inversion is also found in jazz/pop to a much lesser degree, the more prominent and distinguishing feature, particularly in jazz, is the use of chord extension. In jazz, particularly in the past halfcentury or so, triads are rare, and while lead sheets typically indicated seventh chords, these are more often than not extended to the ninth and beyond. In order to promote fluency with the systems, as well as to help illuminate commonalities and distinctions between these two tonal systems, we will at times in our study of Euroclassical repertory apply contemporary chord symbols, and conversely also reduce jazz/pop progressions to figured bass lines.

Inversions Triads and seventh chords can be played or “voiced” in a wide variety of configurations. As Example 5.9 illustrates, when the root is in the lowest voice or position, this note is called the bass; the chord is in root position. For the sake of variety or particular kinds of voiceleading movement, other notes of the chord (called chord tones or partials) may be placed in the bass voice; this is called inversion. The different kinds of inversion correspond to which chord tone is in the bass. When the third of the chord is the lowest or bass voice, the chord is in first inversion. When the fifth is in the lowest position, the chord is in second inversion. When in the case of seventh chords the seventh is in the lowest voice, the chord is in third inversion. Later we will consider the role of inversions in creating melodic motion within a sequence of chords. For now, it will suffice to be aware of the various possibilities

Basic Tonal Materials



regarding how chords may be configured and to begin to become fluid with these configurations when we play chords at the keyboard, write them, and analyze them. Notice in the chord symbols the use of the slash (/) after the root, and to the right of the slash, the note of the chord that is in the lowest voice. Example 5.10 illustrates another way of analyzing root position, first inversion, and second inversion structures, involving Arabic numerals to designate the intervals of each chord tone atop the lowest chord tone. Root position triads will therefore have notes a third and fifth above the lowest note; because that tone is the root means that the chord is in root position. First inversion triads have tones a third and a sixth above the lowest note; second inversion triads have tones a fourth and a sixth above the root. The Arabic numerals used to designate the intervals above the lowest note (which need not be the root) are the “figures” that appear with bass lines in figured bass practice. They also follow Roman numerals in analysis of European classical music to indicate inversions. Let us now look at the inversions of seventh chords. Example 5.11 illustrates seventh chords in the various positions that are possible. Because of the additional tone, a third inversion is possible, where the seventh is the lowest note in the voicing of the chord that is naturally not available with triads. Observe also the figures that are indicated which will be used in analysis of European classical repertory.




Basic Tonal Materials

Chord identification Identify these chords by writing the contemporary chord symbol atop each chord. Indicate inversions where applicable (e.g. Gmaj7/D).

Exercise 5i and Example 5.12

Close Position and Open Position or Spread Voicings The chords in the above exercise are in close position, which means that there are no spaces between any two voices in which another chord tone might be placed. Open position chords—also called spread voicings—are those in which the notes of the chord are spread out, which can produce a more resonant and expansive sound. Example 5.13 illustrates this. Notice that even with the same chord symbol, chords may be voiced in very different ways when it comes to the use of close and open position. The two Cmaj7 chords in the following example, one in close position and the other in a spread voicing or open position, illustrate this. The first of the two Cmaj7/G chords shows that close position is possible even when chords are inverted. The second shows the same chord in open position voiced with intervals of sixths and a seventh between notes; even larger intervals will sometimes be found in the bass clef between the bass note and the next lowest chord tone. While inversion is indicated in chord symbols, whether or not the chord is in close or open/spread position is not. Example 5.14 shows an inverted chord whose notes are spread out through treble and bass clefs, thus making it challenging to determine the root of the chord, let alone the inversion. Nonetheless, there is a simple way to make both kinds of determination. The first step is to arrange the notes of the chord in thirds; the note at the bottom will be the root. When we align the notes of the chord configuration on the left in thirds, we identify the chord as an Fmaj7 chord, but since note A and not F is in the bass, we recognize the chord as being in first inversion, indicated in this case as Fmaj7/A.


Basic Tonal Materials


Scrambled chord identification Identify and provide the correct chord symbols for each of these chords. Observe that, even if the notes are spread out, some are in root position because the root is the lowest voice (at the bottom). Others are spread out but some note other than the root is the lowest voice; in such instances the inversion must be indicated.

Exercise 5j and Example 5.15 Scrambled chord identification Continue with these chords, which are voiced in two staves. Remember to stack in thirds to determine the root, after which the proper inversion will be readily identifiable.



Basic Tonal Materials

Exercise 5k and Example 5.16

Write out chords Write down each of the chords, which are listed here in root position, in at least three different inverted configurations (e.g. as in Exercise 5k). Of the three inverted configurations, one should be in close position; the other two should be spread or open voicings that span two clefs. Adjust the chord symbol accordingly atop each configuration to indicate the proper inversion used (e.g. A maj7 becomes A maj7/E ).




A maj7 E7 D min7 Dmaj7/A C#min7( 5) G 07 A 7




Exercise 5l and Example 5.17



Gm7( 5)




G min7/B




Basic Tonal Materials


Keyboard Realization There is no more effective way to develop an understanding of tonality than to realize harmonic structures at the keyboard, where we can experience the sound and feeling of particular chords and progressions, as well as gain analytical understanding of them. Combined with the various improvising, composing, aural training, rhythmic exercises, and analyses that comprise this course of study a truly formidable kind of mastery is possible. The keyboard exercises in this book are designed for musicians who have had little or no contact with the keyboard. While it is ideal that students take the basic keyboard class that is required of most music majors prior to or concurrently with this course of study, it is possible to fully engage with and derive benefits from the exercises even without this concurrent or prior training. Seminal Keyboard Project 1 Play major seventh chords around the cycle of fifths at the keyboard as indicated in this pattern (e.g. Cmaj7-Fmaj7-B maj7-E maj7, etc.). Your task is to continue the pattern without notating the chords. Two versions are provided: one (A) in which there is greater movement between voices and hand position when moving from one chord to the next, and the other (B) involving smoother motion. You are encouraged to utilize format B as soon as you are comfortable doing so, since it is musically more desirable. However, you may use format A at first, since it facilitates getting the correct notes under your fingers. Do not be concerned that the bass line leaps up a fourth or down a fifth moving from one chord to the next; this is not only inevitable with this kind of root movement, it is musically satisfying. Use the fingering format provided in Example 5.7.



Variation: Improvise a vocal line while playing the keyboard, using the exact same rhythm of the keyboard part. In other words, your vocal rhythm will match the keyboard rhythm. You can sing just one note per chord, and then change vocal notes when the chord changes. It is neither necessary nor encouraged that you try to be consciously aware of what chord tone you happen to sing; this is a purely aural exercise that connects the voice with the keyboard realization process. This is an ideal format to utilize the hearing in advance technique first introduced in Chapter 1: on each chord, try to aurally anticipate the next note you will sing.



Basic Tonal Materials

Exercise 5m and Example 5.18

A further word about the use of the keyboard in this chapter and the remainder of the book. The above format is one that will be central to both our keyboard realization of chord progressions and written realizations of these progressions. The very four-note structure we play in the right hand at the keyboard, which is generally in treble clef range, and a single bass note (either the root, or if the chord is inverted, some other tone) in the bass clef, will be the basis for how we proceed in our written work. From this foundation, we will also explore other configurations of chords that can be uniquely applied through written formats. Root position chords (chords in which the root is in the bass) will be our focus at the keyboard for the following few chapters, for two reasons. One has to do with one of the basic principles underlying this approach to musicianship, that of the contemporary entry point. We approach the past through the lens of the present. Therefore, given the two prominent tonal music traditions in the musical world, our initial forays into tonality are through jazz and pop practice. Because jazz, moreover, provides us with a more elaborate and systematized harmonic system (which includes almost everything found in popular music, whereas the reverse does not hold), we will adopt a jazz-oriented approach. And because jazz, particularly in what might be called its “common practice” period (1935–1960, not to be confused with what for many is the more familiar Euroclassical common practice period of around the seventeenth to nineteenth centuries), is largely a root-position music, which will be our orientation in this phase of musicianship training. As stated earlier in this chapter, whereas central to the richness of European classical harmony is the use of inversion to yield melodic tapestries through which underlying harmonies are able to unfold; central to the richness of jazz is the extensive use of chord extension and frequent harmonic movement between close and distant tonal regions, which make possible different kinds of melodic tapestries. The latter practices are facilitated by root-position harmonies. A second, highly practical reason extends from this approach. This involves the handson application to which this approach is conducive, whereby focus on root-position harmonies in diatonic and non-diatonic contexts enables a kind of basic fluency with harmonic structures and functions that will enhance engagement with inversions and the various more advanced structures found in both jazz/pop and European classical repertory.

Basic Tonal Materials


Fortification Exercises: Aural and Analytical Here are a few more drills that will greatly assist in gaining fluency in chord spelling (the final set will also fortify knowledge of the modes). It is not recommended that you complete all the exercises in each section before proceeding to the next, nor that you complete all the exercises in this chapter before proceeding to the next (unless you find yourself so absorbed and enthralled by them that you cannot help yourself!). Better to spend some time in each section and identify the ones that are particularly challenging and then chip away as you move forward. As with the aural transposition work begun earlier in the book, if you establish as part of your regular routine the habit of devoting some time to these kinds of fortification drills, you will be well on your way to gaining the fluency required. You can be working on material several chapters from this one and return to these exercises until you have completed all of them. Moreover, particularly with the ear-training work, it may take further keyboard work and other kinds of activity to make breakthroughs in this realm. Clearly, some form of ear training should be part of your daily routine; however, if you find yourself entirely stymied by one or more of the above exercises, you may return to it. This advice is predicated on an important assumption, however, which is that you have achieved a basic level of understanding of the chord structures we are dealing with. Even if it may take you a moment to spell a given chord, if you have a basic grasp of the principles involved (e.g. the difference between Ab7 and Abmaj7) then you may move forward and return to these exercises to gain added fluency. But if you are finding that you have significant gaps in basic chord spelling, then it is advisable to spend more time on these drills.

Ear training with a partner Player A plays different kinds of seventh chords (minor 7, major 7, dominant 7) at the keyboard in root position. B identifies the chord type. • Variation: B sings the chord tones.

Exercise 5n

One-person ear-training/vocal exercise This is a modified version of the second part of Exercise 5j that can be practiced on your own and yield considerable benefits. Sit at the keyboard and play random triads and seventh chords and sing the notes of each chord (without arpeggiating the chords). When you start to gain proficiency at this, try playing the structures with a single staccato chord and see if you can retain the pitches in your ear and reproduce them vocally.

Exercise 5o


Basic Tonal Materials

Ear training Player A plays or sings a tonic note, and then specifies a chord to be sung atop that note. Player B sings the tones of the chord.

Exercise 5p Variation Player A plays or sings a note other than the root and indicates what chord tone it is of the chord. Player B sings the remaining notes.

Exercise 5q

Modes Let us extend upon our work with modes that began in Chapter 2. The following example will refresh your memory. Chords may be thought of as vertical structures within pitch regions, while scales or modes may be thought of as horizontal structures within pitch regions. When we improvise on chord progressions (beginning in Chapter 6), we will correlate particular modes/scales with particular chords. Fluency with modes will thus be important to this work. Example 5.19 lists the seven diatonic modes and correlates them, using Roman numerals, with a scale degree of the major scale. It will be important to learn these correlations: the Ionian mode is built on I of major, Dorian on II, Phrygian on III, Lydian on IV, Mixolydian on V, Aeolian on VI, and Locrian on VII.


Modemaster Drills Modemaster drills are a form of “musical gymnastics” designed to help further fortify your command of basic tonal materials. The procedure is simple. A mode is specified as well as

Basic Tonal Materials


a scale degree, and you are asked to name the diatonic triad or seventh chord that is built on that degree of the mode. The term “diatonic” simply means that the triad or seventh chord will comprise the notes of the mode specified (similarly to when we derived triads and seventh chords from the major scale). This may be done by simply stacking notes in thirds above the specified degree of the mode. For instance: “Name the diatonic triad built on the fourth degree of a D Dorian scale. Provide the names of the notes as well.” Response: G major triad. Notes: G-B-D. Analysis: Recall that the D Dorian mode is built of the notes of the C major scale. G is the fourth degree of the D Dorian mode. When we stack notes atop G in thirds using the notes of D Dorian (from key of C), we get G-B-D. Another case: “Name the diatonic seventh chord built on the second degree of an F Aeolian scale. Provide the names of the notes as well.” Response: Gmin7 (b5) (or G half-diminished 7 chord. Notes: G-Bb-Db-F. Analysis: F Aeolian is derived from Ab major. The second degree of F Aeolian is G. When we stack thirds on G, using the notes of F Aeolian (or Ab major), we get G-Bb-Db-F, or Gmin7 (b5). If you spend a few minutes a day on the following drills, you will rapidly develop formidable command of your triads, seventh chords, and modes. This ability will be invaluable when it comes to a wide array of musical activities: keyboard work, analysis, harmonization, improvisation, composition, arranging, conducting, transposition. Triads The diatonic triad built on the: 1.

third degree of D Dorian is “F major” Notes “F, A, C”


second degree of A Aeolian is _____________ Notes __ __ __ __


fifth degree of F Mixolydian is _____________ Notes __ __ __ __


seventh degree of E Lydian is _____________ Notes __ __ __ __


fourth degree of B Locrian is ______________ Notes __ __ __ __


sixth degree of A Dorian is ________________ Notes __ __ __ __



Basic Tonal Materials



third degree of A Phrygian is _____________ Notes __ __ __ __


second degree of D Lydian is _______________ Notes __ __ __ __


fifth degree of B Dorian is ________________ Notes __ __ __ __


seventh degree of E Aeolian _____________ Notes __ __ __ __


fourth degree of C Lydian is ______________ Notes __ __ __ __


seventh degree of A Phrygian is ___________ Notes __ __ __ __


fifth degree of F Mixolydian ______________ Notes __ __ __ __


fourth degree of G Locrian is ______________ Notes __ __ __ __


seventh degree of E Lydian is _____________ Notes __ __ __ __


fifth degree of C Dorian is _______________ Notes __ __ __ __


third degree of A Mixolydian _____________Notes __ __ __ __


sixth degree of F# Lydian is _______________Notes __ __ __ __


second degree of F Phrygian is _____________Notes __ __ __ __


fourth degree of B Mixolydian _____________Notes __ __ __ __




Exercise 5r

Seventh chords The diatonic seventh chord on the: 1.

third degree of A Dorian is ________________ Notes __ __ __ __


seventh degree of A Lydian is _____________Notes __ __ __ __


fifth degree of A Lydian is _________________Notes __ __ __ __


second degree of E Aeolian is _____________ Notes __ __ __ __


fourth degree of B Dorian is _______________ Notes __ __ __ __




b fifth degree of Eb Lydian is ________________Notes __ __ __ __ seventh degree of Eb Dorian is _____________ Notes __ __ __ __ second degree of Db Lydian is ______________Notes __ __ __ __


fourth degree of E Mixolydian is ___________ Notes __ __ __ __

6. 7. 8.

sixth degree of B Mixolydian ______________Notes __ __ __ __

Basic Tonal Materials



sixth degree of A Dorian is _______________Notes __ __ __ __


seventh degree of D Phrygian is ___________Notes __ __ __ __


third degree of D Locrian is _______________ Notes __ __ __ __


fifth degree of G# Locrian is _______________Notes __ __ __ __


fourth degree of A Lydian is _______________Notes __ __ __ __


seventh degree of F# Lydian is _____________Notes __ __ __ __


fourth degree of A Mixolydian ____________Notes __ __ __ __


second degree of C Phrygian is _____________Notes __ __ __ __


fourth degree of A Aeolian is ______________ Notes __ __ __ __


second degree of B Lydian is ______________ Notes __ __ __ __


third degree of B Mixolydian is ____________ Notes __ __ __ __


sixth degree of C Dorian is ________________Notes __ __ __ __


sixth degree of C# Phrygian is _____________ Notes __ __ __ __


fifth degree of G Locrian is ________________Notes __ __ __ __


seventh degree of A Dorian is _____________ Notes __ __ __ __



Exercise 5s


chapter 6

Harmonic Functions

In this chapter, we: • Learn about basic chord functions and Roman numeral analysis. • Work with the prominent II–V–I sequence through written exercises, keyboard realization, and improvisation. • Study chord–scale relationships for use in improvising. • Create our own chord progressions using free-tonicization techniques.

Having begun to develop facility with basic chord structures, we can now begin to examine more closely how chords function to uphold tonal areas. Some chords are stable, conveying a sense of arrival within a harmonic progression; others are less stable and suggest movement toward other chords. An important factor in the function of chords is which scale degrees are contained within them. Different scale degrees uphold different tendencies within the scale, and these shape the tendencies of chords that are formed from the scale tones. Example 6.1 lists the names that correspond to each scale degree and corresponding chord functions. Also indicated are the two points in the scale in which notes are only a half-step apart; these are significant in that there is an inherent attraction between these tones. Strongest is the tendency of scale degree seven, aptly called the leading tone, to resolve to the root tone of the scale, which is the tonic (although we will see an important exception to this shortly). Movement from scale degree four to three is also prominent. Other types of movement that occur frequently is the dominant to tonic or V to I movement of chord roots. Somewhat less prominent but evident enough to warrant mention is downward


Harmonic Functions


movement by a whole step, as in scale degree two resolving to the tonic, that occurs frequently in melodic contexts.

Tonic–Subdominant–Dominant Functions Within the seven kinds of functions, three in particular are prominent in tonal music: tonic, subdominant, and dominant, or I, IV, and V. The tonic chord is the most stable, target sonority of the three. The dominant is among the least stable, possessing a strong drive to resolve to I for reasons we will examine below. The subdominant chord serves as a preparation for the dominant and often follows I or some closely related chord. In fact, closely related chords—chords that share two or more common tones—may be identified for each of these chord categories, thus making it possible that chords other than I, IV, and V assume or serve in place of tonic, subdominant, and dominant functions. For instance, III and VI will sometimes be used in place of I; II in place of IV; and VII in place of V. Example 6.2 illustrates the tonic–dominant–tonic sequence in one of its most basic forms: I–IV–V7–I. Half step and V–I root movement are indicated. Another common version of the tonic–subdominant–dominant–tonic sequence in European classical music is shown in Example 6.3. Here the subdominant function is upheld not by IV but by the closely related first inversion of II7 (IImin7 in jazz/pop), which is followed by the I chord in second inversion—labeled here as I 64 but in effect upholding a dominant function (the chord is sometimes analyzed as V 64)—and then V7. The I 64 (or V 64) chord is called the cadential six-four chord owing to its pivotal role in leading to V which in turn leads to I. Example 6.4 illustrates a contemporary tonic–subdominant–dominant–tonic sequence. Here the I chord is followed by the submediant chord, VImin7, which leads to the IImin7 chord, which (as above) may be thought of as upholding the subdominant function (even if now, due to the root position version of the chord, the bass note is II not IV of the key), which leads to V7 and then to I. Notice that whereas the minor quality chords in the prior example were analyzed in lower case Roman numerals, consistent with analytical protocol in European classical music, in contemporary tonal contexts we retain upper case Roman numerals, followed by the quality as indicated in the suffix, for all chords. Nonetheless, it



Harmonic Functions



should be clear that the two tonal languages share much in common when it comes to chord function, particularly in the way subdominant (or closely related) harmonies prepare the dominant chord, which resolves to the tonic. While exceptions to these tendencies are to be found in both jazz and European classical harmony, the fact that they have predominated over the course of several centuries underscores the coherence and resonance of the tonal system. However, one important exception is found in the contemporary cadential movement that is shown above: the third of the V7—the all important leading tone of the key—does not resolve to the tonic note when it appears in the upper and often the middle voices, but instead serves as a common tone between the V7 and I to form a Imaj7. This will generally not be found in European classical harmony. While major seventh chords are found in European classical music, they virtually never occur in the context of a V7 to I cadence, whereas V7 to Imaj7 is predominant in jazz (where the V7 to I major triad pervasive in Euroclassical music is rare).

The Dominant Seventh Chord Let us examine the intervallic makeup of the dominant seventh chord in order to understand why it uniquely drives toward the tonic. This will shed light on the predominance of

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the V–I sequence throughout centuries of tonal music, and also the interesting impact that results when this tendency is thwarted. Example 6.5 shows two important features in this regard. The first is that this chord contains both scale degrees 4 and 7, which form the highly unstable tritone interval and which are a half-step apart from more stable scale degrees (7 is a half-step lower than 1, 4 a half-step higher than 3). A chord with even one of these tones will possess a significant tendency to resolve to a chord that contains its target note; that the V7 contains both tones results in a particularly strong pull toward the I chord.


Another feature of the dominant seventh chord which influences its drive toward I is that its root is a perfect fifth above the tonic note. Because the perfect fifth is one of the early overtones—the second overtone generated after the octave, as seen in Appendix 2—there is a strong attraction between this note and the tonic. This combined with the first features mentioned illuminates why the V7 chord so forcefully pushes toward I, and why the V–I sequence is as prevalent today in jazz and popular music as it was centuries ago in European classical music. Moreover, even when we extend the dominant seventh chord to include ninths, thirteenths, and a variety of altered extensions (e.g. b9, #9, b5, b13), producing significantly different sounds than heard in classical music, the core structure—the tritone and the root of the chord—that underlies this drive to I remains intact.

Cadence Whether or not it is prepared by a subdominant harmony, the resolution of the V7 chord to the tonic chord is a common type of cadence. A cadence refers to the arrival point in a harmonic progression, which is usually framed by the final two or three chords in a sequence. The most final sounding cadence is the V7 to I cadence, and there are several types of V7–I cadences that are distinguished according to the note of the chord that sounds in the melody. For instance, the root of the I chord sounds in the top voice in what is called an authentic cadence, something that is rarely found in jazz due to the more common instance of some other chord tone or chord extension (the ninth is often used in the top voice on the final chord of a passage) sounding in the top voice on the final I chord. Not all cadences end on I; the plagal cadence terminates with a IV–I sequence, the half cadence with I–V, and the deceptive cadence with a V7 to VI sequence that is both unexpected in thwarting the sense of closure that V7 to I provides yet is in no way jarring due to the common tones VI shares with I. Indeed, the effect is usually a resonant and colorful


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alternative to the anticipated I chord. We will later consider progressions in which V7 resolves to more distantly related, non-diatonic harmonies such as bVI and bII. While the V7 to I cadence, therefore, is prevalent in both European classical and contemporary tonal practice, the two tonal streams differ in how this cadence is used. As we will see later, these chords are generally extended in jazz pop, whereby the I chord will at least include the major seventh and often the ninth and even #11, and the V7 will commonly include the ninth and thirteenth. As discussed previously, the I chord in Euroclassical music is almost always a triad, and the V7 is rarely extended beyond the seventh. A second difference involves how the V7 chords are prepared in the two tonal streams. The V7 is commonly preceded in Euroclassical music by either IV, II in first inversion, or I in second inversion (these will be taken up later). In contemporary tonal practice, the IImin7 (or ninth) commonly precedes the V7 chord, yielding the pervasive IImin7–V7–Imaj7. It is this sequence to which we now turn. II–V–I Progressions

We can refer to this sequence as II–V–I for the sake of ease; however, when we do Roman numeral analysis of jazz and pop music, we will always specify the quality of each chord exactly as is specified in our contemporary chord symbols. Thus a Cmaj7 chord in the key of C will be analyzed as Imaj7. Example 6.6 illustrates a notated II–V–I sequence, which utilizes the “keyboard style” format we use in this book. Notice two versions, where the first involves each right-hand voicing configured in a 1,3,5,7 structure, resulting in correct notes but awkward and choppy movement between chords. It is acceptable to use this pattern at first as you get the chords under your fingers and their sounds in your ears. But the second voicing pattern is much more desirable, and you are encouraged to use this version as soon as you can—perhaps you might challenge yourself to use it from the outset. Smooth voice leading, where we retain the common tone (shared notes between two adjacent chords) when possible, and moving the other tones to the closest note, is a high priority in both our keyboard realization and our writing.


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Keyboard Application This keyboard project will entail realizing IImin7–V7–Imaj7 chords in all keys. Movement from one key to another will occur using the pattern shown in Example 6.7, where sequences move down by a whole step (e.g. II–V–I in C, then Bb, then Ab, etc.). Each I chord is followed by a minor seventh chord on the same root, and this minor seventh becomes the II of the next sequence; this serves as a handy reference point in case you get lost, and it also promotes smooth movement between the sequences. When you proceed this way, you will eventually arrive at the original key (e.g. the pattern begins in the key of C and proceeds to Bb, Ab, Gb or F#, to E, to D, and back to C). At this point you start the sequence again in a key either one half-step higher or lower than the one that initiated the prior sequence (thus C# or B), thereby enabling you to cover all 12 keys. Before realizing these chords at the keyboard, let us re-emphasize the importance of playing with steady rhythm. This will engage you more deeply in the music and cultivate the sense of flow that is conducive to maximum mastery. While this is possible when playing the chords in the rhythms notated in Example 6.7, it will likely be more interesting, as well as productive, to play them with more lively rhythmic patterns. Several possibilities are presented below.


Rhythm in Keyboard Realization

Example 6.8 illustrates a set of rhythmic patterns you can use when playing chord progressions at the keyboard. It begins with the most basic pattern consisting of simply whole notes to be played in both right hand and left hand simultaneously. While pattern A is perfectly acceptable, you are encouraged to use pattern B or those that follow not only for the sake of interest but because they will likely enhance your growth. They pose minimal additional challenges in terms of piano technique. When you realize patterns in 12 keys by yourself or accompany (“comp” for) an improvising partner, playing with steady “time” is of the utmost priority. (Here it may be noted that in ensemble formats with full rhythm sections, the nature of comping changes; the bassist will play bass lines that are much more involved than the left-hand patterns provided here, and keyboardists in those situations will not double the bass lines but play two-hand chord voicings from the middle of the keyboard


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on up using rhythmic patterns closer to the right-hand patterns shown here.) Many other variations of these patterns are possible, including the use of walking bass lines for swing feels (see Chapter 9 for a sample walking bass line), and more authentic Latin jazz patterns for even-eighth note feels.


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Seminal Keyboard Project 2 (6a) Realize II–V7–I in all keys, according to the above harmonic pattern (sequences moving down by whole steps shown in Example 6.7) and one of the rhythmic patterns identified in Example 6.8. Vocalize as you play the chords at the keyboard, singing improvised melodic lines in the rhythm of the progression. An important complement to realizing harmonic patterns in all keys at the keyboard, which is an excellent way to train the ears and fingers, is to be able to realize chords from contemporary chord symbols. Here we are not concerned with transposing a pattern to multiple keys but simply seeing a chord symbol and playing it correctly at the keyboard. This will enable us to accompany (or “comp”) each other for improvisation practice. It is important to emphasize that in this as well as in all our keyboard realization practice we do not write out the notes of the chords but rather learn to directly translate chord symbol into correct chord sound. (6b) Play at the keyboard the following progression from the given chord symbols.




Dmin7  G7  Cmaj7  Cmaj7  Fmin7  B 7  E maj7  E maj7  Emin7  A7  Dmaj7  Dmaj7  Gmin7  C7  Fmaj7  Fmaj7 





B min7  E 7  A maj7  A maj7  Amin7  D7  Gmaj7  Gmaj7 



Cmin7  F7  B maj7  B maj7  Bmin7  E7  Amaj7  Amaj7 

Exercises 6a and 6b

Improvising on the II–V–I Progression The Jazz Etudes in Appendix 4 provide both ample opportunities to improvise on the II–V–I sequence as well as examples of melodies that strongly outline this sequence. You are encouraged to use the melodies as launching pads for your improvising, perhaps beginning your solos with these lines or embellishments of them before spinning off entirely new melodies. Listen to the recorded examples of the Jazz Etudes and begin to practice with the Jazz Etudes play-along tracks on the accompanying CD.

First II–V–I improvisation: soloist and comping, partner exercise Player A plays the keyboard and selects a IImin7–V7–Imaj7 progression he or she is comfortable with; it is essential that the progression be played in steady time. Player B improvises atop the progression, using the notes of the key and letting the ear guide the decision-making process. (We will consider further strategies whereby specific modes are correlated with specific scales below). Shift roles.



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IImin7  V7  Imaj7  Imaj7 : • Variation: If A feels capable of playing a second II–V–I pattern in time, then a progression may be created that shifts back and forth between the two keys. For instance: Gmin7  C7  Fmajor7 (F major):

IImin7  V7  I maj7  Imaj7 :



Fmin7  B 7  E maj7


(E major): IImin7  V7  I maj7  Imaj7 : The II–V–I sequence is embedded in another common chord progression: Imaj7  VImin7  IImin7  V7  I maj7 :

Exercise 6c

The following exercise has you realize the I–VI–II–V–I sequence in all keys, moving around the cycle of fifths/fourths with a device that is used frequently to move from one key area to another. This entails interpolating a dominant seventh chord that is V7 of the new key area. As the sequence below indicates, the movement from the original key, whose tonic chord is Imaj7, to the next key in the cycle, which is IV (down a fifth, up a fourth) of the original key, occurs through the use of a V7 of IV chord. In other words, if we want to modulate to the key of IV we can interject a V7 of that key. Upon closer inspection, we realize that V7 of IV (V7/IV) is derived simply by lowering the seventh of the Imaj7; in essence, after the Imaj7 a I dominant seventh chord sounds and propels us to the new key. When the progression moves to the IV chord, this becomes the new I and the same sequence then occurs on that new pitch level. In this way the progression proceeds through all keys via the cycle of fifths. The V7/IV chord is an example of a secondary dominant or applied dominant chord, which we will take up in greater detail in Chapter 10. Imaj7  VImin7  IImin7  V7  Imaj7  V7/IV  IVmaj7 (which becomes new I chord) Cmaj7 Amin7  Dmin7 G7  Cmaj7 C7  Fmaj7  Dmin7  etc. I–VI–II–V7 Realize the Imaj7–VImin7–IImin7–V7-I–V7/IV progression in several keys at the keyboard according to the above framework.

Exercise 6d

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Integrating Diverse Forms of Musical Knowledge Having played II–V–I progressions in all keys at the keyboard, and having improvised and composed on these progressions, you have begun to lay aural, physical, and theoretical groundwork for further mastery of chords. In other words, you have begun to experience— by sound, touch, feeling, and perhaps to a lesser degree by analytical understanding—these chords and how they move. As you practiced your II–V–I progressions at the keyboard, you may have felt that once your fingers and ears became accustomed to the pattern, you were able to play the sequence correctly but did not always have full awareness of precisely what chords you were playing. While naturally an important goal is to develop this kind of integrated understanding—so that we are aware of what we are playing when we play it— the fact that the experience of a harmonic structure sometimes precedes intellectual or analytical awareness of it should not be a cause for alarm. Actually, this is an ideal progression of events in the learning process because now an aural and tactile foundation is in place for optimal analytical fluency. Important to gaining this fluency will be the combination of realization of chords from Roman numeral functions as well as chord symbols, in addition to the many other forms of engagement in this book—improvisation, composition, aural training, writing, and analysis. Now that we have played II–V7–I progressions at the keyboard, let us begin to improvise over these progressions. Here a useful analytical tool helps us determine what scales or modes we can improvise with in relation to each chord or group of chords.

Chord-scale Analysis Chord-scale theory has evolved as a useful tool in improvising and composing in contemporary tonal (and modal) formats. The basic principle is that each chord implies one or more closely related scales or modes, and that these can guide our improvising and composing. As we go into this concept, it is important to emphasize that this approach, as with much music theory, is an analytical representation of what many master artists did intuitively. While many great contemporary jazz musicians use some version of chord-scale analysis, many of their forebears did not. As always, theory is at best a kind of guide, a means for approximating a certain kind of result. But ultimately the ear must be the final authority, as it has been through the ages of musical practice. There are two levels to chord-scale analysis, both of which are applicable depending on the situation. One is the individual chord-scale approach, where we correlate a different scale with each chord. A second is the “parent”-scale approach, in which we identify an overarching scale that we can improvise with relative to a group of chords that are diatonic to a given key area. There is a place for both approaches, and in certain instances they will overlap, while in others one or the other will be more applicable. For instance, when we encounter a II–V–I sequence, we can improvise over these chords by relating a particular scale or mode with each chord (individual chord-scale approach), or we can improvise with the notes of the major scale of the I chord (parent-scale approach) since all the chords are diatonic to that key. In this instance, the second is more efficient and more in line with the


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approach of most master improvisers. We will therefore recommend using the parent-scale approach as much as possible; the scale brings us into the general arena when it comes to what notes will sound good over a given chord sequence and our ears can take over from there. However, inasmuch as most progressions involve chords that are non-diatonic to that key—e.g. chords that use accidentals and derive from other keys—the parent chord-scale approach will only go so far. The individual chord-scale approach becomes necessary in these instances. The basic principle underlying individual chord-scale relationships is that a chord will take the scale or mode corresponding to that chord’s function. If a chord functions as II, then it takes Dorian because Dorian is the mode built on the second degree of the major scale or key of the piece or passage. If a chord functions as VI, it takes Aeolian for the corresponding reason (Aeolian is the mode built on VI of major); V takes Mixolydian, IV takes Lydian, etc. Later we will consider some slight variations of these principles to provide more options, but this simple format will go a long way. The following chart shows the chord-scale relationships for the Fmaj7  Dmin7  Gmin7  C7  progression.






Roman numeral:


VI min7



G Dorian

C Mixolydian

Chord scale (parent): Individual chord scales:

F Ionian F Ionian

D Aeolian

It cannot be emphasized strongly enough that chord scales are a general guide to a set of notes that resonate while a given chord sounds. They are not exhaustive of the possibilities open to the creative improviser. Nor are they intended to suggest that we must begin our melodies on the tonic notes of the scales and improvise scalar passages either up or down from that note. Chord scales may be thought of as horizontal representations (chords are vertical representations) of a given pitch region at a given point in time; one can enter the pitch region from any note. This will become clearer when we begin to work with chord extensions in Chapters 12 and 13; there we will see that extended chords include almost all scale tones and thus may be conceived as scales configured vertically. Scales, therefore, may be conceived of as chords placed “on their side.” Analysis Provide key, Roman numeral analysis and identify individual chord scales as well as the overarching parent scales for improvising purposes on these progressions. Then learn the changes at the keyboard (each sequence in one key). Optional: if you feel secure, comp for a partner to improvise on the progression. Then switch roles.

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Dmin7  G7  Cmaj7  Cmaj7 : Dmin7  G7  Cmaj7  Amin7 : Cmaj7  Cmaj7  Fmaj7  Fmaj7  Emin7  Amin7  Dmin7  G7 :



Fmaj7  Fmaj7  Dmin7  Dmin7  B maj7  B maj7  Gmin7  C7 :

Exercise 6e

You may recall encountering in Chapter 2 the scale pattern drill that corresponds to the last of the above chord progressions (Example 6.9). Example 6.10 shows an arpeggio pattern that also works for the same progression.



II–V–I in Minor The II–V–I progression is also common in minor keys, but involves different kinds of chord structures due to the different diatonic triads and seventh chords generated by the minor scale. Examples 6.11 and 6.12 illustrate, respectively, the diatonic triads and seventh chords


Harmonic Functions




that occur on the natural minor scale, which is generally the version of the minor scale that prevails in tonal music. However, a very important exception to this is found in the use of the raised leading tone—scale degree 7—in chords built on V and VII. This is shown in Example 6.13 where, by raising the C to C#, what would have been a Vmin7 chord assumes the properties of the dominant seventh that propel movement toward the tonic. The V7 chord in minor is thus precisely the same structure as is found in major. The VII chord, which in major we encountered as a half-diminished seventh structure, in minor becomes the even more powerful VII07 (fully-diminished) chord. Whereas the half-diminished seventh chord’s movement toward I was driven by its tritone, the fully diminished seventh chord contains two tritones, rendering it all the more unstable and wanting to resolve to I. The raised leading tone mentioned above—which is the third of the V7 chord—is seen in Example 6.13. In the above illustration, the V7 resolves to the I minor triad, allowing the leading tone to clearly follow its inherent trajectory and land on the tonic note. In the following minor

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II–V–I examples (Example 6.14), the V7 resolves to a I minor seventh chord, in which case this leading tone-to-tonic melodic resolution is replaced by a common alternative in jazz— which is virtually never found in European classical music—where the leading tone moves down a half-step to the minor seventh of the I chord (C# to C). The V-to-I movement in the bass upholds the sense of finality nonetheless. Two voicings for the same progression are provided; notice the difference in effect when the leading tone-to-b7 resolution (C# to C), as shown in the second version, occurs in the middle of the voicing as opposed to the top voice. Now the denial of this anticipated melodic movement is somewhat neutralized. In the Example 6.15, a slight change in the structure of the V7 chord produces a richer sonority, one that is commonly used in jazz. This involves the use of the b9 extension instead of the root in the treble clef/right-hand voicing for the V7. Notice that the b9—which is Bb on an A7 chord—is the same note as the b5 of the IImin7(b5) chord. Because of this shared tone, the IImin7(b5) is almost always followed by V7(b9) when occurring in a II–V relationship. You might also observe a useful principle for deriving V7(b9) voicings: build a diminished structure on the third of the chord. For instance, as shown below, the voicing for the A7(b) chord is a C#07 structure, used here in two different inversions in order to follow smoothly from the preceding IImin7(b5) chord. We will take up chord extensions extensively in Chapters 13 and 14. In the next keyboard exercise, where you realize the minor II–V–I sequence in multiple keys, you may choose to use either the V7 with or without the b9.



Harmonic Functions

Keyboard exercise




Play IImin7( 5)-V7-Imin7 or IImin7( 5)-V7( 9)-Imin7 in these keys: C, F, G, A, D, E. Play the roots first, and then work out the chords.

Exercise 6f Improvising on II–V–I in Minor

Recall that in improvising on chord sequences, we identify parent scales and individual chord scales. This becomes rather more complicated in minor since we are raising the leading tone on the V chord, but then on the I chord we are playing natural seventh. So it doesn’t appear that we can identify a single parent scale as we could with II–V–I in major. In fact, we can use a modified parent-scale approach where we still use the natural minor scale as the overarching scale, but we raise the leading tone when we get to the V chord. If this seems unwieldy and too much to keep track of, it is actually possible to simply improvise with the natural minor scale atop the entire II–V–I. Would this note create a clash on the V chord if the improviser plays a natural seventh and a raised seventh is played by the comping instrument(s)? In fact, the flat seventh will sound fine even with the raised seventh because it is a #9, which we will later see is one of the available tensions for use on a dominant seventh chord. Minor II–V7 improvising TRACK 13

Improvise with a partner and also with the accompanying CD on the II–V–I progression in these minor keys: A minor, C minor, D minor, E minor. The CD repeats each sequence twice. Then examine and listen to Jazz Etude #15, which provides an example of the IImin7( 5)–V7( 9)–Imin7 progression, and play along with that track on the CD.



Exercise 6g

Writing and Analysis Exercises Written exercises complement the creative and analytical aspects of our development. In this course, written work follows keyboard work so that whatever we write has a direct aural, tactile, and intellectual foundation. We call this “keyboard style” realization, where a threeor four-note chord is written in the treble clef, and a single note—for present purposes, the root of the chord—is written in the bass clef. Since the act of writing, unlike our keyboard and improvisation work, does not take place in real musical time—but rather gives us provision to pause, ponder, and edit our choices— it allows us to attend to details in a way that would not be possible in performance. Voice leading, which pertains to how individual voices move within a harmonic texture, is one aspect. As discussed in our first keyboard projects, smooth voice leading is a priority when

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we play, which is easily attained by simply moving to the closest voicing configuration rather than allowing our right hand to jump around excessively. In our written work, smooth voice leading is readily achieved by retaining the common tone between any two successive chords and then moving the remaining notes to the next closest notes. Let us introduce additional principles that will allow us to achieve an even richer voice-leading texture in our written work.

Voice Leading In traditional four-part chorale-style writing, where triads are prominent (one voice is doubled to make four parts) with some seventh chord use, voice-leading considerations pertain to all four voices. In other words, the way each voice moves in relationship to each other voice is essential to the harmonic texture and flow. Therefore, to provide one example, parallel perfect intervals are to be avoided between any two voices because they obscure the independence of the parts within the relatively thin triadic texture of that particular style. The much denser harmonic textures of contemporary tonal and modal music, in which triads are rare and the seventh chord is the basic harmonic unit atop which extensions are commonly added, bring into play new strategies. Now our voice-leading concerns are directed more toward the outer voices—the melody (highest note in the treble clef ) and bass (lowest note in the bass clef ) notes. There are four types of voice-leading motion that are possible between any two voices, as illustrated in Example 6.16. Interval sizes are listed above each set of notes to show the different kinds of movement. Contrary motion is when each voice moves in opposite directions (e.g. one voice moves up and the other down). Here independence between voices is optimal, as the ear perceives two very distinct kinds of melodic movement. Oblique



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motion is when one voice does not move and the other does. A sense of independence between voices is moderate. Similar motion, when both voices move in the same direction, produces a weaker sense of independence as the ear has more difficulty distinguishing between the voices. Within the category of similar motion is parallel motion, where voices not only move in the same direction, but they move by precisely the same interval (e.g. both voices move down a third, or fourth, or fifth, etc.). Here the sense of independence is weakest, as the ear has difficulty in perceiving separate voices and instead perceives an overall texture but not the particular voices that make up this texture. Among the various kinds of parallel movement, parallel perfect intervals—unisons, fourths, fifths, and octaves—most prominently obscure the sense of independence between voices. Accordingly, while the other kinds of parallel motion are acceptable, as well as the other kinds of voice-leading movement (e.g. contrary, oblique, similar), parallel perfect intervals are to be avoided between the outer voices in our contemporary, five-part written work. The examples and exercises below will illustrate these principles and allow you to use them in your own writing. A notated harmonic sequence will be provided, as shown in Example 6.17, and you will be asked to provide contemporary chord symbols, key, Roman numeral analysis, as well as two kinds of chord scale analysis—individual chord scale and parent scale—as shown in Example 6.18. The contemporary chord symbols are listed above the notated passage. This is standard procedure in jazz and popular music. Roman numerals are listed below the staves. To reiterate the protocol introduced in the previous chapter, when applying Roman numerals to contemporary chord symbols, we include the chord quality following the Roman numeral. We will use a modified approach when we analyze selections from European


EXAMPLE 6.18 The same progression with the completed analytical information

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classical music. Notice the bracket underneath the II–V sequence, and the arrow indicating its resolution to I. This is a useful practice in harmonic analysis as it helps us establish the habit of identifying cadential, key-defining movement and seeing chords in relationship as opposed to isolated entities. This will be particularly helpful when we later look at progressions that move considerably between different tonal centers. The abbreviated names of the chord scales are listed in between the staves. Because all the chords in this passage are diatonic to the key of F major, and thus it is possible to improvise on the whole passage just using the parent scale of F Ionian (or F major), identification of individual chord scales may seem unnecessary. However, not only can the individual chord scales be of use in helping us hone our note choices, they will be essential when it comes to progressions—which is the vast majority of harmonic progressions—in which not all chords are diatonic to the primary key. It should also be emphasized that the progressions used for analysis in this chapter are to be analyzed in a single key. In other words, even if momentary cadential activity may briefly suggest some shift in key—which in this chapter, since all chords are diatonic, would only involve a shift from major to relative minor or vice versa—the chord movement in these drills is more appropriately analyzed within a single key. In instances where that determination nonetheless seems to be elusive, a general strategy that will be of use in both of these preliminary exercises, as well as the more complex ones to follow, is to simply take an inventory of the cadential movement in the passage and determine which of the potential key centers is targeted by that activity. In other words, the ear will tend to hear as the tonic key that which is most frequently suggested through cadential activity in that key. In this regard, take care not to be deceived by occasional passages in which a chord that is leading to a target is mistaken as a target chord and thus erroneously as the I chord. A case in point is found in the V7 to Imaj7 to IV sequence, where the I chord is sometimes mistaken as the dominant of IV since its (the I chord’s) root is a fourth below or fifth above the IV. Here chord quality is the telltale sign; the Imaj7 cannot be V7 since it is not a dominant structure chord. Now use the above procedure with Exercises 6h–6k. Using the above model, provide contemporary chord symbols, key, Roman numerals, and chord scales for these progressions.

Analysis (6h)


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Exercises 6h–6k and Examples 6.19–6.22 Written exercise Two sets of chord symbols are given, and you are asked to do a written realization in keyboard style and then provide the key, Roman numerals, and chord scales. When two chords are listed per measure, realize the chords in half-notes; when only one chord is listed, use whole notes. Be sure to bracket all II–V sequences and indicate resolution to I with an arrow.

Harmonic Functions




Fmaj7 Dmin7  B maj7 Gmin7  Emin7( 5) Amin7  Gmin7 C7  Fmaj7  G#min7( 5) C#min7  Bmin7 E7  F#min7 Bmin  C#min7 F#min7  Bmin7 E7  Amaj7 


Dmaj7 

Exercise 6l Written exercise Do a written realization of these progressions that are indicated by Roman numerals. Although not specified by the Roman numerals, realize all chords as seventh chords— using the sevenths that are diatonic to the key. Provide chord symbols.


A : I IV III VI II V I  B: I VII VI III II V I  Bmin: I  IV  II V  I  VI  IV  II V  I 

Exercise 6m

Idiomatic Progressions The Roman numeral sequences presented below delineate basic diatonic chord patterns commonly encountered in contemporary tonal music (jazz/pop). Realizing them in multiple keys at the keyboard will help further internalize the concept of chord function, which— like all theoretical concepts—attempts to describe how structures are actually heard. Inasmuch as realizing all the sequences in all keys will take some time, this project should be approached in small bits, where you allot some time on a regular basis to working them out in just a few keys. Fluency with these basic patterns will provide invaluable foundation for further harmonic skills. a. IImin7 b. IImin7 c. Imaj7 d. Imaj7 e. Imaj7 f. Imaj7 g. Imaj7 h. Imaj7

V7 Imaj7 V7 Imaj7 VImin7 IImin7 V7 Imaj7 VImin7 IImin7 V7 IIImin7 VImin7 IImin7 V7 Imaj7 IVmaj7 IIImin7 VImin7 IImin7 V7 Imaj7 VImin7 VIImin7(b5) IIImin7 IVmaj7 IImin7 V7 Imaj7 IIImin7 IVmaj7 IImin7 VIImin7(b5) Imaj7 VIImin7(b5) IIImin7 VImin7 IImin7 V7 Imaj7 VImin7 IVmaj7 IImin7 IIImin7 VImin7 IImin7 V7 Imaj7


Harmonic Functions

Keyboard exercise An excellent way to begin getting these diatonic harmonic sequences—which we will later extend to include non-diatonic chords—under your fingers is to take each pattern and select a key, preferably other than C, and realize the progression in that key. You might begin by just playing the roots, and then add the chords once you are comfortable playing the roots.

Exercise 6n Written exercise Select one of the Roman numeral sequences from above, choose a key, and do a keyboard-style written realization of it. Strive for smooth voice leading between chords as well as, when possible, contrary motion between outer voices.

Exercise 6o Dictation exercise To be done with a partner. Create patterns based in whole or in part on the above Roman numeral sequences, play them at the keyboard, and have your partner identify the patterns by ear. Ideally, do not give your partner any information and have him or her provide the Roman numeral functions of the progressions you play. One variation is to tell your partner the key in which you are playing and have him or her name the contemporary chord symbols you are playing.

Exercise 6p Jazz Etude exercise Select a Jazz Etude in Appendix 4. Comp the chord changes at the keyboard and sing the melody.

Exercise 6q Jazz Etude exercise Select a Jazz Etude in Appendix 4. Comp changes for partner who will improvise on principal instrument or voice. Switch roles.

Exercise 6r

Harmonic Functions


Written exercise Write out notes of the chords in Jazz Etudes 1 through 5, identify key, do Roman numeral analysis.

Exercise 6s Keyboard exercise Realize this progression in all keys at the keyboard, using the standard format we have been using (four-note chord in right hand, bass note in left). Imaj7  IVmaj7  IIImin7  VImin7  IImin7  V7  Imaj7  Imaj7 

Exercise 6t Random II–V–I progressions: ear training, partner exercise Player A moves freely from one II–V–I pattern to another but does not indicate to Player B, who is to improvise atop each pattern, the key in which the pattern is played. Hence Player B must proceed entirely by ear. It is important that Player A stays on one pattern— repeating it as long as necessary—until Player B “finds” (e.g. begins to play notes that match) the key area. Player A may want to select a few keys in advance. Switch roles. This is great practice for both keyboardist and solo improviser.

Exercise 6u

Turnarounds Because jazz chord progressions serve as cyclic backdrops for improvisation, they will often employ a chord sequence at the end of the form that leads back to the top of the form. This is called a “turnaround.” Often the turnaround involves a faster harmonic rhythm and cycle of fifths movement, as seen in the last two bars of the following progression. Fmaj7  Bbmaj7  Amin7  Dmin7  Gmin7  C7  Amin7 Dmin7  Gmin7 C7 : Imaj7  IVmaj7 IIImin7 VImin7 IImin7  V7  IIImin7 VI min7 IImin7 V7 : Here is another turnaround at the end of the same opening chord sequence, which you can listen to and play along with on the accompanying CD. This one makes use of non-diatonic chords, which we will take up later. Nonetheless, the effect of propelling the harmonic movement back to the top of the form via faster harmonic rhythm and cycle of fifths movement (Eb-Ab-Db) should be quite clear.



Harmonic Functions

Fmaj7  Bbmaj7  Amin7  Dmin7  Gmin7  C7  Fmaj7 Abmaj7  Dbmaj7 Gbmaj7 : Imaj7 bIIImaj7  bVImaj7 bIImaj7 :

Free-tonicization Strategies Level I We close this chapter with further strategies for developing harmonic fluency. These are called free-tonicization strategies in that they move freely from one key area to another through the use of II–V, II–V–I, and other chords we have encountered so far. However, unlike the above notated harmonic passages as well as the series of Roman numeral sequences provided—all of which include chords that are diatonic to a single key—the following strategies will take us to wide-ranging key areas. While this movement might at first glance seem to be a form of modulation, we will use the term tonicization owing to the temporary nature of this movement in any given key. Modulation presumes a new key area is established sufficiently to replace that which had been heard as the previous I chord with a new I chord. Tonicization involves a more fleeting kind of movement to a new key area, which is more characteristic of the strategies discussed below. Here it should be emphasized, therefore, that while Roman numerals will be used to refer to localized relationships between chords—e.g. IImin7–V7—they do not presume an overarching I chord to which these and the other Roman numerals would all relate, but rather the relationship of these chords to the key area which is implied by that particular moment in time. Generally, only two or three chords from any given key area—four maximum—will sound in succession; Roman numerals from any of these brief key-defining moments apply only to that temporary key area. The V7 in one bar will be different from the V7 in the next. In this first set of free-tonicization strategies, these principles serve as a guide for the construction of chord progressions. 1 Any major seventh chord may be treated as a temporary I or IV chord, and thus be followed by any of the other diatonic chords in that particular key:











Imaj7-VIImin7( 5)

IVmaj7-VIImin7( 5)







Harmonic Functions


2 Any minor seventh chord may be followed by its related V7 to form a IImin7–V7 link: Cmaj7 Fmaj7 Fmin7 Bb7 3 Any II–V may be followed by its I, or any other II–V, or II–V–I sequence (see insert): Cmaj7 Fmaj7 Fmin7 Bb7 Bbmin7 Eb7  Abmaj7  4 Any min7(b5) chord can be followed by a minor seventh chord up a fourth to form a VIImin7(b5)–IIImin7 sequence, or a dominant seventh chord up a fourth to form a IImin7(b5)-V7 sequence: Cmaj7 Fmaj7 Fmin7 Bb7 Bbmin7 Eb7  Abmaj7  Gmin7(b5) Cmin7  While strategy 3 allows us to create a chain of II–V or II–V–I sequences that move randomly from one key area to another, a number of systematic approaches are also possible. For example, if you follow the tonic chord of a II–V–I by a minor chord on the same root— which is precisely the pattern we saw in an earlier keyboard exercise (6a) and will use frequently—you end up with tonal centers moving down by whole step (e.g. Dmin7 G7  Cmaj7  Cmin7 F7  Bbmaj7  etc.). If you use the same approach to II–V sequences that do not resolve to their implied tonic chords—thus each V chord is followed not by I but by a minor seventh chord built on the same root as the V—you end up with tonal centers moving by fourths (e.g. Dmin7 G7  Gmin7 C7  Cmin7 F7  etc.). If you follow each V7 with a minor seventh chord down a whole step, the result is tonal centers that move in minor thirds (e.g. Dmin7 G7  Fmin7 Bb7  Abmin7 Db7  etc.). The same result is achieved when you follow each I chord by a minor seventh chord up a fourth (e.g. Dmin7 G7 Cmaj7  Fmin7 Bb7  Ebmaj7). These are just a few of the many ways of systematically linking II–V and II–V–I sequences together. The following is a progression that makes use of the above principles and moves through 12 key areas, establishing each key area with at least two chords diatonic to it. Notice the occasional break from the two-chords-per-bar movement—this is called the harmonic rhythm, the frequency with which chords change—in order to provide moments of repose.




Fmin7 B 7  Amin7 D7  Gmin7 C7  Fmaj7  E min7 A 7  F#min7 B7  Emin A7


b b b b Bmin7 E7  Amaj7  Cmin7 F7  Ebmin7 Ab7  Fmin7 Bb7  Ebmaj7 



Dmaj7  Dmin7 G7  Emin7 A7  B min7 E 7  A maj7  A min7 D 7  G maj7 E min7 

C#min7 F#7  B maj7 Emaj7  G#min7 C#7  F#maj7 

Using the above principles, we can easily create progressions that move freely through a number of key areas. Here is a continuation of the progression begun above that moves through 12 key areas and uses each strategy at least once. The following exercise has you create your own progression following this approach.


Harmonic Functions

Free tonicization Create a free-tonicization sequence utilizing the above strategies. Delineate the sequence using contemporary chord symbols; do not write out the notes, as you will realize the progression at the keyboard without the aid of notation. The resultant progression should utilize each of the five strategies listed (it is not necessary to use all of the variations of all strategies) at least once and cover all 12 key areas at least once. At least two chords are needed for a key area to be considered covered; avoid using more than four chords from any given area in succession. Be able to play at the keyboard the progression you create.

Exercise 6v

Create additional sequences through the above method and utilize them for practice in sight-reading chord progressions at the keyboard. Exchange sequences with your friends for additional sight-reading practice. Additional free-tonicization exercises will be presented in later chapters. Seminal Keyboard Project 3 SEMINAL KEYBOARD PROJECT 3

(a) Play the chord symbol sequence you created for Exercise 6v. (b) Play Imaj7 VImin7  IImin7 V7  Imaj7  V7\IV  IV sequence in all keys through the cycle (review Exercise 6d; each IV chord becomes the new I).

Exercise 6w

SUMMARY QUESTIONS 1 Name the three basic categories of chord functions (contained within the seven functions based on each scale degree) and list the Roman numerals that correspond to each category. 2 These three categories of tonal harmonic functions (from above in question 1) are found in both European classical and jazz/pop music. True or false? 3 Identify a prominent difference between European classical and jazz/pop practice involving the resolution of the leading tone in V to I cadences. 4 What are the two facets of the structure of the V7 chord that propel it toward I? 5 Name the three-chord sequence that is prominent in much jazz and popular music. 6 What is the purpose of chord-scale analysis and what are the two kinds of chordscale analysis presented in this chapter?

Harmonic Functions

7 It is best when improvising to always begin on the tonic note of the mode/scale corresponding to the chord sounding at the time. True or false? 8 Identify the chord scales for each of the three chords of the sequence identified in Question 5. 9 How does the II–V7–I progression in minor keys both resemble and differ from the II–V7–I progression in major keys (what chord is the same)? 10 What are common tones? 11 Smooth voice leading is not possible between chords from distantly related key areas. True or false?


chapter 7

Swing: Global Rhythmic Gateway

In this chapter, we: • Explore the swing conception that has been central to jazz. • Emphasize the need for aural immersion in order to become fluent in this musical language. • Work with practical exercises to develop swing articulation. • Explore the blues form. • Begin transcription work.

As mentioned in Chapter 3, among the most predominant aspects in today’s musical world are the rhythmic time feels whose origins can be traced primarily to African music and whose evolution has been informed by a wide range of global influences. Musicians commonly identify two major types of time feels—even-eighth note and swing—with an infinite variety of subsets and hybrids that may fall within or traverse these categories. Eveneighth feels are characteristic of much popular, rock, funk, folk, hip-hop, and globally influenced amalgams and have also become prominent in jazz over the past several decades. Indeed, the label “even-eighth” evolved in order to distinguish this time feel from swing, historically the rhythmic core of jazz, in which eighth notes are played with a more lilting approach. However, as we will discuss in this chapter, this lilting quality derives more from the inflections, accents, and phrasing that define swing than any disparity in note lengths. While even-eighth note-time feels have arguably become as prominent as swing in today’s jazz world, a strong case may also be made that jazz’s swing foundation served as a basis for the evolution of some of the most interesting and sophisticated even-eighth notetime feels to be found, as well as swing/even-eighth hybrids. An argument may also be made that mastery of the swing time feel may greatly enhance your ability to interact with musicians from other cultures and to infuse their rhythmic features. This chapter takes a brief look at the origins of swing, identifies its key features, and presents exercises as practical vehicles to help you become fluent with this important musical language. This will serve as a preparation for work with the Jazz Etudes in Appendix 4. As has been

Swing: Global Rhythmic Gateway


emphasized at length in earlier chapters, theoretical and technical study will be meaningless if not rooted in extensive aural immersion. You are thus encouraged to continue investing time with the listening resource list provided at the end of Chapter 3 as well as building your own library of recordings.

Elements of Swing Let us begin with a look at the inner workings of swing and its possible origins. While there is little disagreement about swing’s African roots, there is also very little in the way of theoretical models that point to the particular African practices from which this contemporary time feel may have evolved. The following analysis ventures briefly into this emergent and elusive area. Example 7.1 shows three important rhythmic layers of the swing time feel. Three rhythmic features are significant in the example. One is the 2:1 ratio between the melodic line, which consists primarily of eighth notes, and the quarter notes that are characteristic of the walking bass line. Listen to the Jazz Etudes in Appendix 4, most of which involve walking bass lines. Which of the Etudes do not? Second is the prominence of triplets (quarter and eighth-note groupings, as seen on beats two and four in 7.1) in the ride cymbal. The coexistence of triplet and eighth-note figures forms a 3:2 relationship that is prevalent in much of African music and is key to the swing feel. While swing eighth notes in melodic contexts are sometimes explained as triplets, thus perhaps suggesting that any 3:2 ratio exists only in notation but not in sound, this understanding of swing eighths is erroneous. As will be explained below, only in a very small part of the swing spectrum are eighth notes actually articulated as triplets. A third feature, the walking bass line, may appear to be the least significant in comprising a constant stream of quarter notes. However, very different from the effect of a sequence of quarter notes in even-eighth note-time feels, swing quarter notes serve as a kind of portal into the swing universe by containing both the triplet and eighth-note rhythmic impulses— thus the 3:2 polyrhythmic ratio characteristic of African music—even if these note values




Swing: Global Rhythmic Gateway

generally do not manifest in the bass line. That they are felt in the swing quarter notes is where the walking bass line derives its power. Let us explore this further by looking at a polyrhythmic practice that is prominent in traditional West African music. Example 7.2 shows two rhythmic patterns, one that tends to be felt as a three-beat phrase, the other as a four-beat phrase. The co-existence of the two phrases creates an exciting polyrhythmic texture, which you can hear on the website. Sing each part separately in order to get the sense of their respective implied phrasing. Then try to sing the top line and tap the bottom. Ideally, stand up and establish the bottom line by walking and sing the top line. It may take a while to be able to do this, but once you get it you will likely feel yourself locking into a compelling three against four groove, of which the 3:2 polyrhythm discussed above is a subdivision. EXAMPLE 7.2

Now alternate between playing the bottom line alone and then adding the top line to it, so that when the bottom line sounds by itself, you still feel the top line in relationship with it. There has been speculation that the walking bass line originates in this polyrhythmic relationship, and thus in essence contains both triple and duple rhythmic layers, which is what gives the line the buoyancy and drive that make it swing. While walking bass lines are, out of convenience, notated as quarter notes in 4/4 meter, whose predominance likely resulted because swung melodic eighth notes are more readily notated in duple than in triple meters, the fact that we can also hear implicit triplet patterns in these lines—even when we hear them in isolation—differentiates them fundamentally from sequences of quarter notes outside of swing contexts. Whether or not this line of analysis proves to be valid over time remains to be seen. If nothing else, it helps underscore the importance of mastering swing primarily through aural immersion.

Swing Articulation In terms of the application of swing articulation to melodic lines, we can make some generalizations that may be helpful when accompanied by aural grounding in this musical conception. Most prominent is a kind of lilting articulation of eighth notes and frequent— though not constant—emphasis on weak parts of beats (e.g. off-beats) and weak beats within a measure (e.g. beats 2 and 4 in 4/4). Therefore, in a sequence of eighth-note lines,

Swing: Global Rhythmic Gateway


the second of each two eighth notes will tend to receive more accentuation than the first. Examples 7.3 and 7.4 illustrate two ways of achieving this effect. Here, however, it cannot be emphasized strongly enough that these or any theoretical descriptions about swing articulation can serve as but the most general of guidelines in conveying the features of this rhythmic language and how to authentically “speak” it. Passages in which all eighth notes on off-beats are accentuated, as suggested in the above examples, would sound rigid. As always, aural immersion, the ultimate pedagogical tool, is therefore essential. Attempts to depict swing eighth notes as triplets, often used to help classical musicians articulate swing passages (as shown in Example 7.5), may be even more limiting. For one thing, this rendering of swing eighths in a melodic context as triplets is incorrect from a mathematical standpoint—swing eighths tend to be closer to even-eighths in terms of duration than to the proportion indicated, with exceptions found only within a very small range of styles and tempi. For instance, composed medium tempo eighth-note lines played by big band horn sections (trumpets, trombones, or saxophones) may approximate the triplet conception (with the second note being accented). However, improvising soloists in this format will not use this triplet conception when playing eighthnote lines, but rather something involving a less pronounced disparity between first and second eighth notes. Accordingly, the notion of swing eighths as triplets appears to have been promoted not from an improvisatory perspective but from an interpretive performance standpoint. EXAMPLE 7.3



Blues One of the primary forms through which swing evolved is the blues, which has long been the foundational structure in jazz and popular music. Blues heads are excellent vehicles for learning swing articulation and one is provided below for this purpose. While any of the recordings of jazz artists on the listening list (Chapter 3), the Jazz Etudes on the website,


Swing: Global Rhythmic Gateway

or the recommended listening tracks cited throughout the text, will serve as useful aural models (blues and swing feel articulation, generally speaking, are not fundamentally different); two blues compositions by Thelonious Monk, which the following piece is inspired by, are particularly relevant here: “Blue Monk” (Monk’s Blues, Sony 1968); and “Straight No Chaser” (Straight No Chaser, Sony 1979; originally released 1958).

EXAMPLE 7.6 Ed Sarath, “Blues in F”

While our primary purpose is to play the head with an authentic swing feel, a few words about the harmonic structure of the blues are in order. We encountered the blues in minor in Chapter 4, which was based in the standard blues form: I


(or IV)  I  I 

IV  IV  I  I  V

IV  I  I 

Many variations of this basic form have evolved over the years, several of which are found in the above piece and will be taken up in later chapters. First, the piece utilizes altered chords, as found in bars 8 and 10. Second, the last four bars return to I not via V–IV–I (which is found in many rock-and-roll blues forms) but by II–V–I, which is far more common in jazz blues forms. Third, in bars 11–12, we find an example of a turnaround as discussed in the previous chapter. Some thoughts on improvising on blues forms should also be mentioned. Chord-scale analysis reveals elaborate possibilities, with altered chords taking altered scales, and even unaltered chords inviting extensive use of chromaticism. Again, these are issues to be taken up later. A simpler approach may also be noted, which is the use of the “blues scale.” The most basic form of the blues scale may be thought of as a minor pentatonic scale with a lowered fifth degree (Figure 7.7). This scale uniquely conveys the blues feel and can be played on virtually the entire progression in the above blues. At first glance this may seem counter-intuitive, as, for example, the F blues scale contains Ab, and the I chord, F7, of the progression contains A natural. However, the Ab is a vintage “blue note” that is very effective when played against the F7. And while technically the V7/II in bar 8 and the turnaround

Swing: Global Rhythmic Gateway



might suggest other options, even at these points in the form the blues scale will be heard as passing melodic motion and thus be minimally problematic.

Transcription Format A common practice that has been central to the development of many if not most jazz improvisers is transcription. Transcription entails copying the playing of a master improviser from a recording note-for-note, inflection-for-inflection, in order to internalize foundational aspects of the musical language. A counterpart to transcription in jazz is found in the visual arts, where painters through the ages would copy the works of the masters; even today, one will find aspiring artists at art museums sitting with their sketchpads in front of the works of Vermeer, Caravaggio, and Rembrandt. In jazz, since it matters little whether or not one actually writes down the solo being copied—what is most important is that one is able to play (and ideally also sing) the solo and capture all its nuances—the term transcription may be somewhat of a misnomer. It is important to bear in mind the purpose of transcription, which is primarily to assimilate style or language features from master practitioners rather than (as some would have it) to stockpile a collection of idiomatic phrases that one might call upon when improvising. While some aspect of the second might be inherent in the first, it is important to maintain a commitment to the evolution of the personal voice when engaging in these kinds of emulative practices. One way to ensure this is to sustain engagement in the range of trans-stylistic and style-specific practices presented in this book. At first, transcription may seem daunting, and it is wise to begin with solos that are more lyrical and at slower or more medium tempos. It is also important to find solos that you are absolutely captivated by—solos that inspire you to learn what a particular artist is playing and thus put in the hard work that is required of transcription. Oftentimes the bulk of a solo will be quite manageable, with the exception of a few fast flurries; in such cases do not let the difficult passages deter you—give them a shot, and then pass over them to transcribe the rest of the solo. You can then return to the more challenging parts. You will likely notice even during the course of your first transcription project that your ear will become sharper, and that the pace of transcription will increase, as well as the difficulty level of the passages you are able to transcribe. You will also likely notice during the course of your first transcription that the length of the phrases you are able to transcribe at a time expands. At first, you may have to adhere to a note-by-note method, where you need to press the stop button after just one or two notes as you piecemeal phrases together. There is absolutely nothing wrong with this, and the recommended procedure is that you sing each note or phrase immediately after you hit the stop button, and then find on your


Swing: Global Rhythmic Gateway

instrument the notes you just sang. You can then write them down. But strive to be able to learn and sing back the longest phrases possible; before too long you will be singing much longer phrases, having only heard them once or twice, than you could at the outset. By then transferring them from voice to instrument, you have achieved yet another strategy for building the all-important linkage between ear, voice, and instrument that is essential to creative musicianship. While our primary emphasis here is on transcribing the improvised melodies of jazz masters, you are also encouraged to attempt to transcribe the harmonies behind the solos you are copying. This generally represents a greater challenge to most musicians and thus may need to be preceded by a phase of melodic transcription as well as further keyboard work. In terms of integrating the influences gained from a solo into one’s playing, students are encouraged, either after an entire solo is completed or at any point in the process, to identify one or two phrases that are particularly compelling and to create aural transposition exercises based on these phrases. Here one can either use the phrase exactly as it is found on the recording, or alter it somewhat to make it suitable for aural transposition purposes. Finally, let us address a common question that arises: Should one transcribe master artists who play one’s primary instrument, or might it also be beneficial to transcribe master artists on other instruments? Both are beneficial. It may be easier at first to transcribe solos by artists on your instrument due to the familiar timbre and the greater likelihood that the lines will play well on the instrument. For this very reason, however, transcribing solos of artists on other instruments can be highly beneficial in stretching your technical and conceptual horizons. Furthermore, musicians who play instruments such as the oboe and bassoon will have far fewer recorded examples to choose from and thus may have little choice but to transcribe solos by saxophonists, trumpeters, or other instrumentalists. The following transcription project is inspired by the saxophonist David Liebman, who asserts the need to transcribe a minimum of “five major solos” as a basic foundation for the aspiring jazz artist. Needless to say, the amount of transcribing that is appropriate will vary from one individual to another. Solo transcription Transcribe a solo from a recording of a jazz artist and play the solo in class along with the recording, striving to match the master artist’s every note and nuance as closely as possible. Be prepared to say a few words about the artist and the piece. In addition, be prepared to cite one or two favorite passages in the solo.

Exercise 7a

Swing: Global Rhythmic Gateway


Scale and Chord Exercises for Cultivating the Swing Concept II–V7–I scale pattern Extend these II–V7–I chord-scale patterns which utilize swing articulations, to all keys.

Exercise 7b and Example 7.8

This pattern is not only useful as a means for mastering swing articulation, it is also useful as a preparation for improvising on chord progressions, as the scales help internalize the sounds of the chords and how they move. The next two exercises also serve this purpose. Exercise 7c presents an arpeggio pattern. Exercise 7d presents a broken arpeggio pattern. II–V7–I arpeggio pattern Continue this II–V7–I arpeggio pattern in all keys. Instead of applying the above articulation, simply provide a slight accent on the second of every two eighth notes. Strive for the combination of legato phrasing and strong rhythmic integrity.

Exercise 7c and Example 7.9


Swing: Global Rhythmic Gateway

Broken arpeggio pattern Continue this II–V7–I broken arpeggio pattern in all keys. Again, provide a slight accent on the second of every two eighth notes, striving for legato phrasing and strong rhythmic integrity.

Exercise 7d and Example 7.10

The above pattern will be particularly useful in expanding your use of larger intervals. Since it presents technical challenges and may take some time to master in all keys, you need not achieve this mastery prior to working with the Jazz Etudes. What is important is to sustain in your daily practice a regular regimen of aural transposition that proceeds incrementally according to your ability. As with all aural transposition practice, you are encouraged to take some time to improvise with the shapes so that they begin to inform your playing. You are also encouraged to apply some form of arpeggio exercise, whether Exercises 7c or 7d in this chapter or some alternative, to whatever chord progressions you set out to improvise with. This will greatly aid in your hearing how the chords flow and your ability to spontaneously create melodies on those chords.

chapter 8

Melodic Line Construction and Harmonization

In this chapter, we: • • • • •

Fine-tune our abilities for improvising and composing melodies. Learn about target notes and passing notes. Learn which notes are effective and which are problematic on different chords. Work with guide tones, approach tones, surround tones, and the bebop scale. Begin to harmonize melodies.

Composing and improvising are contrasting yet highly complementary modes of musical expression. Both are capable of standing on their own as rich forms of creativity. Improvisation uniquely enables a kind of real-time, spontaneous invention and interaction that is not possible through the discontinuous temporality of composition, where pieces are melded over a series of creative episodes that may span weeks or months. On the other hand, the very discontinuous temporal framework of composition is uniquely suited to another kind of expressive result—the design of rich formal architectures. As the saxophonist Steve Lacy remarked, “there is a music that must be composed, there is another music that can only be improvised.”1 Engaging with both processes can greatly enhance the development of musicianship skills. Improvising can generate ideas for composition; composition can provide a kind of structural awareness that feeds back to improvisation, just to mention a few ways these practices can interact. In the earliest days of the European classical tradition, this synergistic

1 Steve Lacy, Findings: My Experience with the Soprano Saxophone. Paris: Outre Mesure, 1994, p. 21.


Melodic Line Construction and Harmonization

relationship between the processes was alive and well as most musicians improvised, composed, as well as performed—which has been the case in jazz since its inception. This complementarity in classical music has sadly become lost in a “division of labor” which has prevailed in that tradition for the past century and half, where the majority of musicians specialize in performance, a distinct minority composes, and improvisation has become almost extinct. From this standpoint, a strong case could be made that jazz is more closely aligned with the artistic legacy of Bach, Beethoven, Mozart, Schubert, and Liszt than the current musicianship paradigm that is confined to performance of these (and other) masters’ works. Happily there are signs that this paradigm is beginning to change, albeit slowly, as more and more classical musicians are beginning to rediscover the gap in their artistic lives created by the absence of these core creative processes. In this chapter we explore compositional strategies as a means for both developing skills as composers as well as enhancing our improvisatory development. Stepping back from realtime improvised performance and fashioning musical ideas and notating them over time can help refine our melodic conception, knowledge of harmonic structures, chord scale possibilities, and a host of other skills. We will now continue this work within the expanded parameters of contemporary tonal music.

Composing Melodic Lines on Chord Changes Creating melodies atop chord changes is not fundamentally different from creating melodies atop the minor pentatonic bass lines we have worked with previously. In each instance a pitch field is implied that can be delineated by a scale or mode from which melodies may be fashioned. Within the scale, some tones are more consonant in relationship to the underlying line or chord and some are more dissonant. The most interesting melodies are those that maintain a balance within the consonance–dissonance spectrum, as this is essential to the interplay of tension and repose in the melody. While some sonorities that have been considered dissonant in previous eras have become perfectly acceptable to the contemporary ear, constraints nonetheless exist that determine what tones more closely define a tonal center and what tones create tension or movement away from that center. The following principles will serve as a guide in the construction of melodies that align with the sonority of the chords against which they sound, yet also make effective use of tension for the sake of variety. The first is that in any given phrase, the majority of tones will tend to be contained within the chord scale that is implied by the harmony sounding at the moment. This is not to suggest that significant use of chromaticism is not possible; in fact, melodies in tonal formats may make use of all 12 chromatic tones. However, generally speaking, chromatic tones will play more of a passing function rather than a target function. Target notes will tend to be diatonic notes contained within the chord scale. Let us consider briefly the distinction between passing and target notes. Passing notes are those that, in any given phrase, move toward a target note; target notes function more as landing points. In phrases involving notes of varying duration, passing notes will tend to be shorter, target notes longer.

Melodic Line Construction and Harmonization



In phrases where all notes are of equal duration, target notes will tend to be those on strong beats. In Example 8.2 the first of each four eighth notes (beginning with beat three of the first bar) may be considered a target note in relationship with the melodic cells that precede it. Each of these notes not only falls on a strong beat, but also is prepared by tones a step below and a step above, thus further accentuating the note. Accordingly, such notes will generally be within the chord scale as opposed to chromatic tones. Here it is important to not confuse what we are calling passing notes with what are termed “passing tones,” one of several “non-harmonic” tones, as categorized in European classical theory, although some similarities exist. Passing notes are defined largely by their rhythmic placement in a melodic phrase, regardless of what harmonic structures are sounding at the time. Passing tones are defined in relationship to the harmonic structures that sound; they are non-chord tones that connect one chord tone with another and are usually approached and resolved by stepwise motion. Passing notes can move by step or leap. We will look at passing tones and other non-harmonic tones in European classical theory in Chapter 9. A second principle is that within any given chord scale, certain tones are more conducive to playing a target function than others. Table 8.1 delineates which diatonic tones are more effective as target notes. The Arabic numerals indicate both the relationship of a given tone to the chord and the scale, as this relationship is the same (the third of the chord is the third note of the related chord scale). Here we encounter for the first time the concept of chord extensions—the use of ninths, elevenths, thirteenths, etc.—as devices that create richness in sonority. We will later take these up more formally at the keyboard. For present purposes, extensions may be thought of simply as octave displacements of basic chord-scale tones: the ninth of a chord is the same as the second degree of the scale, the eleventh the same as the fourth degree, the thirteenth the same as the sixth degree.



Melodic Line Construction and Harmonization

Diatonic Target Notes TABLE 8.1 Effective and problematic target notes Chord type

Chord scale

Notes with Also possible most direct target function

Problematic tones

Minor 7th chord (II)


1, 3, 5, 7, 9, 11

6 (or 13)

Sometimes 6 (or 13)

Dominant 7th (V7)


1, 3, 5, 7, 9,13

Chromatic extensions to be considered later

4 (or 11)

Major 7th (I)


(1), 3, 5, 7, 9

#11, 6 (or 13)

4 (or 11)

Later we will add chromatic tones, particularly on the dominant seventh chord, to the spectrum of possible extensions. Even from a diatonic standpoint, however, inasmuch as almost all notes of a given scale are available as target notes (and thus also as passing notes), it is clear that we have much more latitude here in our note choices than in our species work. Whereas in species contexts seconds, fourths, and sevenths are considered dissonant tones and have to be treated with care (e.g. resolved stepwise, preceded or followed by consonance), in contemporary tonal or modal formats, all of these tones, depending on the chord quality, may be perfectly acceptable and even sound as consonant as the basic tones of the chord. Let us take a closer look at these possibilities. The IImin7 chord is unique in that virtually all seven diatonic tones of the Dorian mode are available as target (and thus passing) notes. A partial exception to this principle is the sixth degree, which must be treated with care if used as a target note in that it forms a tritone relationship with the third of the chord. Generally, the sixth will be approached and resolved by step when functioning as a target note. The V7 chord involves tighter constraints in that within its corresponding Mixolydian scale the fourth degree of the scale—which is the fourth or eleventh of the chord—is not available as a target note. Whereas the sixth degree on the minor seventh chord was a delicate tone, the fourth degree on the V7 is more problematic. The reason for this is that this tone forms a minor ninth interval with the third of the chord, which is generally jarring to the ear (although an exception will be found on the V7(b9) chord). The same holds for the fourth degree of the Ionian scale as it relates to Imaj7 chord. The fourth degree may be used as a passing note, but not as a target note. Accordingly, the fourth degree when used on melodies supported by these chords will not be longer in duration than the notes preceding or following it.

Melodic Line Construction and Harmonization


Problems With the Root of the Major Seventh Chord in the Melody In the last box of Table 8.1, which pertains to the major seventh chord, the root of the chord is in parentheses. The reason for this is that the root, perhaps ironically, can be somewhat problematic due to either the interval of a minor ninth that may form between it and the seventh of the chord, depending on how the chord is voiced, or as seen in Example 8.3, a half-step between the top note of the voicing and the melody note. The effect may either be jarring or at least obscure the melody note, which is usually a tone that needs to stand out atop the harmony. If the root-as-target note is not excessively long, perhaps just a quarter note at a medium tempo, particularly if a longer target note follows within a reasonable amount of time, then the use of this tone may be acceptable; the ear hears it as motion along the way to a stronger landing point. However, if the target note is a half note or longer, then the half-step or minor ninth relationship will likely be not the most desirable choice (although notable exceptions to this are found in a variety of repertory). Example 8.3 illustrates the problematic resolution (a), followed by several alternate strategies (b–e). This can be remedied through several different strategies. One, as shown in 8b, is to change the major seventh chord to a major sixth chord, one of several new chord types we are about to encounter. The major sixth chord includes a major sixth instead of a major seventh. Play through Example 8.3 and notice that the problem with the half-step at the top of the voicing is now resolved. However, you may find, as do some musicians, that the major sixth sonority is somewhat “dated” and perhaps want something a bit richer. So try the next solution (in 8c), which is



Melodic Line Construction and Harmonization

to use a major 6, 9 chord. Now the ninth is used in the voicing instead of the third, one of the few instances in which the generally essential third is not included. Because of the strong IImin7 V7 activity leading to this chord, the third is nonetheless implied and there is no less a sense of finality in the major key. Does this chord sound a bit richer to your ears? Two more possibilities with slightly more contemporary sonorities are also available to solve the problem. One is to use a “sus chord” (shown in 8d), which is simply a triad in which the third is replaced by the fourth (or eleventh), the latter note being “suspended.” Second is to use a “sus 9 chord,” in which as the label in 8e indicates, a ninth is now added to the sus chord. These particular constraints aside, contemporary tonal practices provide considerable latitude in terms of what notes may serve as important melodic tones. In Example 8.4 the target note on the Gmin7 chord is an A, which is the ninth. In a species format this interval would be considered dissonant, but in a contemporary tonal format (where seventh chords are the basic unit), the ninth is perceived as consonant as any of the basic chord tones. This is evident when one plays the next example (Example 8.4): the ninth is just as resonant or stable a target note as the target notes in the second and third bars, which are, respectively, the seventh and third of their corresponding chords.


Melodic Analysis In Example 8.5, Arabic numerals are shown that indicate the relationship between each tone of the melody and the chord sounding at the time. This kind of melodic analysis, also encountered in our species work, is helpful in refining the capacity to improvise and compose coherent and compelling melodies atop chord progressions. It is not that one will necessarily be consciously aware of these particular numerical relationships during the creative flow. However, attending to this kind of detail in these exercises will help fine-tune the connection between ear and intellect, and thus the ability to create melodies that are closely aligned with the chords.


Melodic Line Construction and Harmonization


Melodic analysis Provide a melodic analysis for this melody. Circle target notes. Identify with an asterisk (*) any flaws you detect according to the principles discussed above.

Exercise 8a and Example 8.6

Let us now go further into the inner workings of the melody–harmony relationship.

Guide Tones Recall that at the beginning of Chapter 6 we examined the major scale and the key role the half-step relationship played in defining the melodic tendencies inherent in that scale. Also of importance were considered downward stepwise scalar motion (e.g. 2 to 1) and root movement by fourths and fifths. This brings us to the concept of guide tones, which are essential notes that uphold the quality and function of a given chord. They are the tones that, if one were to remove all the other tones, are most capable by themselves of upholding the harmonic movement. Our primary concern here are guide tones in a IImin7-V7-Imaj7 context, where the guide tones are the thirds and sevenths of the chords. Consistent with our approach to all harmonic materials, we will realize guide tone lines at the keyboard, shifting from our customary five-part approach to a three-part approach. You may be surprised to hear that even the seemingly thin three-part texture comprising bass notes (left hand) and thirds and sevenths (right hand) is able to capture the richness and coherence of the II–V7–I harmonic movement. Later we will see that this foundation supports the most lush chord extensions and alterations. Example 8.7 provides the core guide tone pattern in a few II–V7–I sequences. Observe an interesting voice-leading tendency where, between any two chords within a given



Melodic Line Construction and Harmonization

II–V7–I, one of the guide tones serves as a common tone and thus does not move while the other guide resolves down a half-step. Understood another way, the third of the IImin7 is the same tone as the seventh of the V7 and thus remains stationary between the chords, whereas the seventh of the IImin7, which would be the fourth degree of the V7, resolves down a half-step to the third of the V7 chord, thus harkening back to the centuries-old 4-3 suspension that was found frequently in European classical harmony. Keyboard exercise Realize the remainder of the above sequence (Example 8.7) at the keyboard in all keys without the aid of notation.

Exercise 8b

As always, strive to play with a steady rhythm—speed is not important but solid pulse is—and in each moment, hear in advance, or allow your awareness to sense, the next sonority. Note that because this II–V–I sequence moves down by whole steps (II–V–I in C, then in Bb, then Ab, etc.), you will return to the original key after six sequences (as you did in prior keyboard exercises). At this point, begin the sequence once more a half-step higher or lower than where you initially began, and you will cover the remaining six keys. In the next exercise, the guide tones are reconfigured so that instead of beginning with the seventh of the II chord on top, the third of the II chord is on top.

Keyboard exercise Continue the sequence of guide tones through all keys at the keyboard without the aid of notation.

Exercise 8c and Example 8.8

Melodic Line Construction and Harmonization


Singing guide tone sequence Divide the ensemble or class into three groups. Group A sings the roots, Group B begins with the third of the II min7, Group C begins with the seventh of the II min7. After six keys, switch parts. Maintain a steady pulse at all times; it may be helpful to have someone conduct.

Exercise 8d

Written Application Example 8.9 presents II–V–I progressions that move freely and randomly (following no set pattern) between key areas. Consistent with the above illustrations, all voices move only by stepwise motion within a given II–V–I and there is always a common tone between any tone chords within any given II–V–I sequence. This takes the concept of smooth voice leading to a new level, however, by retaining a common tone between all chords—even those at the borders between two very distant tonal areas. In fact, the guide tones for the Gmaj7 chord that ends the first sequence are precisely the same tones—just spelled enharmonically to reflect the shift from G to Gb—for the Abmin7 chord that functions as II of the next sequence. When that sequence cadences on Gbmaj7 and is followed by a Cmin7 chord, the guide Bb is retained and the guide tone F just needs to move down only a step even though the roots of the chords are a tritone apart. The same smooth voiceleading practices are found when the Bbmaj7 is followed by the F#min7 which is II of the final II–V–I sequence.


Written exercise Using the above format, write a sequence of guide tone lines in the treble clef, with roots in the bass clef, corresponding to the chords indicated. Be sure to use the


Melodic Line Construction and Harmonization

smoothest voice leading possible not only within diatonic areas, but when moving from one key area to another (e.g. never use larger than a second between the upper four voices and retain common tones when possible).

Exercise 8e and Example 8.10

Melodic Line Construction and Harmonization


Written exercise Example 8.11 provides only the guide tone lines, omitting the bass notes. Your task is to fill in the bass notes and provide the chord symbols.

Exercise 8f and Example 8.11

Incorporating Guide Tones in Melodic Lines Let us now examine how melodic lines can incorporate guide tones to create a strong relationship with the underlying harmony. Recall from the previous chapter that guide tones are the thirds and sevenths, prominent active or tendency tones, of chords. At first glance it may seem that one strategy for aligning melodies with chord changes would simply be to create lines in which most of the notes are guide tones. This is neither necessary nor, for the sake of interest, advisable. In fact, much more important than how much of a given line comprises guide tones is where guide tones occur. Strong lines—those that follow principles of contour and internal coherence (e.g. melodic cells, target notes, etc.)—and that use guide tones at strategic points may be more closely aligned with the chord changes than weaker lines that make extensive use of guide tones. This will be particularly evident in the following lines, which consist primarily of eighth notes in order to exemplify the 2:1


Melodic Line Construction and Harmonization

principle central to mastering time-feel improvising (always keeping in mind that all rhythmic relationships are possible and necessary to musical vitality). These illustrations of quasi-improvised lines show how guide tones, used at strategic points, can help align a melody with the chord changes sounding. One strategic point is where the guide tone occurs on a strong beat in the measure or phrase (e.g. the first beat of the measure, or the first of four successive eighth notes). Second is when the contour of the line shifts (e.g. a change in direction) or the prevailing interval shifts (e.g. stepwise motion is followed by an interval larger than a second). The ear perceives these points where some prevailing pattern shifts as structurally important. When guide tones sound at these points they attract attention, and given the inherently close link between guide tone and harmonic function, this reinforces the impact of the guide tone. In Example 8.12, our focus is on the use of guide tones on the II and V chords, and less with its usage on the I chord. The reason for this is that the sense of finality or closure may be produced by a variety of tones other than three and seven, as the examples indicate. There is prominent use of chord scale degree five as the final note; degrees five and nine in fact create as much or more sense of closure than the guide tones. To the contrary, the conveying of movement on the II and V chords can be uniquely enhanced by strategic use of guide tones, as these lines illustrate. While the following lines—which are excellent for aural transposition practice—are internally coherent as well as clearly aligned with the chord changes, jazz improvisers commonly employ chromaticism in varying capacities, particularly on the V7 chord. Example 8.13 shows an additional series of lines that, as with those above, make strategic use of guide tones, but also incorporate chromaticism in several different yet closely related capacities. In bar 1, the chromatic note is preceded and followed by a half-step and thus assumes a passing function. In bar 2, the G and E# approach the F#—which it must be emphasized is the third of the D7 and thus diatonic to the key area—from above and below; while G is not a chromatic tone, it functions in tandem with the E# as a surround tone that leads to the F# target. The term derives from the fact that the tones frame—and thus surround—the


Melodic Line Construction and Harmonization



target from a half-step above and below. The same effect is found in bar 3 where the A# and C approach the target note B from above and below, and again in bar 4, where the A and F# approach G from above and below. In bar 5, the D# serves as an approach tone to the arpeggio that follows and lands securely on the fifth of the I chord. In Example 8.14, a chromatic tone serves as a lower neighbor in bar 2, and another use of surround tones is shown in bar 3. Example 8.15 is an illustration of chromaticism resulting from the frequently used bebop scale. It shows the scale, which is a Mixolydian mode with both minor and major seventh degrees, followed by a phrase that incorporates the scale on the V7 chord in an idiomatic manner. Notice that the chromatic motion in the bebop cell from C to B to Bb is interrupted by a leap up to D before continuing to A.




Melodic Line Construction and Harmonization

Examples of the bebop scale are found in Jazz Etudes 7 and 14 in Appendix 4. Lower neighboring tones are found in Etudes 14 and 17, approach tones in 10, and surround tones in 17.

Two Approaches to Composing Melodies on Chord Changes As we begin to develop our composing abilities in chord changes formats we will pursue two different approaches, both of which we have already encountered in our small group work. Recall from the small group framework outlined in Chapter 4 the tasks of creating a main theme, or what is called the “head,” and also a quasi-improvised, tutti line (so called in that it is intended to sound like a written-out improvisation). We will refer to the first of these approaches (main theme, or head) as a song-form approach, which will generally result in a simpler, more symmetric, perhaps predictable kind of melody for which one might imagine lyrics being created. Song-form themes will tend to make more use of antecedent-consequent, or question-answer phrases than quasi-improvised lines, which will generally employ faster moving notes (with prominent use of eighth note lines) and, like much improvisation, are not as predictable. Observe both the use of motivic development (motive 1 in the first two bars, repeated on a different pitch level in bars 3 and 4) and antecedent-consequent structure, where the new melodic material in bars 5 and 6 serves as a kind of response to the question posed by the first two motives. Notice also that in bars 1, 3, 4, and 5 there is an eighth note on the second half of beat 4 that is tied over the bar line, yet the chord symbol is listed on the first beat of the next bar. The question arises: Which chord change applies to such notes—the chord of the present measure or the new measure? In other words, is the G at the end of bar 1 harmonized by Bbmaj7 or Ebmaj7, which is listed to sound one half-beat later? In fact, the G is harmonized by Ebmaj of bar 2, even though the chord is indicated to sound on bar 1. A second category of composing on chord progressions is one we have already encountered in the tutti melodies we created in the small group mode-rhythmics frameworks. Called the quasi-improvised melody, it is intended to sound like a written-out improvised line that embodies salient features of time-feel-based improvising. These include the prominent but not exclusive use of eighth notes, and instead of antecedent-consequent


Melodic Line Construction and Harmonization



phrases that create a sense of melodic symmetry, they involve more of a forward motion and spinning out of new ideas. Example 8.17 is written on the same chord changes as the song-form melody in Example 8.16. Written exercise Compose two kinds of melodic lines on the progression: song-form and quasi-improvised lines. Provide Roman numeral analysis of the progression and melodic analysis of your melodic lines. Dmaj7  Bmin7  Gmaj7  Emin7  C#min7(b5)  F#min7  Emin7  A7  Dmaj7 

Exercise 8g

Harmonizing Melodic Lines So far, our consideration of melody–harmony relationships has involved pre-established chord progressions. In other words, we have not yet created harmonies but rather have been given harmonic progressions and played them at the keyboard, and improvised and composed melodies atop them. Now let us consider the melody–harmony relationship from the standpoint of a melody without chords, and thus which we must harmonize (come up with chords that fit the melody). This will be invaluable to our work in creating jazz and pop compositions.

Top–down Harmonization at the Keyboard A series of preliminary harmonization exercises that are done at the keyboard is presented below. The exercises provide a melody note and a chord symbol; your task is to play the melody note and fill in the remaining notes below it. This means we end up with the same


Melodic Line Construction and Harmonization

four-note voicing in the right hand, and the root of the chord in the left hand, that we have been employing so far. However, instead of seeing a chord symbol and voicing the chord from the root on up, now we see a chord symbol and a melody note and voice the chord from the melody note on down. Now, in the right hand, the little finger becomes the guide, as it is the finger that will often play the top and most prominent melody notes. Here it should be emphasized that it is essential to keep the melody note on top as the ear hears this tone as the most prominent. This principle is also important in arranging and orchestration. As a general rule (there are always exceptions in music!), the highest note in a voicing is most prominent, and thus harmonies are voiced below rather than above melodic lines. Example 8.18 provides a melody consisting only of half-notes in order to demonstrate the harmonization principles involved, with chord changes. Observe the use of skips in the melody, which will require the voicings to employ similar skips. Although thus far we have stressed smooth voice leading in our keyboard realizations where we use minimal shifting in hand position, the reason for this was to develop the ability to voice our chords in multiple positions (instead of playing every right-hand voicing 1, 3, 5, 7) that can be adapted to the musical situations encountered. Now that we are harmonizing a given melody—and most melodies employ leaps at least occasionally—we need to be able to follow the melodic contour in our harmonizations. Accordingly, Example 8.19 shows one way of voicing this progression with the melody on top and the other notes filled in within reach. Example 8.20 provides another version of essentially the same voicing scheme, except now rhythmic variety is introduced. This not only lets the music breathe a little by moving away from block chords, it also creates the sense of top–down voicing, where the melody note sounds first, and the harmony follows a half-beat later. Notice that this pattern is a top–down version of one of the basic comping patterns provided in Chapter 6; in those patterns, the bass note would sound first, and the chord a half-beat later.



Melodic Line Construction and Harmonization



Harmonization Harmonize these melodies using either one of the two top–down approaches (block chords or more rhythmic approach) illustrated above.

Exercise 8h and Example 8.21

Needless to say, most melodies consist of more than just half-notes, and so let us proceed to apply these principles to melodic lines that are more florid—where more than one melody note sounds against any given chord (Example 8.22). To harmonize this type of melody, let the chord ring by use of the sustain pedal after playing the first melody note, and then play the remaining melody notes before releasing the pedal and moving to the next chord (Example 8.23).


Melodic Line Construction and Harmonization



Keyboard exercise Play the following melodies and chords at the keyboard using the above approach.

Exercise 8i and Examples 8.24–8.25

Melodic Line Construction and Harmonization


Harmonic Rhythm Let us now consider strategies for harmonizing a given melody in which no chords are given. The first step in this process is to determine what is called the “harmonic rhythm” that is implicit in a given melody. Harmonic rhythm pertains simply to the frequency with which chords change. A piece in which chords change every measure has a slower harmonic rhythm than pieces which involve two chords per bar. In Example 8.25 the harmonic rhythm changes—the piece begins with chords changing once per measure, and the harmonic rhythm increases to two chords per bar in the second and third measures from the end. The reason in this case was that the succession of half-notes in the melody suggested that to change chords with each note would be an effective way of bringing out this particular melodic passage. More than one harmonic rhythm may be effective for any given melody. Example 8.26 shows two harmonic rhythms applied to the well-known theme from the last movement of Beethoven’s Ninth Symphony. Harmonization 1 follows Beethoven’s approach to the theme for much of the movement and consists only of I and V chords, with one chord per measure. Harmonization 2 consists of a much faster harmonic rhythm that involves a chord change each beat. Notice the contrary motion between melody and bass that is created through the more frequent chords, as well as use of inversion, in harmonization 2. When the melody ascends, the bass descends, and vice versa. A second step in harmonizing a melody is to make sure that the melody notes which occur within the length of time a given chord sounds are part of the chord scale. This pertains not only to target notes but to passing notes. Here is where chord-scale analysis for improvising purposes is highly useful for composing. If there are melody notes outside of the chord scale, then they need to be approached by step, in the same way we approached dissonance in our species counterpoint writing. Third, make sure that in the harmony you choose, target notes are not only included in the chord scale, but are not among the problematic tones we have identified above. Generally, your ear will tell you when problems arise. One way of avoiding this situation is



Melodic Line Construction and Harmonization

to place target notes as priorities when creating harmonizations. Harmonize these first, finding the best sonority for these tones, and then see if the other melody notes of that phrase—or whatever length passage is to be harmonized by a given chord—also fit within that harmony. More often than not, if you arrive at an effective harmonization for a target chord, that chord will also work well for the passing/connecting melodic notes leading up to it. Thus the process of harmonizing a melody does not necessarily have to follow the timeline of the music (e.g. proceeding from the first melody note sequentially through the melody). This process can begin with some target point well into the melody—even the final phrase or note—and work backward from that point. Once you come up with a workable chord at one point, be open to an even more compelling option to present itself as you work out the other chords. This leads to a further principle. Your sequence of chords needs not only to fit with the melody, it needs to sustain coherence on its own. Suffice to emphasize here the importance of playing the chord sequence apart from the melody and using your ears and instincts to determine the degree to which your chord sequence maintains this kind of internal integrity. As you play your sequence, use different configurations of the chords. We are not yet using inversions, just staying with root-position harmonies (where roots are in the bass), but you can vary the way you voice the chords in the right hand when you play them at the keyboard. Strong progressions will generally sound coherent even when played in a variety of configurations. Harmonization exercise Choose a familiar melody and, without referencing a notated version of it, come up with your own harmonies. Again, do melodic analysis, sing the melody and play the chords at the keyboard.

Exercise 8j Compose your own melody Compose your own melody and harmonize it. Do melodic analysis, sing, and play as above. Work with a partner who will play the theme and then improvise on it, with you providing accompaniment (“comping”).

Exercise 8k

Small Group Application Begin to compose compositions and tutti passages for your small group, using the principles introduced in this chapter. Be sure to use these approaches when you compose tutti lines for your performances of the Jazz Etudes (Appendix 4).

Melodic Line Construction and Harmonization

SUMMARY QUESTIONS 1 What kinds of musical expressions are possible through improvisation, but not possible through composition, and vice versa? 2 What did Bach, Beethoven, Mozart, and Liszt have in common with today’s jazz musicians? 3 Identify the notes of the chords and chord scales that can serve as target notes on the three chords of the II–V–I progression. 4 The ninth is too dissonant a tone to serve as a target note on any of the chords of II–V–I. True or false? 5 Why can the root of the major seventh chord be problematic when used as a melody note that is sustained for a half-note or more in duration? What steps might be taken to rectify the situation? 6 What are guide tones? 7 Guide tones provide a greater sense of finality or closure on the I chord than tones 5 or 9. True or false (circle one)? 8 How does the bebop scale differ from the Mixolydian mode? 9 One of the first steps in harmonizing a melody is to determine the frequency with which chords will change, as implied by the melody. This frequency with which chords change is called the ________ _______. 10 The best way to approach harmonizing a melody is always to work from beginning to end; in other words, to first harmonize the first measure, then the next, then the next, and so on. True or false? 11 One of the most effective chords to harmonize an F in the melody, particularly when it functions as a target note, is an F major seventh chord. True or false? Defend your answer.


chapter 9

Chord Inversion Present and Past

In this chapter, we: • Examine the use of chord inversion in contemporary and older formats. • Compare non-harmonic tones in European classical music to chord extensions in jazz. • Analyze Bach chorales via Roman numeral analysis. • Play chord inversion exercises at the keyboard.

Chord Inversion in Jazz Although much jazz harmony involves root-position chords—with richness and variety achieved through frequent use of extensions, alterations, and fluid movement between close and distant key areas—the use of inversions also plays an important role in repertory created or adapted by jazz musicians. Example 9.1 illustrates one of the most common uses of inversion in jazz, involving a chromatically descending bass line which forms a counterpoint line that is complementary to, yet independent of, the melody.

Recommended listening: Many recordings of this piece are available, including J.J. Johnson, Proof Positive (Impulse 1964); Ahmad Jamal, Ahmad Jamal Live (Passport Audio 2006, originally released 1958); Carmen McRae, Carmen McRae Sings Great American Songwriters (UMG 1993; originally released 1955); and Chet Baker, My Funny Valentine (Blue Note 1994).

Notice two contrapuntal relationships between the descending chromatic bass line that is created by the use of inversions and the melody. The first is shown in Example 9.2. Between bars 1 and 2 and 3 and 4, with the melody note moving upward by step from C

Chord Inversion Present and Past


EXAMPLE 9.1 Rogers and Hart, “My Funny Valentine” © 1937 Chappell & Co., Inc. All rights for the extended renewal term in the U.S.


to D, the bass line moves in contrary motion from C to B and then Bb to A. If we then look at the opening melodic phrase in broader terms as a kind of elaboration of the tonic note C—notice that the melody returns to C every third bar in the first six measures—we find a type of oblique motion forming between the melody and descending bass line (again, C-B-Bb-A-Ab). This is illustrated in Example 9.3. Notice as well two new chord types in the above progression, both of which are shown in root position in Example 9.4. One is the minor-major seventh chord, which involves a minor triad and a major seventh interval (notice that the major seventh is indicated by M7 within the parentheses for ease of reading). Another is the minor sixth chord, which is a minor triad with a major sixth. The minor sixth chord may also be thought of as a minor7(b5) chord in first inversion. Be careful not to think of the minor sixth chord as including a minor sixth, which is a common error; this would make it a major seventh chord in first inversion. Minor sixth chords may be easily remembered as the counterpart to the major sixth chord encountered in the previous chapter. Whereas the major sixth chord includes a major triad and major sixth, minor sixth chords include a minor triad and a major sixth.


Chord Inversion Present and Past


Steve Swallow’s composition Falling Grace also makes use of inversion to create half-step motion in the bass. Here, however, the overlying chords change as the bass notes change, thus resulting in two kinds of voice-leading activity: one involves the chromatically descending bass line, the other the movement of chord tones inherent in the overlying harmonies (the overlying chord structure remained constant in My Funny Valentine).

Recommended listening: Chick Corea and Gary Burton, Crystal Silence (ECM 1973).

Because jazz harmonies are usually extended beyond the seventh even if only the seventh is indicated in the chord symbols—a topic we will take up in depth in Chapters 13 and 14— an interesting situation arises when it comes to chord inversion. Generally speaking, when a chord inversion is indicated, the chord is not extended, as this may obscure the effect of the contrapuntal movement between bass and melody created by the inversion and, in fact, suggest an entirely different chord.

EXAMPLE 9.5 Steve Swallow, Falling Grace. © Celestial Harmonies. Used by permission.

Chord Inversion Present and Past


In European classical music, the frequent use of triads and some seventh chord activity rather than chords extended beyond the seventh yields a harmonic texture particularly conducive to chord inversion, since the relationship between bass line and upper voices is able to assume prominence. Exercise 9a illustrates how, through the use of inversion, an effective counterpoint can occur between melody and bass while sustaining a harmonic rhythm in which a chord changes with each note. This provides our first encounter with the figured bass line, which is a bass line using Arabic numerals to indicate when chord inversion is used. If no figuration is provided, the bass note is the root of a triad diatonic to the key (hence a C with no figuration in the key of C indicates a C major triad). Recall from Chapter 5 the particular inversions indicated by each figure as you complete this exercise. Keyboard exercise Fill in the Roman numerals under the bass clef (Example 9.6). Then play the example at the keyboard and fill in the missing chord tones in between the melody and bass notes.

Exercise 9a and Example 9.6

Non-harmonic Tones We will shortly look at the use of inversion in Bach chorales as exemplary of this practice in European classical music. Prior to doing this, it will be important to examine what are called non-harmonic tones. Non-harmonic tones, as the heading suggests, are tones that are not contained in the harmony that sounds at a given moment. It is interesting to note that no such heading exists in jazz, largely because the denser harmonic texture—where the basic unit is the seventh chord, which is often extended—supports a much wider array of tension atop the basic chord. To give an example: whether or not the ninth of a chord is specified in the chord symbol or played by the pianist or guitarist in a jazz group, this tone can sound as resonant as any chord tone, even when sustained, when played by the improvising soloist. European classical music, on the other hand, involves a thinner harmonic texture in which the triad is the basic unit, with occasional seventh chord activity, as we will see in Bach chorales, thus yielding a different framework for tones that are outside of the harmony at a given moment. Here non-harmonic tones require more delicate treatment when it comes to their approach and resolution. Whereas in jazz we can leap into


Chord Inversion Present and Past

and out of ninths and raised elevenths on major seventh chords, for example, in European classical harmony so-called dissonant tones are generally approached and resolved by step. It is thus important to emphasize that the terms dissonance and consonance relate to particular style periods in tonal music. Much of what had been considered dissonant, as suggested above with chord extensions, sounds consonant to the contemporary ear. Still, some common threads may be identified between contemporary and past tonal practice. For example, we still hear the fourth (or eleventh) degree of the major or dominant chords as wanting to resolve to the third. Four types of non-harmonic tones are of interest here. Passing tones, the most common type of dissonance, move by step and connect two different chord tones a step apart, as shown in 9.7a. Neighboring tones move either a step up or down from a chord tone and then return to that tone. 9.7b shows a lower neighboring tone, 9.7c an upper neighbor, and 9.7d double neighboring tones, those that move a step above and below the note they serve to embellish. 9.7e illustrates an anticipation, which is a non-harmonic tone when it first sounds (here as a B on the D7 chord) but when the harmony changes (to G, which includes the tone) and the tone is repeated, it is now a chord tone. The ear groups the two functions of the same tone into a sequence that moves from tension (non-harmonic function, thus dissonant) to repose or release (harmonic function, consonant). Suspensions are tones that begin as chord tones and are tied over the bar line (thus suspended) to become dissonances, because they are now a non-chord tone, when the chord changes. Bach chorales are an ideal format for studying the use of inversion. Several excerpts are given in Examples 9.8 to 9.12. Needless to say, not all the chords are inverted, but the instances where inversion is used are idiomatic of European classical common practice. In analyzing these chorales according to the following specifications, not only will it be necessary to stack notes in thirds in order to determine their roots, but it will also be necessary to determine which tones are chord tones and which are non-chord (or nonharmonic) tones. Passing tones, for instance, may occur either on the strong part of the beat or the weak part of the beat, and it will thus be necessary to examine these notes in terms of what precedes or follows them.


Chord Inversion Present and Past


Analysis of Bach Chorales Bach chorales Provide contemporary chord symbols, key, and Roman numerals for these Bach chorales. Use both kinds of Roman numeral analysis systems (Euroclassical and jazz/pop), as shown. Circle non-harmonic tones (e.g. passing tones, suspensions). Be sure to indicate in both your contemporary chord symbols and Roman numerals the proper inversion. (e.g. I6;Fmaj7/A). The first exercise (9b) provides a sample of the correct information to get you started.

Exercises 9b–9f

Exercise 9b and Example 9.8 JS Bach, Chorale 153

Exercise 9c and Example 9.9 JS Bach, Chorale 22

Exercise 9d and Example 9.10 JS Bach, Chorale 65


Chord Inversion Present and Past

Exercise 9e and Example 9.11 JS Bach, Chorale 42

Exercise 9f and Example 9.12 JS Bach, Chorale 26

Mozart, A Major Piano Sonata Provide contemporary chord symbols, key, and Roman numerals for this excerpt from the Mozart A Major Piano Sonata (Example 9.13). Notice that this passage contains one nondiatonic tone—a note outside the key of the piece. While we have not yet dealt with non-diatonic harmonies, after determining the chord of which the tone is a member, do your best to describe how that chord functions and assign it a Roman numeral.

Chord Inversion Present and Past


Exercise 9g and Example 9.13 Mozart, Sonata, K. 331, 1

Recommended listening: Daniel Barenboim, Mozart: The Piano Sonatas (EMI 1991).

The remaining exercises involve further instances of inversion in jazz and popular music contexts. Notice the contrapuntal line created between top voice and bass that is created by the use of inversion (contrary motion in 9h, oblique in 9i). Notice also how the sonorities of the most common diatonic chords (e.g. I6 and V6) are changed through the use of inversion. Keyboard and written exercise Play this progression, making sure that the notes given are the top notes of the voicings. Then write out in the very keyboard style you use to play the chords (two staves, threeor four-note voicing in treble clef, bass note—which is not always the root of the chord— in the bass clef).

Exercise 9h and Example 9.14 Written exercise Write a melody on these same chords and inversions, making prominent use of the notes given but with more florid rhythms.

Exercise 9i

Exercise 9i uses inversion to create a pedal effect, where chords change atop a stationary bass note. Notice the effect that results when the G pedal resolves down a half-step in bar 3


Chord Inversion Present and Past

to the first inversion V6 chord. Observe also the use of a non-diatonic chord in the first bar, which gives a glimpse of forthcoming terrain. How might this chord be analyzed in terms of a Roman numeral? Keyboard and written exercise Play this progression and then write it out in keyboard style.

Exercise 9i and Example 9.15 Written exercise Write a melody on the above chords, making prominent use of the notes given, but with more florid rhythmic values.

Exercise 9j

Pedal Point and Inversion Another approach to inversion is through the use of the pedal point, which is either a sustained or repeating single note in the bass atop which chords change. While pedal notes need not be chord tones, notice that in Example 9.16 the pedal note is indeed a member of each chord that sounds above it, even while these chords are derived from quite disparate key areas. Play the progression and notice how the pedal note upholds a strong unifying function amidst this harmonic movement.

Chord Inversion Present and Past



Written exercise Choose a pedal bass note and see how many different kinds of chords you can create above it.

Exercise 9k Composition exercise Create a composition in lead sheet form (melody and chord changes) in the following format. For the first eight measures use a pedal point, for the next eight (or more) bars move away from the pedal point and use chords with changing bass notes. In the second part, make some use of inversion to create a contrapuntal relationship between the bass line and the melody, along the lines of My Funny Valentine and Falling Grace.

Exercise 9l

chapter 10

Non-diatonic Harmony I: Applied Chords

In this chapter, we: • Begin work with non-diatonic harmonies in the form of applied chords (secondary dominant and secondary seventh chords), passing diminished seventh chords, and substitute dominant chords. • Do corresponding keyboard realization work. • Learn chord–scale relationships that correspond to non-diatonic harmonies. • Expand our free-tonicization work to include non-diatonic principles.

So far our consideration of tonality has been largely confined to diatonic harmony, where all chords encountered comprise tones within an overarching key area. Now we turn to nondiatonic harmony, in which some of the chords encountered contain tones that are not within the key. Non-diatonic harmonies can add color and variety to a given key and can manifest both as temporary movement to a new key, which is called tonicization, or a more permanent shift from one key area to another—called modulation—where the ear no longer hears the original I chord as the tonic but in fact hears a new chord as I. The first type of non-diatonicism we will examine involves applied chords, which come in two forms: secondary dominant chords (also called applied dominants) and the closely related secondary leading tone chords. Secondary dominants will be dominant-structure chords, as occur on scale degree V in major and minor keys; secondary leading-tone chords will be half-diminished (or minor7b5) structures as occur on VII in major keys, and fully diminished seventh chords as occur on VII in minor keys. In Chapter 11 we will take up another kind of non-diatonic practice called modal mixture, where chords are borrowed from a different mode than that in which a piece or section is rooted (e.g. a piece in major mode using a I minor or IV minor chord). We will see a fundamental distinction between the two kinds of non-diatonicism to be as follows: secondary dominant or secondary leading-tone

Applied Chords


chords will be either dominant, diminished, or half-diminished in quality, whereas modal mixture chords will be major or minor quality chords.

Secondary Dominant Chords Let us begin with the common diatonic chord sequence examined in the previous chapter: Cmaj7  Amin7  Dmin7  G7  I  VI  II V  Here is a common variation of this sequence, where a non-diatonic harmony is introduced: Cmaj7  A7


 Dmin7  G7 

 V7/II  II

V 

Example 10.1 provides notated versions of the two above closely related progressions:


Whereas the Amin7 chord, diatonic to the key of C, is analyzed as VI in the first example, the A7, which is non-diatonic (it contains a C#), must be analyzed differently. The


Applied Chords

A7 is a secondary dominant chord, and we analyze it as V7 of II or, as indicated, V7/II. Let us go into the reasons for this. Beginning with the differences in how the diatonic Amin7 and non-diatonic A7 sound: Play the two progressions at the keyboard. Notice that both chords follow smoothly from the I and lead smoothly to the II. But when the diatonic VI chord is changed to a dominant structure chord that is non-diatonic to the home key, additional color is added to the progression. Moreover, you will probably agree that the A7 drives more strongly than the Amin7 to the II chord. We call the A7 a secondary dominant chord because it functions not as V in the home key, but as V of another key center within the home key. In this case, the A7 is dominant in relationship to D, which is II in relationship to the home key of C. Following this same principle, a D7 chord in the key of C would by a V7/V; the D7 is non-diatonic to C since it contains an F# (and thus we cannot analyze the D7 as II even if the root of the chord is the second degree of the key) and, since D7 is V of G, which is V in the key of C, we arrive at the V7/V analytical description. A very simple formula can be identified here that helps us easily determine secondary dominant chords in any key: When a dominant structure chord is encountered that is not diatonic to a key, we call it V (or V7) not of the home key, but of the key or chord that the chord is V7 of. We can think of that implied destination—which as we will see is not always arrived at as the target key or chord. The relationship between the target key/chord and the home key is indicated to the right of the vertical slash (e.g. V7/V, or V7/II, or V7/III, etc.). Keyboard exercise Play the following progression in all 12 keys at the keyboard, proceeding chromatically or around the cycle of fifths. Imaj7 V7/II  IImin7 V7  Imaj7 

Exercise 10a

Let us now bolster our analytical grasp of secondary or applied dominant chords. Example 10.2 provides a handy illustration of the secondary dominants that are V of each diatonic chord in major.


Applied Chords


These drills will help you hone your understanding of these principles and enable you to become fluent in secondary dominant chords. Drills In the key of F, a D7 chord is analyzed as _____________. In the key of G, a B7 chord is analyzed as _____________.

b In the key of Ab, a Bb7 chord is analyzed as ____________. In the key of B , a D7 chord is analyzed as ____________.

In the key of A, a C#7 chord is analyzed as _____________.


In the key of G , an F7 chord will be analyzed as ________.

Exercise 10b

Secondary II–V7 Sequences Applied or secondary dominant chords are often preceded by their IImin7 chords to form a II–V relationship. So if we take the standard Imaj7  V7/II  IImin7  V7  sequence considered above, we can interject in the second bar the II of the applied dominant (not to be confused with the II of the tonic key) to form a secondary II–V7 sequence: Cmaj7  Emin7


 Dmin7  G7 

IIImin7 V7/II





Notice that the Emin7 can be analyzed in two ways—as IIImin7, since it is diatonic to the key of C, or as part of the II–V7/II sequence it forms with the A7. By including the II within the bracket we differentiate it from the ordinary, diatonic II chord. While each of the two interpretations is technically correct, analyzing chords in relationship with other chords is, generally speaking, preferable and thus we favor the second approach when the options present themselves. This situation arises in the following exercise and a number of others that follow. Provide both analytical interpretations in such instances.


Applied Chords

Analysis Identify the chord symbols, key, and Roman numerals for this progression (the progression is in a single key, which is not discernible by looking at the key signature due to the use of accidentals). Be sure to label secondary dominants properly, including bracketed II–V and secondary II–V sequences and arrows indicating resolution to target chords, as appropriate.

Exercise 10c and Example 10.3 Keyboard exercise • Realize this progression in several keys at the keyboard. Notice that the IVmaj7 chord becomes the I of the new key, necessitating that this sequence proceeds around the cycle. Imaj7 IV IIImin7 V7/II  IImin V7 I maj7 V7/IV  IVmaj7 new key: I maj7  IVmaj7 IIImin7 V7/II IImin7 etc. • Realize the following chord symbols.




Gmaj7 E7  Amin7 D7  Dmin7 G7  Fmin7 B 7  E maj7 C7  A maj7  D maj7  Cmin7  F#in7 B7  Emaj7  C#in7 F#7  Bmaj7  Gmin7 C7  Fmaj7  A min7 D 7  G maj7 





Exercise 10d

Secondary Dominant Chords of Non-diatonic Target Chord/Key Areas In each of the above exercises, the secondary dominant chord is V7 of a chord whose root is diatonic to the key, which is the most common form of secondary dominant harmonies. However, sometimes the target chord is non-diatonic to the key and must be indicated accordingly when we do Roman numeral analysis. To illustrate, a C7 chord (which contains a Bb) in the key of G is analyzed as V7/bVII: C7 is V of F, which is bVII in G. To call this C7 chord V7/VII would be incorrect, because VII in G is F#, and V7 of F# is C#7.

Applied Chords


Chord function analysis In the key of B, an A7 chord will be analyzed as ____________.

b b In the key of Gb, an E7 chord will be analyzed as ___________.

In the key of E , an A 7 chord will be analyzed as __________.

In the key of A, a C7 chord will be analyzed as _____________. In the key of G, an F7 chord will be analyzed as ____________.

Exercise 10e

Delayed Resolution of Secondary Dominant Chords Secondary dominant chords do not always resolve immediately to their implied target chords, and in some instances they never arrive at those destinations. However, the ear hears this chord as suggesting movement toward those targets, and the delaying or denying of the resolution can bring an element of surprise to the harmonic flow. The following is a common instance whereby the resolution is delayed:

Gmaj7  A7  Amin7  D7  Gmaj7 G: Imaj7  V7/V  IImin7  V7  Imaj7 Play the progression at the keyboard. The A7 V7/V clearly implies resolution to some kind of D chord, but the Amin7 thwarts this resolution momentarily. However, the fact that the A7 is followed by a minor chord on the same root maintains some degree of connectivity between the chords. And since the D7 comes shortly thereafter—so that the ear still retains the sound of A7—the sense of resolution, albeit with brief delay for variety, is upheld. Here are two more illustrations:

 Dmin7  Gmin7 Bbmaj7  D7 b B : Imaj7  V7/VI  IIImin7  VImin7

C7  Cmin7  F7  Bbmaj7 b B : V7/V  IImin7  V7  I maj7


Applied Chords

Here is another common sequence: Cmaj7  D7  Dmin7 G7  Cmaj7 Imaj7  V7/V  IImin7 V7  Imaj7 Keyboard exercise Realize this progression in multiple keys. Imaj7  V7/V  IImin7 V7  Imaj7 V7/IV  IVmaj7 (becomes new I)

Exercise 10f

Secondary or Applied Leading Tone Chords Because chords built on scale degree VII are quite similar in structure to those built on V— two notes in common between triads built on V and VII, and three notes in common between seventh chords built on V and VII)—secondary leading-tone chords are quite similar in function to secondary dominant chords. However, because the chord types falling on scale degree VII are either half-diminished (in major) or fully diminished (in harmonic minor), we analyze these chords not as V7 but as VII7 of some target chord. Therefore, in the key of F major, a Bmin7b5 is analyzed as VII7/V. Because B is nondiatonic to the key and it is a half-diminished seventh structure, we analyze the chord as VII, but not as VII of the home key of F, which would be E min7 (b5); rather, we analyze it in relationship to its implied target chord, which is C (B is VII of C). Since C is V in relationship to F, we analyze the chord as VII7/V. And in keeping with our policy of specifying chord quality when we analyze contemporary chord symbols, we will further specify that the chord is VIImin7(b5)/V. In Example 10.5, we encounter a fully diminished seventh chord—another chord that functions as VII—and can analyze it using the same procedure we use for the halfdiminished (minor7b5) chord. The chord in question—G#07—is VII of A, and since A is II in the key of G, we thus analyze the chord as a VII07/II.


Applied Chords



Chord function analysis This exercise will help you become more fluent with secondary VII chords:

b In the key of A, a D#min7(b5) chord will be analyzed as _________. In the key of C, a D#min7(b5) chord will be analyzed as _________. In the key of Bb, a Dmin7(b5) chord will be analyzed as _________. In the key of D, an A#min (b5) chord will be analyzed as _________. In the key of E, an A#min7(b5) chord will be analyzed as _________. In the key of Ab, an A min7(b5) chord will be analyzed as _________. In the key of Eb, an Fmin7(b5) chord will be analyzed as __________. In the key of B, a Dmin7(b5) chord will be analyzed as ___________. In the key of Db, a B0 chord will be analyzed as ______________. In the key of F, an Amin7( 5) chord will be analyzed as _________.

Exercise 10g

Passing Diminished Seventh Chords A subcategory of secondary VII chords that is common in jazz and popular music is the passing diminished seventh chord. Common instances are the Imaj7–#I07–IImin7 sequence, where the #I diminished chord smoothly connects the I and II chords, and IImin7–#I07–IImin7, IVmin7–#IV07–V7, and VImin7–#VI07–VIIm7)b5) sequences in which the diminished seventh chords function similarly. One could analyze these chords as VII07/II, VII07/III, VII07/V, and VII07/VII respectively, but because the diminished seventh chords are preceded and resolved by chromatic root movement and thus clearly function as passing chords, we will use the simpler and more pertinent description of how the chord functions. Thus, as illustrated in Example 10.6, a # before the Roman numeral


Applied Chords


will suffice—in this case the D#07 is labeled as #I07—and while it would not be incorrect, one need not indicate that the chord is VII of its target chord. However, if the diminished seventh chord is not preceded by a chord one half-step below yet still resolves one half-step upward, we will analyze it as a secondary seventh and thus VII07 of its target chord. Hence, as illustrated in Example 10.7, the progression Gmaj7–A#07-Bmin7 in the key of G will be analyzed as Imaj7–VII07/III–IIImin7 (and not I–#I0–III). Example 10.8 shows diminished seventh chords serving as embellishments to stationary chords in a II–V–I sequence.



Applied Chords


Substitute Dominant Chords Another non-diatonic practice that is indirectly related to applied chord functions involves replacing the diatonic V7 chord with a dominant chord a tritone away to yield an alternative melodic pathway in the bass to the tonic chord. For instance, instead of Dmin7–G7–Cmaj7, the Dmin7–Db7–Cmaj7 progression is sometimes used. The Db7 is called a substitute dominant chord, or “subV” for short (the abbreviation “sub” should not be confused with an abbreviation for the term “subdominant”). And because the roots of the diatonic V7—the G7—and the subV7—the Db7—are a tritone apart, this practice is also called tritone substitution. The interval of the tritone is also significant when it comes to substitute dominant seventh chords in that the third and seventh—the tendency tones of the chords that are separated by a tritone—are retained despite the substitution process. In other words, the third of the diatonic V7 is the seventh of the subV7, and vice versa, as shown in Example 10.9 (notice the use of enharmonic spelling, where the B of the G7 correlates with Cb of the Db7). The fact that it contains these tendency tones in addition to its strong bass movement is why the subV7 is such an effective alternative to the regular V7 in driving toward I. As shown, we analyze the substitute dominant seventh chord as subV7, although we will also encounter bII7 and even V7/bV (whose rationale is more theoretical than aural; the chord is clearly not heard as movement toward bV) as ways of analyzing these chords.


Secondary SubV7 Chords

Just as secondary dominant seventh chords are possible, so are secondary subV7 chords. For instance, the A7 in this progression: Cmaj7  A7  Dmin7  G7 : Imaj7  V7/II  IImin7  V7 : may be substituted with an Eb7: Cmaj7  Eb7

 Dmin7  G7 :

Imaj7  subV7/II  IImin7  V7 :


Applied Chords

Example 10.10 provides notated versions of these progressions. Observe again that both the V7/II and the subV7/II share the same tendency tones.


Written exercise Write out the listed chords:

Applied Chords


Exercise 10h and Example 10.11

Analysis Provide chord symbols, key, and Roman numerals for these progressions. Be sure to correctly identify the subV7s, secondary subV7s, and other non-diatonic chords. Use brackets to group II–V sequences, and use arrows to indicate when V chords (including subV7s) resolve to their target chords. (I)


Applied Chords


Exercise 10i and Examples 10.12–10.13

Improvising on Chord Sequences with Applied Dominant and Leading Tone Chords Similar to the way we approached improvising on diatonic progressions, our first step in improvising on progressions with non-diatonic harmonies will involve identifying chord–scale relationships. Recall that this entailed identifying an overarching parent scale as well as chord-by-chord scales. However, whereas in completely diatonic progressions the notes of the individual chord scales will all be contained with the overarching parent scale, when non-diatonic chords come into play, this will not be the case. Non-diatonic chords, because they contain tones outside of the key, require new scales that contain these notes. Nonetheless, a very simple principle continues to guide us in our correlation between chords and scales; that is, the Roman numeral function determines the scale that is called

Applied Chords


for. So whether a chord functions as V7 in the home key or as a secondary dominant, say as in a V7/II, both chords take a Mixolydian scale—built on the root of the chord (not the tonic note of the key!)—for improvising purposes. For instance, in the key of D, an A7— the diatonic V7 chord—takes A Mixolydian. And if the A7 chord occurs in the key of G where it is now V7/V, it still takes A Mixolydian. In sum: V7 chords, whether diatonic or not, take Mixolydian. Later we will consider further chord–scale possibilities for dominant seventh chords that involve altered scales. Accomplished jazz improvisers more commonly than not use some form of chromatic alteration on dominant seventh chords even if the chords themselves are unaltered. The same principle applies when it comes to secondary VII chords, and here we will confine our chord-scale analysis to half-diminished seventh (thus minor seventh flat 5) chords. Whether a VIImin7(b5) chord is diatonic or non-diatonic, it will take Locrian mode. Why? Because Locrian is the mode built on VII. Thus, an A min7(b5) chord in the key of Bb, where it functions as VII, or the same A min7(b5) chord in the key of Eb, where it functions as VII/V, will take A Locrian. Other alternatives will be presented in later chapters. Analysis Do Roman numeral analyses, and then chord-scale analyses of the following progressions. Then improvise on the progressions. Fmaj7  Fmaj7  G7  G7  Gmin7  C7  Fmaj7  Fmaj7 : G  E7  Amin7  D7 :


Cmaj7  Cmaj7  Fmaj7  Fmaj7  Emin7( 5)  A7  Dmin7  G7 :

Exercise 10j

Composition Compose a song form melody and quasi-improvised (review Chapter 7) on one of the above progressions, making sure you adhere to chord scales.

Exercise 10k

Composition Compose a quasi-improvised melody (review Chapter 8) on one of the above progressions, making sure you adhere to chord scales.

Exercise 10l


Applied Chords

Analysis exercises In these two exercises, provide key, chord symbols, Roman numerals, and names of corresponding chord scales. Be sure to use brackets and arrows, as indicated in previous examples, as appropriate. 10m


Exercise 10m–n and Examples 10.14–10.15 Written exercise Provide written realizations, key, Roman numerals, and chord scales for the following progressions: B7  Bmin7 E7  Emin7 A7  Amin7 D7  Gmaj7 :




E maj7  Gmin7  Cmin7  F7  B maj7  E maj7 :






Fmin7  B min7  E 7  A maj7  D maj7  Cmin7  F7  B maj7 :


Cmaj7  Bmin7( 5) E7  Amin7 D7  Dmin7 G7 :

Exercise 10o Keyboard exercise Realize in 12 keys at the keyboard the following progression:


Imaj7  VIIm7( 5) V7/VI  VImin7 V7/V  IImin7 V7  Imaj7  V7/IV  IVmaj7  (IV maj7 becomes new Imaj7)

Exercise 10p

Applied Chords


Free-tonicization Strategies Level II Now we continue our work with the free-tonicization techniques introduced in Chapter 6, with the addition of substitute dominant and passing diminished seventh chords (applied chords were implicit in our prior free-tonicization work). Again, the phrase free tonicization, while perhaps suggestive of modulation, involves temporary movement to new key areas (modulation indicates a more permanent establishment of a new key area). Moreover, the progressions we will create here will not be rooted in a single overarching key area in relation to which all the chords may be analyzed. Rather, Roman numerals will be used to explain only relationships between small groups (e.g. II–V–I; or I–IV) of chords that imply a key area in a given moment. As established in Chapter 6, only two or three chords per key area will generally be involved (a minimum of two covers a key area, a maximum of four in succession from any given key area is allowed). The following is a review of strategies introduced in free-tonicization I: 1. Any major 7 chord can be treated as I or IV and followed by another other chord diatonic to that key area. 2. Any major 7 or dominant 7 chord may be followed by a minor chord on the same root: Cmaj7 Fmaj7  Fmin7 3. Any min7 chord may be followed by its related V7 to form a IImin7–V7 link:


Cmaj7 Fmaj7 Fmin7 B 7 4. Any II–V may be followed by its I, or any other II–V, or II–V–I sequence:




 Bbmin7 E 7  A maj7  Cmaj7 Fmaj7 Fmin7 B 7


5. Any min7( 5) chord may be followed by a min7 chord up a fourth to form a VIImin7( 5)–IIImin7 sequence, or a dominant seventh chord up a fourth to form a IImin7( 5)–V7 sequence:








Cmaj7 Fmaj7 Fmin7 B 7 B min7 E 7  A maj7  Gmin7( 5) Cmin7  Let us now add to this list of possibilities. 6 Any V7 may be replaced by its subV7: Dmin7 G7 Cmaj7 Dmin7 D 7 Cmaj7 IImin7 subV7 Imaj7


7 Any two chords a whole step apart may be connected by a passing o7 chord: Cmaj7 C#07 Dmin7 Imaj7 #I07 IImin7


Applied Chords

Seminal Keyboard Project 4 SEMINAL KEYBOARD PROJECT 4



Create a chord sequence, to be notated in contemporary chord symbols, that uses the seven free-tonicization principles presented so far. The sequence should cover all 12 key areas, with a minimum of two chords needed to cover a given key area, and a maximum of four successive chords from any area allowed. Be able to play the sequence from the chord symbols with solid rhythm. No transposition to multiple keys is required. Realize at the keyboard this progression in all 12 keys (review Exercise 10d). Compose melody atop the chords in one of the keys and sing it when you play the progression. Imaj7  IVmaj7  IIImin7 V7/II  IImin7 V7  Imaj7  V7/IV  IVmaj7 (IV maj7 becomes new Imaj7)

Exercise 10q

SUMMARY QUESTIONS 1 Distinguish between diatonic and non-diatonic harmonies. 2 Name the first type of non-diatonic harmony encountered in this book. Provide an example. 3 How would an F#min7 chord in the key of D major be analyzed with Roman numerals? An F#7 chord in the same key?


4 How would an E07 chord be analyzed in the key of B major? (a) If the chord were preceded by E maj and followed by F7? (b) If the chord were preceded by B major and followed by F7?

b b

5 What scale would be used for improvising over these chords in the listed keys: (a) Cmaj7 chord in the key of G major. (b) Fmin7 in the key of D major. (c) D min7( 5) in the key of E major.




chapter 11

Non-diatonic Harmony II: Modal Mixture

In this chapter, we: • Learn a new type of non-diatonic practice: modal mixture. • Do corresponding keyboard realization work, analysis, and writing. • Learn chord–scale relationships that correspond to modal mixture harmonies for improvising purposes. • Expand our free-tonicization work to include non-diatonic principles.

In the previous chapter we examined secondary dominant chords, secondary leading-tone chords, and substitute dominant chords as initial kinds of non-diatonic harmony. Now we consider a second form of non-diatonicism, described variously as modal mixture, modal interchange, or borrowed chords. These terms derive from the practice, common in jazz, popular, and European classical music, of temporarily borrowing chords from a mode other than that which prevails in a given piece or section of a piece. A common case is when a piece is in a major key (which is also referred to as the major mode) and makes use of one or more harmonies that are diatonic to the parallel minor key (minor mode); therefore, a piece in the key of F major might use an F minor chord (which is labeled as I min) or a Bb minor chord (IV min) instead of, or in addition to, F major and Bb major (I and IV) chords. Hence, major and minor modes are being mixed, which is the application to which the heading modal mixture most commonly applies. Modal mixture has the capacity to produce colorful sonorities within a harmonic sequence through the use of chords that introduce two or more accidentals yet do not interrupt but rather enhance the melodic and harmonic flow. The following is a common case shown in jazz/pop chord symbols; modal mixture chords are in bold: Imaj7 Imin7  VIImin7(b5) V7/III  IVmaj7 IVmin7  IIImin7 V7/II  IImin7 V7  Imaj7


Modal Mixture

Notice in the above progression the way modal mixture enables smooth connections between chords. In both instances, modal mixture (I to Imin, IV to IVmin) allows significant harmonic motion to occur above stationary bass notes, which then resolve down by a half-step. Notice also the use of secondary dominant harmonies in the same progression, which resemble modal mixture harmonies in that they are non-diatonic, but differ in their chord structures. Modal mixture chords are generally minor or major quality chords (or minor or major seventh, ninth, or further extended chords), whereas secondary dominant and secondary leading tone chords are the less stable dominant, diminished, and half-diminished structures. In the second category, the tritone interval is critical as it inheres in these chords a tendency to drive toward a target chord, whether or not they actually land on that target. The tritone interval will generally be absent in modal mixture harmonies, with the maj7(#11) chord being one exception that is found in jazz. While modal mixture harmonies, as the above progression shows, can also lead toward target chords, they uphold in these instances more of a passing function than the goal-directed motion that characterizes secondary dominants. The more stable construction of modal mixture harmonies, moreover, allows them to also serve as target chords, which is far less common with secondary dominants and related chords. We will find instances of both below, as well as cases in which the distinctions between passing and target functions are nebulous.

Modal Mixture on Diatonic and Non-diatonic Roots Let us begin by identifying two basic instances in which modal mixture harmonies appear: on diatonic roots and non-diatonic roots. Example 11.1 provides both. The passage is in F major. Notice that an Fmin7 chord appears in the first bar. We analyze this chord as Imin7; the I tells us that the root of the chord is identical to the major I chord and thus diatonic to the key, and the min7 tells us that the quality of the chord is minor and thus nondiatonic. In bar 3 we encounter an Abmaj7 chord. Now our analysis needs to indicate that both the root and the rest of the chord are non-diatonic. We therefore analyze this chord as bIIImaj7. Whereas we analyzed secondary dominants and secondary leading tone chords in terms of their implied target chords (e.g. an A7 in the key of F is V7/VI) in analyzing modal mixture harmonies, all information is provided through the Roman numeral and the quality that is listed after it.


Modal Mixture


Passing and Structural Functions in Modal Mixture Harmonies Now let us consider what kinds of functions the above modal mixture harmonies uphold. Clearly, the Fmin7 in bar 1, as a Imin7 chord that connects Imaj7 and VIImin7(b5), upholds a passing function. An important reason for this is that the chord occurs on the second half of the measure, which tends to be structurally weaker than chords sounding on the first half (an exception to this might be when a major chord on the second half is preceded by its V7). A second reason is the smooth voice leading that this sequence involves: the common tone root movement between the first two chords is followed by half-step movement leading to the VII, and the first two chords share two common tones and only require half-step motion downward in two other voices. That this half-step motion, moreover, involves guide tones—the highly active third and seventh of these chords—is significant as it strengthens the pattern of half-step movement such that the ear anticipates it will continue upon arrival at the VII chord. This expectation is fulfilled as movement in three voices between I min and VIImin7(b5) proceeds by a half-step. Similar smooth voice-leading patterns are evident in the case of the bIIImaj7 (Abmaj7) in bar 3. This chord shares two common tones with the preceding chord, and the bass moves downward by only a half-step. Notice also that stepwise movement, including two halfsteps, is involved when Abmaj7 moves to Gmin7. However, because the Abmaj7 chord occupies an entire measure by itself, it upholds more of a structural than a passing function. This will likely be evident when you play the progression. Example 11.2 presents a chord progression that includes a secondary dominant chord and use of modal mixture. While both chords are movement-driven, the difference in their intervallic structures allows them to uphold this movement in different ways. Play the progression slowly and allow yourself to feel the different sonorities and the expectations that they set up and fulfill. How does the D7 differ in how it sounds, feels, and moves to Gmin7 from the Gbmaj7—clearly a passing chord because of its occurrence on the weak part of the measure and its smooth voice-leading movement—and in how it sounds, feels, and progresses to F7?



Modal Mixture

Keyboard exercise Realize the following three different chord sequences in several keys at the keyboard:

b Imaj7 Imin7  VIIm7(b5) V7/VI  VImin7 V7/V  IImin7 V7  bIImaj7  Imaj7  Imaj7 Imin7  VIIm7(b5) V7/VI  IIImin7 V7/II  bIIImaj7  IImin7 V7  Imaj  Imaj7 Imin7  VIIm7( 5) V7/VI  VImin7 V7/V  IImin7 V7  Imaj 

Exercise 11a Analysis Provide chord changes, key, and Roman numerals for this progression. Be sure to use correct Roman numerals for the different kinds of non-diatonic chords in the sequence. As instructed in the previous chapter, use brackets to group II–V and secondary II–V chords, and arrows to indicate when V7 (including secondary V7) chords resolve to their target chords.

Exercise 11b and Example 11.3

The Brahms excerpt (Example 11.4) shows another instance of modal mixture. Notice that two chords are borrowed from the parallel minor: i6 and bVI6. (Recall our use of small case Roman numerals for minor and diminished chords in European classical analysis.) In addition, appreciate the use of inversion in the borrowed chords to create contrary motion in the outer voices, where an ascending bass line complements the descending gestures in the melody. Recommended listening: London Philharmonic, Brahms, Symphony No. 3 in F major (Naxos 2006)

Modal Mixture


Example 11.5 presents an instance of modal mixture in the music of the legendary Brazilian composer Antonio Carlos Jobim. While it contains a chord type we have not yet encountered, it is closely related to the major seventh structure with which we have now become quite familiar.

EXAMPLE 11.4 Brahms, Symphony No. 3 in F major (piano reduction)

EXAMPLE 11.5 Antonio Carlos Jobim, “Triste.” © 1967 Antonio Carlos Jobim.

Recommended listening: Antonio Carlos Jobim, Wave (UMG 1967)


Modal Mixture

The piece is in A major, and in bars 3 and 4 borrows the Fmaj7(b5) chord from the parallel A minor mode. As the chord symbol specifies, this chord is easily understood to be a major seventh chord with a lowered fifth. In this instance, the chord is found with its third in the bass (hence the Arabic numeral in the underlying analysis), providing an instance of the pedal point technique we considered in Chapter 7 where chords move atop a stationary bass note, in this case A. Somewhat rare in common practice jazz harmony, the major 7 (b5) chord has been used frequently in jazz since the 1960s. We will put this chord to good use in forthcoming chapters as a device that enables us to arrive at several extended and altered chord voicings as well as a chord that stands on its own, as it does here, as an interesting sonority in its own right. Notice that in bar 7, harkening back to a point addressed in the previous chapter, the C#min7 chord is analyzed as both the diatonic chord IIImin7 and also is as part of a secondary II–V sequence (II–V/VI); it is important to recognize both ways of thinking of this chord. Let us look at further instances of modal mixture. Example 11.6 makes more extensive use of the practice in its first two bars where, instead of single non-diatonic chords, a sequence of three such chords is found. Note two effects here. One is the sheer richness of this kind of non-diatonic movement, where wide-ranging key areas are traversed within a short length of time—involving at least two accidentals from one chord to the next. In addition, the relatively equal weight the chords uphold, whereby instead of functioning as connecting links between clear structural points, each chord serves more as an autonomous island unto itself. This is evident the more slowly the progression is played. In bar 2, the Bbmaj7 is not prepared by the Gmaj7, nor does it prepare the Bmaj7 chord (which in turn does not prepare the Emaj7). Rather, these chords are self-contained landing points, even if not very long in duration. This kind of motion is sometimes described as non-linear in nature because each chord functions as a self-contained entity, as opposed to when chords function as interdependent links within a linear chain—an effect that is more prominent in the second part of the progression, where II–V7 sequences assume a much more goaloriented trajectory in leading back to the I chord. Play the progression slowly and compare the sounds and feeling of the two kinds of harmonic activity.


Modal Mixture


Improvising on Modal Mixture Progressions While modal mixture expands our palette of harmonic strategies and colors, the principles involved in improvising on these progressions are similar to those encountered previously with secondary dominants and secondary VII chords. Identification of chord–scale relationships, in fact, is quite easily done with modal mixture harmonies since the chords are either minor or major quality. Accordingly, we have several options with each chord type. Major chords (either major triads, seventh chords, ninth, or # eleventh chords—the latter two extensions to be considered later) will take the Lydian mode, which you will recall is a major or Ionian mode with a raised fourth degree. It is also possible to use Ionian on all but major seventh (#11) chords, although this scale choice does not blend as smoothly into the overall harmonic fabric for reasons to be discussed below. Minor chords (either minor triads, seventh chords, or chords using higher extensions triads) will take the Dorian mode. Aeolian may also be possible, except in the cases of minor sixth or thirteenth chords, although, like the Ionian on modal mixture major chords, this mode choice does not blend as smoothly into the harmonic fabric. Whenever questions arise regarding the choice between two similar scales or modes, the governing principle in both instances is as follows: Consider what chord (and thus related chord scale) comes before and after the chord in question. In nearly every instance, modal mixture major chords are surrounded by chords that mitigate toward Lydian rather than Ionian because the raised fourth degree of the scale will be more prominent in the vicinity of the chord in question than the natural fourth degree of the Ionian mode. Similarly, modal mixture minor chords will be more conducive to Dorian because the raised sixth degree that distinguishes Dorian from Aeolian will be more prominent in the general vicinity of the chord in question. Let us apply these principles to the following progression: Fmaj7  Fmin7  Emin7(b5)  Amin7 Imaj7  Imin7  VIImin7(b5)  IIImin7 The Imin7 (Fmin7) will take Dorian, even if the chord does not function as II. Why? Because the note D, not Db (which would be from an F Aeolian scale), is found in the chord scale of the Fmaj7 that precedes it and is a chord tone of the Emin7(b5) chord that follows it. The co-existence of common tones as well as significant movement outside of the key area contributes to a strong musical flow and coherence.



Modal Mixture

Here is another illustration: Bbmaj7  D7  Gmin7  Gbmaj7  F7  Bbmaj7 Imaj7  V7/VI  VImin7  bIImaj7  V7  Imaj7 The Gbmaj7 chord will take Lydian because the Gmin7 chord prior to the Gb, and the F7 after it, contain a C either in the chord itself or in the chord scale. The Lydian is therefore more consistent with the framework at the time and the C will provide nice connectivity to balance the fairly significant movement outside of the key caused by the Gb chord.


Analysis Provide Roman numeral analysis and chord-scale analysis for the following progressions, and then improvise on them:


Fmaj7  Fmaj7  Fmin7  Fmin7  Emin7( 5)  Amin7  Gmin7  C7 Fmaj7  Fmaj7 : Dmaj7  Dmaj7  Fmaj7  Fmaj7  Abmaj7  A maj7  Gmaj7  F#min7 B7  Emin7 


A7 :

Exercise 11c

Composing Composition Compose melodies in song-form and quasi-improvised styles on the above two progressions using the appropriate chord scales. Comp changes at the keyboard and sing melodies.

Exercise 11d

Modal Mixture


Analysis Exercises The following notated passages include diatonic, and the two categories of non-diatonic harmonies—secondary dominant/secondary VII chords, and modal mixture—that we have covered thus far. While the progressions make considerable use of non-diatonic chord movement, including cadential activity that may imply multiple tonic keys, they are analyzable in a single key and designed such that the ear hears the progression that way. Therefore, it will be necessary to carefully assess which key area is most strongly implied through corresponding cadential movement. In one of the examples no tonic chord is given, yet the progression is still analyzable in that key due to the presence of its V7 and other diatonic chords. The following is a handy guide to the proper way of indicating the different types of chords.

Step 1: Identify chords and label by chord symbol. Step 2: Determine key by identifying cadential activity and real or implied target chords. When two or more keys appear to be viable possibilities, determine which is supported by a greater amount of cadential activity as well as other diatonic chords within that key. Step 3: Once the key is determined, diatonic chords can be analyzed by corresponding Roman numerals. Step 4: In the case of non-diatonic chords, two strategies are possible according to what type of non-diatonic chord is involved. If the chord is 1) dominant, diminished, or half-diminished, it will be analyzable as a secondary dominant (V7/x) or secondary leading tone (VII0/x or VIIm7( 5)/x) chord; or if a 07 chord is preceded and followed by a half-step, analyze it as a passing dim7 chord (e.g. #I07, or #II07).


If the chord is (2) major or minor (including extensions of these chords), it will be an illustration of modal mixture, in which case the scale degree of the root is indicated by Roman numeral (e.g. III, VI) and the quality of the chord is indicated by the same information given in the contemporary chord symbol.


Analysis Provide chord symbols, key, Roman numerals, and chord scales for the following notated progressions. Be sure to provide brackets and arrows as appropriate.


Modal Mixture




Modal Mixture



Exercises 11e–h and Examples 11.9–11.12

The Neapolitan Sixth Chord Closely related to modal mixture is the Neapolitan sixth chord in European classical music, which is a bII chord that is often found in first inversion, hence the “sixth” in the label. The chord is most commonly found in minor keys and usually functions as a preparation for the dominant, as illustrated in the passage from a Chopin prelude shown in Example 11.13. Notice the uplifting sonority and brightness of the chord as it connects the darker i minor 0 and vii chords.

Recommended listening: Rudolf Serkin, Chopin, 24 Preludes (Sony BMG 2004)



Modal Mixture

Free-tonicization Level III We can now expand our list of free-tonicization strategies presented in previous chapters to include modal mixture practices. With full recognition that the scope of possibilities far exceeds what might be practically included in such a list, we will add three practices to our palette that will significantly enhance our capacity to create interesting harmonic progressions. 1 Any Imaj7, IVmaj7, or V7 chords may be followed or replaced by a minor chord on the same root (this is a replication of strategy 2, but in a new context). Cmaj7  Fmaj7  Fmin7 


2 Any IImin7, IIImin7, VImin7, or VIImin7( 5) chords may be followed by a maj7 chord whose root is a half-step below.


Cmaj7  Fmaj7  Emin7 E maj7  Note that there are two common tones—G and D—between Emin7 and E maj7 chords.





3 Any II–V7 sequence may resolve to its IIImaj7, VImaj7, or II maj7.

Let us now recap the complete list of strategies: 1 Any major 7 chord may be treated as I or IV and followed by another other chord diatonic to that key area. 2 Any major 7 or dominant 7 chords may be followed by a minor chord on the same root. 3 Any min7 chord may be followed by its related V7 to form a IImin7–V7 link. 4 Any II–V may be followed by its I, or any other II–V, or II–V–I sequence.


5 Any min7( 5) chord may be followed by a min7 chord up a fourth to form a VIImin7( 5)–IIImin7 sequence, or a dominant seventh chord up a fourth to form a IImin7( 5)–V7 sequence.



6 Any V7 may be replaced by its subV7. 7 Any two chords a whole step apart may be connected by a passing o7 chord. 8 Any Imaj7, IVmaj7, or V7 chords may be followed or replaced by a minor chord on the same root (this is a replication of strategy 2, but in a new context).


9 Any IImin7, IIImin7, VImin7, or VIImin7( 5) chords may be followed by a maj7 chord whose root is a half-step below.




10 Any II–V7 sequence may resolve to its IIImaj7, VImaj7, or II maj7.

Modal Mixture


Free tonicization Create a free-tonicizing progression using all of the strategies at least once, and making sure that all 12 keys are represented at least once (remember: at least two chords are needed to imply a given key area; four chords from a key area in succession maximum). Notate with contemporary chord symbols. Play the progression with steady rhythm. Create further progressions for sight-reading practice.

Exercise 11i

Modal Mixture as an Entry Point into Modal Composition Techniques Modal mixture, as noted at the beginning of this chapter, is a practice that generally occurs within tonal contexts, meaning that a piece in a given major or minor key—as established through ample dominant–tonic chord movement (V7–I) will temporarily borrow one or more chords from the parallel or relative major or minor key, or perhaps some distantly related key area. Modal mixture is thus distinguishable from modal composition, in which dominant–tonic relationships are rare or, as is often the case, entirely absent. We gained an introduction to a more traditional form of modal composition in Modal Etudes 1 and 2, from Chapters 3 and 4, in which whole compositions were constructed using just one (Etude 1) or two (Etude 2) modes. More contemporary modal composition techniques move more freely between modal areas, stretching the traditional definition of modality as confined to a single mode, and some of the modal mixture techniques considered in this chapter open up connections to this kind of approach. The following are several prominent practices: 1 Root Movement by Half-steps and Thirds

Whereas root movement involving ascending fourths and descending fifth intervals, as exemplified in the III–VI–II–V–I sequence, is common in tonal music, modal music makes considerable use of root movement by half-steps and minor thirds, in addition to the juxtaposition of chords from distant key areas. For example, a common type of movement will involve a major seventh chord followed by a minor seventh chord whose root is a half-step above: F maj7  F#min7  Notice that there are two common tones—A and E—between these chords, which creates a unifying effect when they sound in succession. At the same time, the chords derive from very distant modal areas. The co-existence of these highly unifying and diverse tendencies contributes to a colorful harmonic texture. Play the chords, creating a two-chord vamp or repeating pattern with them, so that you can hear both qualities of the sequence. Play the


Modal Mixture

chords in different inversions, always striving for smooth voice leading when moving from one to the other. The following is a continuation of the progression that employs root movement by a minor third in several instances, another common modal practice: Fmaj7  F#min7  Amin7 Abmaj7  Cbmaj7  Cmin7  Ebmin7  Emin7 : Notice that even when the roots move by thirds, significant common tone activity is sustained between chords. For example, F#min7 and Amin7 share A and E; try playing the progression with the E in the top voice through the first three chords. Amin7 and Ab7 share G and C. Abmaj7 and Cbmaj7 share Eb and Gb; try playing the chords with the Eb in the top voice. 2 New Chord Structures

One of the reasons that major 7 and minor 7 chords have become prominent in modal music is that they are more stable than dominant seventh chords, thus allowing a harmonic flow that moves freely between modal areas without a given chord assuming prominence (this presumes that all chords occupy generally the same length of time). In tonal music, by contrast, a single V7-I cadence can strongly steer the harmony toward a given tonal area. However, in order to achieve a level of variety that is not possible with exclusively minor and major seventh chords, other chord structures, even if closely related, have become equally prominent. We have already considered sus chords (Chapter 9), major 7(b5) chords (Chapter 11), and pedal points (Chapter 9) in other contexts. These are effective devices in modal composition. In Chapters 13 and 14 we will consider chord extension, for which modal music is highly conducive due to the increased dissolution of boundaries between chords and scales. As stated previously, a modal area may be thought of as a pitch region that may manifest vertically in the form of chords, or horizontally in the form of scales and melodies. Chords in modal music may be approached as modes stacked vertically, and modes as chords spread out over time. Further modal approaches will be presented in Chapter 16. Composition Compose a modal composition in lead sheet form (melody and chord symbols) that moves between disparate key areas and makes use of the half-step and minor third root movement discussed above. This is not to suggest that other types of root movement are possible as well, but avoid the use of dominant seventh chords. Try to make use of common tones in the melody.

Exercise 11j

Modal Mixture


Creative Synthesis Having immersed ourselves in syntactic study, primarily in the realm of harmony, it can be beneficial to step back and create music with no style constraints specified in advance. Here a return to some of the trans-stylistic strategies introduced in Chapter 1 may both provide welcome variety as well as serve as barometers for the progress you have made. Try improvising with non-syntactic catalysts such as density, dynamics, and registral variety, and you will likely find you will bring a much-expanded skill set to these formats. Creative project Create music in your small group that involves both trans-stylistic improvisation formats—where style constraints are not specified in advance, which allows the music to draw from diverse style sources—and style-based (e.g. time feels, chord changes) approaches to improvising and composing. The piece should comprise several movements, which may be continuous or separated by a break. You are encouraged to use this as an opportunity to let your imagination run free.

Exercise 11k

SUMMARY QUESTIONS 1 Modal mixture is the second form of non-diatonic harmony we have encountered. What forms preceded it? 2 Define modal mixture and provide two other names for this strategy. 3 Of the kinds of non-diatonic harmony we have considered so far, in which is the tritone interval prominent? 4 Provide examples of modal mixture harmonies on both diatonic and non-diatonic roots (e.g. in the key of D major, an example of a modal mixture harmony on a diatonic root would be a _________ chord; on a non-diatonic root would be _________). 5 A modal mixture chord can have a non-diatonic root while the rest of the chord tones are diatonic to the key or key area of the moment. True or false? 6 Modal mixture chords on diatonic roots are a form of diatonic harmony. True or false? 7 Describe the difference in how passing modal mixture chords and structural modal mixture chords function and are thus heard. 8 Modal mixture is unique to jazz and popular music. True or false?


Modal Mixture

9 What is the basic principle that determines whether or not a non-diatonic chord is an example of modal mixture or a secondary dominant or secondary leading tone chord? 10 What is the primary difference in how these different non-diatonic functions (secondary dominants/leading tone chords and modal mixture harmonies) are represented in Roman numeral analysis? 11 Modal mixture major chords will tend to take Ionian or Lydian modes (circle the most common choice) as chord scales for improvising. 12 Modal mixture minor chords will tend to take Dorian or Aeolian modes (circle the most common choice) as chord scales for improvising.

chapter 12

Figured Bass Realization at the Keyboard

In this chapter, we: • Gain a hands-on and theoretical introduction to figured bass realization at the keyboard. • Compare baroque figured bass chord symbols with contemporary chord symbols.

Whereas contemporary keyboardists improvise using modern chord symbols— Amaj7, F7(b9), etc.—to designate harmonic structures and progressions, seventeenth- and eighteenth-century European keyboardists improvised using a different set of symbols that nonetheless provided similar harmonic information. That set of symbols was the figured bass line, which we have already encountered briefly from an analytical standpoint. We will now engage in figured bass realization at the keyboard in order to directly experience this system of harmonic practice. As discussed in Chapter 8, the triadic and seventh chord textures of European classical music make possible uses of inversion and voice leading that are sometimes obscured in the denser harmonic textures of contemporary tonal music. The introductory exposure to these principles provided in this chapter will help us connect with tonality’s roots.

Basic Principles Figured bass nomenclature involves three basic components: a bass line; a set of figures designated by Arabic numerals, which indicate what notes are to sound atop each bass note; and a key signature that indicates the quality of the interval between the bass and upper notes (e.g. whether the fourth above a bass note F is B or Bb). These components indicate precisely what chord is to sound at a given time and its inversion and may be thought of in terms of


Figured Bass Realization at the Keyboard

vertical and horizontal information. Vertical information has to do with the intervals atop each bass note that are specified by the figures; horizontal information comes from the key signature. Whereas contemporary chord symbols do not require consideration of the key signature—an Fmaj7 chord will consist of the same notes whether the key signature is one flat or six flats—a notated F with the figuration 7 above it in the figured bass system could be F7, Fmaj7, Fmin7, F07, Fmin7(b5), etc., depending upon the key signature.

Triads Example 12.1 illustrates how root position and inversions are represented in figured bass nomenclature, using various configurations of an F major triad. For each position, shorthand indications are provided after the complete figures; these are commonly used and it is essential to become familiar with them. Contemporary chord symbols are listed atop each chord. The use of the shorthand indication points to a similarity between figured bass and contemporary chord symbol nomenclature in the representation of root position triads. Just as in contemporary practice, where a letter name by itself will suffice to indicate a root position triad, in figured bass, a bass note by itself will similarly suffice to indicate a root position triad. In the absence of additional information, it is presumed in both instances that notes a third and a fifth are to sound above the bass note. An important difference however is in representing the quality of the triad. Here is where the key signature is critical in the figured bass system. Example 12.2 shows the same F bass note with root position figuration and different key signatures. Consider the different triads that result, even if all are in root position. The


Figured Bass Realization at the Keyboard



second triad is F minor because the third above the bass note is Ab according to the key signature. The third triad is F diminished because the note a fifth above the bass note is Cb. Let us now turn to seventh chords.

Seventh Chords Root position, first inversion, second inversion, and third inversion configurations are possible with seventh chords, as indicated in Example 12.3. Again, we encounter parallels and differences in the two systems. In contemporary chord nomenclature, a letter name with only a seventh indicates a root position seventh chord; in figured bass, a bass note with a figuration of a seventh indicates the same thing. In both systems, the indication of a seventh presumes that a triad will also sound. And once again, key signature plays an essential role in figured bass nomenclature, as the same F bass note with figuration 7 can yield several different chords.




Figured Bass Realization at the Keyboard

Accidentals Having examined the three possible configurations of triads and the four configurations of seventh chords, we now turn to one further aspect of figured bass nomenclature before directly engaging with keyboard application of the principles. This has to do with the way accidentals are indicated in the figures. By placing a flat (b) before a figure, that note is lowered by one half-step. By applying a slash (/) to the figure, that note is raised by one half-step; the slash thus serves as a sharp. A flat appearing by itself—that is, not in front of a figure (but it could be below another figure which it does not affect)—indicates that the note a third above the bass note is to be lowered by one half-step. A sharp (#) appearing by itself (again, could be below another figure) indicates that the note is raised by one half-step (see Example 12.5).


We will soon realize figured bass lines in written and keyboard formats using two clefs. The following written exercise, confined as are the above examples to the bass clef, will help you get a handle on the basic concepts. Written exercise Write out these chords from the figured bass notes given (write notes atop bass note). In addition, provide contemporary chord symbols, making sure to indicate inversion. Key signatures hold until the next key signature change.

Exercise 12a and Example 12.6

Figured Bass Realization at the Keyboard


Voice Leading and Doubling Considerations Recall from our prior consideration of voice leading the following principles. A first priority was that our voice leading is conjunct rather than disjunct, that voices move smoothly from one to another. In order to do this, we retain the common tone when possible and move all other voices to the closest note. We also considered the independence principle, which delineated contrary, oblique, similar, and parallel kinds of motion between any two or more voices. Voices maintained optimal independence when moving in contrary motion, and minimal independence when moving in parallel motion, with independence most compromised when moving in parallel perfect intervals. Recall also the role of musical context in determining the weight of these principles; the thicker textures of contemporary tonality, where all chords are at least seventh chords and are often extended beyond the seventh, not only make adherence to these principles often difficult if not impossible, but the richness of the sonorities renders the principles at times musically irrelevant. When possible we apply them to the outer voices, as these are more prominent in the harmonic-melodic flow. In the thinner textures of European common practice harmony, where triads and moderate seventh chord activity predominate, these principles are more central to the harmonic-melodic flow. As we move into figured bass realization in two-stave formats, let us keep these principles in mind. Example 12.7 shows a figured bass line realized in two clefs. In essence, we have simply taken the realized chords that we had been writing entirely in the bass clef in the previous examples and exercises from this chapter and distributed them to two clefs. Notice that consistent with the keyboard approach we have been using for contemporary chord progressions, a bass note is indicated in the bass clef and the remainder of the chord in the treble clef—in baroque style this is in fact called “keyboard style” realization. Triads are voiced with three notes in the treble clef, and seventh chords are voiced either with three or four notes (for the sake of consistency with contemporary keyboard practice, voicing seventh chords using a four-note voicing in the treble clef, which involves doubling the bass note, is acceptable so long as that note is not a tendency tone). Smooth voice leading remains a priority. Notice also the use of contrary and oblique motion between the lowest and highest voices in the opening two bars. Retaining the common tones and moving the other notes to the next closest notes—the conjunct principle—resulted in an effective realization in the above notation. Problematic parallel motion between perfect intervals was avoided, and a fair degree of independence was maintained in the outer voices through the contrary and oblique motion discussed



Figured Bass Realization at the Keyboard

above. While the conjunct principle in itself will often yield such results, it is important to address situations that require additional attention. A common situation involves doubling strategies. It is not always desirable to double the bass note in the upper realization, particularly when the bass note is a tendency tone. Tendency tones, being inherently unstable, are predominant sonorities in a harmonic fabric whose effect is excessive when they are doubled. The leading tone of a key is a tendency tone that is commonly encountered in the first inversion of the V chord, where the tone occurs in the bass and thus should not be doubled in the upper voices. Example 12.8a shows a problematic passage where the tendency tone is doubled; 12b shows a common way this problematic doubling is avoided.


Let us now begin to realize figured bass lines at the keyboard. The following exercises increase in difficulty. Proceed slowly, learning the bass lines first, and then realize the chords. As with our work in contemporary chord symbol realization, the capacity to play with a steady rhythm is of the utmost importance. Figured bass realization Select two examples from each of the following groups of figured bass lines and demonstrate your ability to realize these accurately and with a steady rhythm: lines 1–14, 15–20, 21–27.

Figured Bass Realization at the Keyboard



Figured Bass Realization at the Keyboard

Figured Bass Realization at the Keyboard

Exercise 12b and Examples 12.9–12.12



Figured Bass Realization at the Keyboard

Seminal Keyboard Project 5 SEMINAL KEYBOARD PROJECT 5

Select three exercises from lines 18–27, at least one of which must be from 21–26. Compose melodies on the bass lines. The melodies should consist of largely quarter notes and eighth notes—you can use the melodies from the Bach chorales considered earlier as models—although somewhat more florid melodies are also possible. Be able to sing the melody as you play the accompaniment.

Exercise 12c

Four-part Chorale Writing The focus in our written work has been on five-part keyboard-style writing because this is directly connected to the central role which keyboard realization plays in this book. Conventional musicianship systems tend to place emphasis on four-part chorale-style writing, with the chorales of J.S. Bach as the ideal. It is but a small step to move from keyboard-style writing to the four-part approach. The following is a brief introduction to the second of these approaches. Example 12.13 illustrates a I IVmaj7–V7–I progression written in keyboard style and then in chorale style.


Notice in the second version the distribution of notes across the two staves; soprano and alto parts in the treble clef, tenor and bass in the bass clef. Whereas in the keyboard-style approach attention to voice-leading concerns (aside from moving voices as smoothly as possible) was primarily concerned with the outer voices, in the more exposed four-part texture it is important to attend equally to inner voices. Accordingly, parallel perfect intervals between inner voices, or between top/bottom and inner voices, are to be avoided. Example 12.14 shows an excerpt from a Bach chorale as a model for the four-part style.

Figured Bass Realization at the Keyboard



Written exercise Do four-part written realizations of three figured bass lines from lines 20–27 in the above exercises (from Exercise 12b).

Exercise 12d

Figured Bass Lines Applied to Jazz Chord Changes Jazz chord symbols may be written in figured bass nomenclature, although as the following example illustrates, the representation of chord extensions and alterations can be a bit unwieldy. Nonetheless, it is instructive for our understanding of both systems to examine what such an application of figured bass chord symbols might look like. Depicted in Example 12.15 are the first eight bars (with a ninth chord added here for the sake of finality) of a common progression in jazz called Rhythm Changes, so-named because the chord sequence derives from George Gershwin’s popular song I Got Rhythm. We will go further into rhythm changes, which has evolved as a fertile vehicle for chord substitution and extension, in Chapter 14. The version that follows provides a good glimpse of these possibilities and perhaps also shows why contemporary chord symbols are the more suitable



Figured Bass Realization at the Keyboard

method for the richness of the current tonal landscape. While Roman numerals are not included in the example in order to avoid excessive information, it is clear that the progression is in F major with a brief tonicization in Bb (IV) via II–V7/IV (bar 3). Notice immediately thereafter the use of passing modal mixture where IV is followed by IV minor (BbM7 to Bbm7) and how this leads smoothly to the final III–VI (V7/II)–II–V7–I sequence. Notice also the occasional disparities between chord partials and extensions as represented in contemporary chord symbols and Arabic numerals. For one thing, the sevenths listed on the I and IV chords, which are major sevenths, are simply listed as 7 in the figured bass line. As explained earlier, this is because in the absence of accidentals corresponding to that particular partial, the key signature tells us what kind of seventh is involved—we simply determine the seventh above the bass note that is diatonic to the key. On the I and IV chords, the diatonic sevenths are major sevenths. While we will begin to look at extended and altered chords in Chapters 13 and 14, it may be of interest to note prior to this that on the penultimate chord of the piece, the Gb7 (#9, b5), the #9 of the contemporary chord symbol—which is the note A—is listed simply as 9. Again, this is because the key signature tells us that A is the note a ninth above Gb; the interval of a #9 is created by lowering the root a half-step. Moreover, the b5 in the contemporary chord symbol—the note Dbb, or enharmonically spelled as C—is listed as 4 in the figured bass nomenclature. Once more, the key signature tells us that the note C is a fourth above the Gb; the augmented fourth/diminished fifth relationship is created by the lowering of the diatonic G bass note to Gb.

SUMMARY QUESTIONS 1 What are the three components of figured bass nomenclature? 2 When realizing contemporary chord symbols, the key signature has no bearing on the quality of the chords (e.g. an Fmaj7 consists of the same tones whether the key signature includes one flat or six sharps) whereas in figured bass realization the key signature plays an essential role in the resultant chord structures (e.g. a bass note F with Arabic numeral 7 results in different chords with key signatures of one flat, two flats, or three flats). True or false? 3 Name a strategy that will help maintain smooth motion between voices. 4 In the case of first inversion dominant chords, it is important to avoid doubling which tone of the chord? Which tone of the key is this? What is this tone called? Why is it problematic when doubled?

chapter 13

Extended Chords

In this chapter, we: • Learn extended chord voicings through keyboard realization, analysis, and written work. • Learn about replacement tones, chord superimposition, and A and B voicings. • Examine chord–scale relationships that correspond to extended chords for improvising purposes.

While significant common ground can be identified between European classical and jazz harmonic practices (e.g. secondary dominant chords and modal mixture are essentially the same devices in jazz and popular music as in nineteenth-century string quartet literature) an important difference is the use of chord extensions to an unprecedented degree in jazz. Whereas in European classical music of the common practice era (from about the seventeenth to the nineteenth century), triads are common and chords extended beyond the seventh are rare; in jazz, triads are rare and chords are commonly extended to include diatonic as well as altered ninths, elevenths, and thirteenths, even if these extensions are not indicated in the chord symbols (e.g. C7 is usually played as C7(9,13) or C7(#9, b13), etc.). These devices add variety and richness atop basic chord functions to which the ear has become accustomed over centuries of tonal practice. This chapter provides a systematic method for creating extended voicings at the keyboard and also presents written exercises that complement keyboard work in order to promote fluency with these structures.

General Principles of Chord Extensions Chord extensions can be most easily thought of as a continuation of the very process of adding thirds to triads that produced seventh chords (see Example 13.1).


Extended Chords


In these chords, the ninth is the same note as scale degree 2, the eleventh is the same as scale degree 4, and the thirteenth is the same as scale degree 6. Why not therefore just label the extensions using the lower numbers? While it may, in fact, facilitate mastery of extensions to think of them in terms of their corresponding scale degrees, we label them as extensions using the higher numeral because these tones evolved and function as additions to the basic chord structures. While we will shortly consider approaches to extended voicings that omit some of basic chord tones in order to facilitate playing the voicings at the keyboard, the ear still hears these extended tones as upper additions to the basic chord structures. This is even the case when the ninth is voiced, as seen in Example 13.2, a step above the root rather than a ninth above.


As we will see, this is but one of the many ways in which chord extensions may be voiced. It is even possible to voice extensions in the bass clef, providing they are not placed so low as to muddle the sonority. Observe also how extensions are indicated in the chord symbols, where they are placed in parentheses after the 7. If multiple extensions are used, they are separated by a comma (e.g. F7(9, 13)). Another approach sometimes used is to indicate just the extension; presuming the chord includes a seventh, Dmin9 is identical to Dmin7(9). However, this is not to be confused with instances whereby a letter is followed by an extension in parentheses, such as D(9), which indicates that only a D major triad and a ninth will sound, without a seventh. Extensions may be raised or lowered by accidentals that precede them, as in D7(#9, b13), which means that atop a D7 chord will also sound the notes E# (or F) and Bb. Enharmonic spellings are often used when writing out the voicings for these chords to facilitate applying them. If no accidentals are indicated, then the extension will be diatonic to the major scale of the chord indicated: Db7(9, 13) will include the notes Eb (the ninth) and Bb (the thirteenth).

Extended Chords


Types of Chord Extensions Different chord types, due to their basic intervallic structures, are capable of supporting different kinds of extensions. For instance, minor7, major7, and dominant7 chords can all support ninths, but dominant seventh chords, unlike the other two chord types, can also support the b9 extension. And when it comes to elevenths, important differences arise, as Table 13.1 indicates (e.g. major seventh chords can take #11 but not natural elevenths). TABLE 13.1 Common chord extensions Chord type:

Available extensions:

Major 7th

Minor 7th

Dominant 7th

Halfdiminished 7th

Diminished 7th

9, #11, 13

9, 11, 13

9, b9, #9, b5, 13, b13

9, 11

Any note a whole step above any chord tone

Example 13.3 provides these correlations between chords and extensions in notated form. The dominant seventh chord can take a wide range of diatonic and non-diatonic extensions. This is because the basic intervallic structure of the dominant seventh is sufficiently dense and unstable—thus heard as motion leading toward a more static goal—to serve as a foundation for the highly complex intervallic relationships involved in altered extensions. The tritone interval between the third and seventh of the chord is key in this respect.



Extended Chords

When you play the various extensions on top of the basic dominant seventh structure, you may find that the altered extensions (e.g. #9, b13), unlike the corresponding diatonic extensions (e.g. 9, 13), sound dissonant—perhaps even clashing to an unacceptable extent. However, by framing these non-diatonic extensions in appropriate voicings, highly rich and resonant sonorities are possible that are appealing to even the most conservative ears. Mastery of voicing strategies for diatonic extensions in this chapter will lay groundwork for voicing altered extensions in Chapter 14.

Replacement Tones and Chord Superimposition As we begin to consider strategies for playing chord extensions, it may seem that extended chords will necessarily include more notes than unextended chords, thus placing newfound demands on our keyboard technique. In fact, while large instrumental ensembles allow chord voicings of enormous scope that would be difficult if not impossible to play at the keyboard, it is possible to produce the richness and density of extended chords using the very same five-note format we have been using thus far. Two strategies make this possible: the use of replacement tones and chord superimposition. Replacement tones simply means that when extensions are used, basic chord tones that are “expendable”—that is, tones whose absence does not significantly detract from the quality and function of the chord—are replaced with extensions. Roots and fifths are the most common expendable tones in right-hand voicings that are replaced by extensions, although we will still play the roots in the bass. We will shortly build extended voicings on the II–V–I progression through what is called the 9-for-1 (9-1 for short) replacement technique; here the root is replaced by the ninth in the right hand. Replacement strategies enable us to create rich sonorities within the five-note voicing framework we have been using. Appendix 5 introduces new approaches to five-note voicings that may be added to one’s palette, once one has gained a foundation with extended chords in the current format. Working in tandem with replacement strategies is the use of chord superimposition to facilitate arriving at the extended voicings for the different kinds of chords. Chord superimposition involves building—or superimposing—a particular kind of basic, unextended chord structure atop a basic chord tone of the chord that is being extended. For instance, in order to voice a minor ninth chord, we simply build a major seventh chord on the third of the chord; the voicing for Dmin7(9) is achieved by building Fmaj7 on the third of D. While it is possible to arrive at accurate voicings by stacking notes in thirds and then replacing the expendable tone with the desired extensions, chord superimposition provides a much more rapid approach. In addition, when it comes to extended dominant voicings, which are not arrived at by stacking tones in thirds, chord superimposition becomes a necessity. We will complement replacement and chord superimposition strategies, which may be thought of as largely vertical approaches to chord extensions, with horizontal procedures by which extensions are arrived at through voice leading. For instance, once one has created the extended voicing for the IImin7(9) chord, resolving the seventh of that chord down one half-step produces the V7(9, 13) voicing. Facility with these different angles will enable optimal fluency with these structures.

Extended Chords


Extended II–V7–I Voicings Example 13.4 illustrates a standard approach to extended chord voicings for the IImin7–V7–Imaj7 sequence, which becomes IImin7(9)–V7(9,13)–Imaj7(9).


Table 13.2 gives a list of chord superimposition and replacement tone strategies for arriving at the above voicings. TABLE 13.2 Chord superimposition and replacement strategies Chord type

Chord superimposition strategy

Replacement tones (right hand only)


Build a major 7th structure on the (minor) 3rd of the IImin7 chord


V7(9,13) Imaj7(9)

Build a major 7th(b5) structure on the 7th of the V7 chord Build a minor 7th structure on the (major) 3rd of the Imaj7 chord

9-1, 13-5 9-1

Let us first look at the voicings of the IImin7(9) chords and the Imaj7(9) chords, as these are the most clear-cut. There is a kind of symmetry here that is easy to remember: On the third of the IImin7 we build a major seventh structure, and on the third of the Imaj7 we build a minor seventh structure. This strategy allows us to spontaneously arrive at voicings in which the ninth replaces the root—hence the 9-1 replacement—without even thinking about it. Since these voicings may also be arrived at by simply stacking notes in thirds atop the thirds of the respective chords, one might well wonder if chord superimposition strategies are even necessary. Whether or not one chooses to use these strategies for IImin7(9) and Imaj7(9) chords, chord superimposition is essential when it comes to the more elusive extended voicing for the V7 chord. For now, we are incorporating not only the ninth but also the thirteenth and,


Extended Chords

if we are to adhere to our commitment to manageable voicings that fall comfortably within the hand, this cannot be arrived at by simply stacking notes in thirds. Another problem with achieving the extended dominant voicing by stacking notes in thirds is that this approach would include the eleventh, which is not an available extension on this chord. So we need a new strategy for arriving at the extended dominant voicing. By superimposing a major seventh (b5) structure atop the seventh of the V7, as in example 13.4, we derive the desired voicing. While we have not yet encountered the major7(b5) chord, it is readily understood in relation to what is by now the highly familiar major seventh chord—we simply lower the fifth. Notice that the right-hand voicing on the V chord in Example 13.5 is an Fmaj7(b5) structure. We need only play this structure on the seventh of the V chord and we automatically get the desired tones without even thinking about what is being replaced by what. It is only in retrospect that we recognize the replacement strategies: 9 replaces 1 (9-1) and 13 replaces 5 (13-5).


Smooth Voice Leading Example 13.5 shows the smooth voice leading that is possible through the use of extended voicings. Notice that only one note changes between the IImin7(9) and the V7(9, 13) chords: the seventh of the II chord resolves down a half-step to the third of the V7 chord. All other notes remain the same between these two chords. Indeed, smoother voice leading is often more possible with extended chords than with unextended chords. Awareness of this smooth voice leading not only enhances our understanding of the corresponding chord extensions, it points to yet another strategy for arriving at the extended V7 voicing. For now one need only arrive at the extended IImin7(9) voicing and allow the seventh of the II chord to resolve down one half-step to produce the extended V7(9, 13) voicing. Needless to say, this strategy will not be helpful in instances where V7 is not preceded by II, at which point the chord-superimposition strategy becomes essential. Nonetheless, some individuals may find that this approach provides the easiest entry point to mastering the extended V7(9, 13) voicing. It is ideal to integrate the various approaches. As you practice the next keyboard exercise, employ the “hearing in advance” technique on each II chord—whereby you hear the seventh resolving to the third of the V7 before actually playing the V7. This will help you integrate the voice-leading principle.

Extended Chords


Seminal Keyboard Project 6 At the keyboard, continue the following pattern, which is notated in three keys, to all keys without the aid of notation. Because each II–V–I moves down a whole step, after six keys you will return to the first (e.g. C, B , A , G , E, D, C), thus requiring that you begin the sequence again a half-step above or below the first key (e.g. D , C , A, G, G, E ) in order to cover the remaining keys.

b b b

b b


Exercise 13a and Example 13.6

Once you begin to get these chords under your fingers, you will inevitably become quite fond of these sounds. This is particularly true in the case of the extended dominant seventh chord. Whereas minor and major seventh chords are acceptable when unextended, although given the choice most musicians will prefer the extended voicing, the unextended dominant seventh chord is, in fact, not an acceptable option in a contemporary format. It is simply too bland, too dated a sound. The unextended dominant seventh chord sounds beautiful in Beethoven, Mozart, and Schubert. However, amid all the common threads among harmonic practices over the past centuries, the unextended dominant seventh chord is a relic of a bygone era. This will likely become clear once you begin to internalize dominant extensions and hear and feel the richness of these sonorities. Here an important point bears emphasis; that is, extensions may or may not be indicated in contemporary lead sheet formats, particularly in jazz. Rather, the chord symbol indicated may just say Fmaj7, or Ab7, or E7. Nonetheless, it is customary to extend these basic structures in order to achieve the harmonic richness that is possible and characteristic of contemporary practice.



Extended Chords

Written exercise



Write extended II–V7–I voicings in these keys: F, A , B, G, B , D.

Exercise 13b and Example 13.7

Written exercise Notate this chord progression with extended voicings on all chords, two chords per bar (except for the last bar in which only B maj7 sounds). Use the smoothest voice leading possible. Notice the use of dominant seventh chords that are not preceded by their respective II chords, thus requiring the chord superimposition technique. Then play the progression without reading the notated version, just the chord symbols.






F maj7 A 7  D maj7 E7  Amaj7 C7  Fmaj7 A7  Dmaj7 G 7  Bmaj7 F7  B maj7 :

Extended Chords


Exercise 13c and Example 13.8

Multiple Configurations of Extended Voicings: A and B Voicing Patterns The extended voicings we have considered thus far have followed a consistent pattern that is based on the II–V7–I framework and begins with the 3, 5, 7, 9 in the right hand on the IImin7(9) chord. The renowned jazz pianist/teacher/author John Mehegan called these A voicings. Other configurations, using the same notes but in different placements, are also available, and it behoves us to be able to play and write a range of configurations for the sake of variety and smooth connections between chords. The B voicings use the fifth in the upper voice on the II chord, as in Example 13.9.



Extended Chords

Written exercise

b b


Write A and B voicings for extended II–V7–I chords in these keys: G, B , D , E, F, A .

Exercise 13d and Example 13.10

Exercise 13e provides melody notes that you are to harmonize utilizing the extended chord voicings as indicated in the chord symbols. In other words, the top note of the voicing is given—it is standard practice for the melody note to appear in the upper voice, as harmony atop the melody can obscure the melody—and you will fill in the rest of the voicings below it. Also fill in the roots of the chords in the bass clef. Since almost all of the melody notes are chord extensions, you will find that you can use either A or B voicings to harmonize them. However, since the melody notes often move by more than a step between the chords, you may have to use an A voicing on one chord and a B voicing on the next. This will help you build fluency in using these voicings.

Written exercise Write out the rest of the voicings beneath the melody notes, including the roots of the chords in bass clef. In no instance should any notes be placed above the melody note, as this obscures the prominence of the melodic line.

Extended Chords


Exercise 13e and Example 13.11

Written exercise Write out the rest of the voicings beneath the melody notes as in the previous exercise. However, not all melody notes are chord extensions in this exercise; nonetheless, the extended voicings will fit readily beneath the melody notes. Here you will not only need to use both A and B voicing configurations but also other configurations as required by each situation.


Extended Chords

Exercise 13f and Example 13.12

Written exercise These II–V7–I sequences include right-hand voicings but not the roots. After determining the chords, fill in the bass notes and write the chord symbols—including extensions— atop the treble clef. Observe that accidentals carry through the measure.

Extended Chords


Exercise 13g and Example 13.13

Extended II–V–I Voicings in Minor Let us now consider voicings for extended chords in minor, using the II–V7–I progression in minor as the basic framework. We have already encountered a preliminary version of this in Chapter 10, where we saw that the b5 of the II chord was the same note as the b9 of the V7, and thus realized that we could arrive at a V7(b9) chord by simply building a 07 structure on any of the chord tones (except the root), with the chord tone as the root of the 07 structure. In other words, to arrive at a D7(b9), we could just build an F#07 structure on the third of that chord and it would give us the 3, 5, 7, and b9. While that voicing may still be used, we will now look at another possibility for voicing the V7(b9) chord that flows nicely from the extended II chord in minor that precedes it. Minor II–V–I progressions commonly use these extensions: IImin7(b5,11); V7(b9); Imin7(9). Arriving at these voicings is facilitated by further use of the chord superimposition


Extended Chords

principle. As Example 13.14 shows, on the II chord we build a major7b5 structure of the b5 of the chord. This same structure also enabled us to arrive at the V7(9, 13) voicing introduced above. We will make further use of this very handy structure when it comes to altered extensions in Chapter 14, and it will be advantageous to appreciate this connection as it will greatly facilitate learning these voicings.


Notice also that the IImin7(b5,11) chord omits the third, a practice that may seem unusual given the importance the third of the chord usually assumes in defining the basic chord quality (thirds are primary determinants of whether a triad or seventh chord is major or minor). Indeed, the omission of the third may seem to violate a cardinal rule in harmonic construction. Why would the IImin7(b5) be an exception? The reason is not that the third does not sound good; in fact you can play the voicing below as is, and then add the third by playing a fifth note in the chord voicing with the fourth finger, and you will see that it is in fact difficult to hear the difference between the two chords. And if you played the third instead of the eleventh, the chord would still sound acceptable and certainly uphold the function of II chord in minor. But the chord would not be nearly as rich as when it includes the eleventh, and, inasmuch as (1) the third neither adds to nor detracts from the resonance or function of the chord, and (2) it is easier to omit the third (which is a second away from the eleventh) from simply a technical standpoint; the indicated voicing is preferable. Moreover, this voicing only requires the half-step resolution of a single chord tone in order to arrive at the V7(b9) voicing. Smooth voice leading is thus one more mitigating factor in the omission of the third in the extended II chord in minor. The I minor chord may be arrived at by building a major seventh chord on the third of the I, yielding the minor ninth voicing. Keyboard exercise Play extended II–V–I chords in these minor keys: A minor, D minor, F minor, E minor, B minor, G minor, C minor.

Exercise 13h

Extended Chords


Example 13.15 illustrates the V7(b9) chord resolving to another kind of minor I chord, the Imin7(9, 11) chord. The voicing used for the Imin7(9, 11) chord, as does the IImin7(b5, 11), omits the third. However, just as with the extended minor II chord, the absence of that tone does not significantly detract from the resonance or the function-defining sonority of the chord. In addition, the superimposition of a minor seventh chord on the fifth of the minor I chord produces this particular voicing.


Written exercise Write extended II–V–I chords in these minor keys: B minor, C# minor, E minor, F# minor, A minor.


Exercise 13i and Example 13.16




Extended Chords

Written exercise Write extended voicings, as indicated in the chord symbols, below these melody notes.

Exercise 13j and Example 13.17

Written exercise These minor II–V7–I sequences include right-hand voicings, but not the roots. Fill in the roots in the bass clef, and the chord symbols, indicating the extensions used, above the voicings in the treble clef. Reminder: accidentals carry through the measure.

Extended Chords


Exercise 13k and Example 13.18

Extended Substitute Dominant Chords In Chapter 10, we examined the use of substitute dominant chords to create variety. Recall that the substitute dominant, or subV7, retained the same tritone interval as the regular V7, and at the same time replaced the V to I movement in the bass with the smooth bII to I movement; thus allowing the chord to lead to I as effectively as the regular V7. Atop these basic structural features may be added extensions that further enrich the substitute dominant function. Here we can utilize the very same extensions we applied to the regular V7 chord: the ninth and thirteenth. As in example 13.19, we arrive at these voicings through the same chord superimposition process—where we build a major7(b5) structure on the seventh—which we used with regular V7(9, 13) chords. Observe that the sequence is written in two versions, corresponding to what we considered above as A and B voicings. This allows us to see two configurations of the


Extended Chords


subV7(9, 13). However, these two sequences deviate from the use of A and B voicing positions introduced in regular extended II–V7–I sequences—now the positions are alternated within the same sequence. The II chord in the first sequence is in B position— with the fifth in the top voice—and the subV7(9, 13) is in A position. This shift of position is necessitated when we use the subV7 instead of the regular V7 and yet still seek to retain smooth voice leading. This provides all the more reason for developing a fluency with these chords and voicings that enables us to use them in a variety of positions.

Keyboard exercise Realize IImin7(9)–subV7(9,13)–Imaj7(9) in all keys, utilizing the pattern we have used on regular II–V7–I progressions where key areas proceed down by whole step (e.g. II–V–I in C, then B , then A , etc.). Practice beginning with both A and B voicings on the II chord, which will necessitate using both voicing positions on the subV7.



Exercise 13l

Written exercise Provide voicings beneath the melody notes.

Extended Chords


Exercise 13m and Example 13.20

Keyboard exercise These II–subV7–I sequences include right-hand voicings, but not the roots. Fill in the roots in the bass clef, and the chord symbols, indicating the extensions used, above the voicings in the treble clef. Accidentals carry through the measure.


Extended Chords

Exercise 13n and Example 13.21

SUMMARY QUESTIONS 1 Define the two extension approaches—replacement and chord superimposition strategies—discussed in this chapter. Give examples of each. 2 Name the replacement strategies used to create extended chords on the II-V-I sequence. 3 In contemporary music, what chord type most strongly calls for extension? (Unextended, this chord sounds particularly bland.)


4 Name the two extended voicings that are created by superimposing the major7( 5) structure. On what chord tones is this structure placed to yield the desired voicings? 5 Name a diatonic extension that is not available on major seventh chords or dominant seventh chords.

Further Reading John Megehan, Tom Glazier, and Bill Evans, Jazz Improvisation: Contemporary Piano Styles. New York: Watson-Gupthill Publications, 1965. Phil DeGregg, Jazz Keyboard Harmony. New Albany, IN: Jamey Aebersold Jazz, 1994. Frank Mantooth, Voicings for Jazz Keyboard. Milwaukee, WI: Hal Leonard, 1986.

chapter 14

Altered Extensions

In this chapter, we: • Learn altered extended chords through keyboard realization work, analysis, and writing. • Study replacement tone and chord superimposition strategies. • Compare altered dominants in jazz with augmented sixth chords in European classical music. • Learn chord–scale relationships that correspond to extended altered chords for improvising purposes.

Our work with natural extensions in the previous chapter prepares us for the study of chromatically altered extensions, which will further enrich our harmonic palette. We will explore this area through similar approaches we applied to natural extensions, creating altered extensions through chord superimposition as well as through voice-leading strategies. We will continue to see the major7(b5) structure as a useful chord-superimposition device; in addition to its role in creating the V7(9, 13) and V7(b9) voicings in the previous chapter, we will now apply it to create chords with altered extensions.

The Altered Dominant Chord We begin with the altered dominant seventh chord. Example 14.1 shows several common altered dominant chords found in jazz. Notice the tritone interval that is common to all the voicings. As we have considered previously, the density of the tritone interval supports overlying density, which altered extensions amply provide. Of the four types of altered dominant chords, our focus will be on the G7(#5, #9) chord, because its voicing is most directly related to strategies we have used for creating unaltered extensions. Once fluency with this chord is gained, the other altered chords will be easily arrived at as variations thereof.


Altered Extensions


The #5,#9 chord is also commonly labeled as a #9, b13 chord because the enharmonic spelling of the #5 as b13 facilitates playing, writing, or analysis. This alternative labeling also facilitates the chord-superimposition technique we will use to voice it; this entails building a major7(b5) structure on the third of the chord. Moreover, this labeling also conveys voiceleading movement from the extended II chord that often precedes the #9, b13 chord.


We will discuss the chord-superimposition strategy for arriving at this voicing below. Let us first examine the V7(#9, b13) from a voice-leading standpoint. Observe how the ninth (E) of the II chord resolves down a half-step to the b13 (Eb) of the V7, and how the fifth (A) of the II chord resolves upward a half-step to the #9 of the V7. The strength of this voice-leading movement takes precedence over the minimally awkward practice of using both a flat and a sharp in the same voicing as well as a chord symbol; indeed, from this standpoint, the #9, b13 label most aptly describes what is happening musically. It also points to a way of arriving at the voicing from the II chord—we simply lower the ninth of the II chord a half-step and raise the fifth a half-step. An additional strategy for arriving at the voicing is provided in Example 14.3, in which the altered-extended dominant is preceded by the unaltered-extended dominant. Here the same voice-leading movement that is found when the altered dominant is preceded by its II is followed; the only difference is that now this chromatic motion is launched from the V7(9, 13). Example 14.4 presents a passage from the bridge of the piece “Invitation” which, as with much repertory that was first created for Broadway, became a jazz standard. Unaltered and altered extensions are used in the melody to coincide with the underlying harmony. Although the melody uses b9 instead of #9 the basic principle still holds.

Altered Extensions



EXAMPLE 14.4 Webster and Caper, “Invitation”

Recommended listening: John Coltrane, Standard Coltrane (Fantasy 1990, original release 1958)

Keyboard exercise Realize this chord pattern (notated in Example 14.3 in two keys) in all keys, proceeding with downward movement by whole step (e.g. in C, then B , Ab, G , etc.; be sure to begin the sequence up or down by a half-step once you return to the original key).



IImin7(9)  V7(9,13) V7(#9, 13)  Imaj7(9) 


Exercise 14a

Chord Superimposition Strategy: Build a Maj7(b5) on the Third to Yield V7(#9, b13) An even more direct way of arriving at the V7(#9, b13) voicing is to superimpose the major7(b5) structure on the third of the V7. This is our third application of this structure,


Altered Extensions

and there is one more to follow. In other words, as seen in Example 14.5, the G7 altered chord may be understood as a Bmaj7(b5) chord built on the third (B) of the G7. Example 14.6 shows the same chord sequence in a different configuration, where the superimposed Bmaj7(b5) structure is in this case configured in “root position”—a description that is used provisionally to refer to the superimposed structure and not the actual G7(#9, b13) chord of which it is a part. This allows smooth voice leading from the IImin7(9), which is in a different configuration than that of the previous illustration. Observe also the use of enharmonic spelling in the above instances. Again, voice-leading considerations are important criteria. In Example 14.5, the b13 of the G7 is written as Eb and nicely conveys the E–Eb–D movement in the upper voices of the three chords. In Example 14.6, the same partial of the G7 altered chord is spelled as D# to convey the function of the tone as a kind of lower neighbor in the E–D#–E movement which results from the different positions of the voicings. While technically a case could be made to call the G7 a #5,#9 chord, the #9, b13 label has become a generic category and it is important to be fluent with the enharmonic variations that may sometimes be at odds with the actual way in which the tones are written. Enharmonic respelling of this chord also helps avoid awkward use of accidentals. An E#, for instance, will often be written as F, B# as C, and double flats and double sharps will often be replaced by their enharmonic equivalents that use no accidentals (e.g. A instead of Bbb). To illustrate; if we build an F#7(#9, b13) chord using the same strategy as above—superimposing a major7(b5) structure on the third—it is easier



Altered Extensions


to think of superimposing a Bbmaj7(b5) chord than an A#maj7(b5) chord on the third of the F#. The second option would include three notes with double sharps. Therefore, we will favor the easier spelling even if from a technical standpoint what we are strategizing as a #9 (which should technically be G double-sharp) ends up really being a b10 (the note A), which—and this is most important—is the same sound as G double-sharp. In order to reinforce the principle of chord superimposition involving the major 7 (b5) structure, let us take a moment to review the three applications of this chord we have dealt with thus far: 1 By placing the maj7(b5) on the seventh above the V7 root, we create a V7(9, 13) voicing. 2 By placing the maj7(b5) on the b5 above the root of a II chord, we create a IImin7(b5, 11) voicing. 3 By placing the maj7(b5) on the third above the root of a V chord, we create a V7(#9, b13). Seminal Keyboard Project 7 Continue this IImin7(9)-V7(#9, 13)-Imaj7(9) sequence in all keys at the keyboard without the aid of notation. Proceed as above, moving down by whole steps, e.g. II–V–I in C, B , A , etc. Be sure to begin the sequence up or down a half-step once you return to the original key.




Exercise 14b and Example 14.7

The above notated examples show V7(#9, b13) preceded by IImin7(9); the chord may also be preceded by IImin7(b5, 11) and be used in place of the customary V7(b5) that follows that chord. Example 14.8 illustrates this application, as well as the colorful effect that results when the lush and dark V7(#9, b13) chord is followed by the very bright sounding Imaj7(9).

Extended and Altered Substitute Dominant Chords As we first considered in Chapter 7, in order to create variety in moving from V to I, jazz musicians sometimes replace the V with a dominant chord on the bII degree of the key.



Altered Extensions



In the previous chapter, we looked at ways of extending the substitute dominant, or subV7, to further create variety and color. Now we will alter the extensions of the subV7. But first let us have a look at what may be an interesting connection between the natural extensions of the subV7 and the altered extensions of the regular V7. Compare the two voicings as they are shown in Example 14.9. You may be surprised to see that they are identical. The only difference between the chords is the bass notes. Hence, by simply changing the bass note, the voicing for the altered dominant may be used to produce the natural extended voicing for its subV. The converse, then, also holds: the natural extended voicing of the subV produces the altered extended voicing for the V7. As one might expect, further correlations of this sort are found between the naturally extended V7(9, 13) chord and the altered subV7(#9, b13) chord, as illustrated in Example 14.10. Again, the voicings are identical; only the bass notes change.


Altered Extensions


In summary: the altered extensions of the subV7 chord are the exact same notes as the diatonic extensions of the regular V7, and the diatonic extensions of the subV7 chord are the same notes as the altered extensions of the regular V7. In the case of altered subV7, the chromatic movement of the bass line renders what would ordinarily have been diatonic extensions to be altered extensions. In other words, if we played II–V–I roots under the right-hand notes, we would get V7(9, 13). But by playing II–bII–I in the bass, those same right-hand notes yield subV7(#9, b13). Seminal Keyboard Project 8 Realize this progression in all keys at the keyboard without the aid of notation.

Exercise 14c and Example 14.11

Involving diatonic and altered extensions as well as cadential movement that is common in European classical music, this progression spans several centuries within eight measures and serves as the culminating pattern of our basic keyboard realization sequence. It is recommended that you first memorize the bass line as you would a melody and be able to play it by ear in multiple keys prior to adding chords. The next step will be to



Altered Extensions

recognize the patterns that define the overall harmonic structure; this conception of the whole will greatly facilitate how the various parts—the chords—fit within it. As with project 6, the progression consists of four parts. First are two II–V7–I sequences in major, followed by II–V7–I in the relative minor. However, instead of moving back to the relative major, this progression stays in the minor and ends with a i6/4–V7–i (or V6/4–V7–i) cadence that is commonly found in European classical literature. Within this overall structure, it is easy to keep track of where subV7s are used in place of regular V7s: in bar 3 of the relative major portion, and in bar 6, where the subV7(b5)/V in minor sets up the final cadence. Notice that this is a new chord type—a dominant seventh structure with a lowered fifth—but it is easily configured and understood in relationship to the familiar, unextended dominant seventh structure; one simply lowers the fifth. We will shortly examine this interesting and colorful chord as a unique link between contemporary and older practice. Notice also that this chord is analyzed as subV7/V, because the E that is its target is V of A, the new I. This progression therefore modulates from major to relative minor, following one of the more common patterns of modulation in tonal music. Modulation to a key a fifth away is another common pattern. Finally, it should be particularly helpful to recognize that, as indicated in the example, three different chords use the exact same voicing—which exemplifies the usefulness of the major7(b5) chord superimposition strategy. In addition, the voicing for the abovementioned V7(b5) chord is achieved by simply changing the superimposed structure— Fmaj7(b5)—into an F7(b5) structure that is the actual chord intended (in other words, what was a superimposed structure to aid in voicing other chords now becomes, with a slight alteration, both the voicing and the chord intended to sound.

Further Keyboard Work The subsequent keyboard exercises 14d–14f will help further your fluency with altered extensions.

Keyboard exercises (14d) Top–down harmonization. Melody notes are given. Play the melody note with the little finger of the right hand and fill in the remainder of the voicings underneath. Play roots in left hand.

Altered Extensions

(14e) Proceed as in Exercise 14d.



Altered Extensions

(14f) Proceed as with the above exercise, where melody notes are given, and play the voicing below the melody. Here the melodies are more florid on the altered chords; use the pedal to sustain the voicing as you play the melody notes. Release the pedal on the I chord.

Exercises 14d–14f and Examples 14.12–14.14

Written exercises (14g) The melody notes are given; voice the chords in notation down from the top note as you would at the keyboard. Be alert to enharmonic spellings that appear to conflict with the altered extension indicated (e.g. a melody note written as 10 instead of #9; you can nonetheless use the chord superimposition strategies that most readily facilitate arriving at the correct voicing and need not modify the chord symbols or the notes given).


Altered Extensions



Altered Extensions

(14h) This exercise provides right hand voicings, including extended and altered chords, for II–V7–I progressions. No roots are provided. Determine the roots of the chords and the proper chord symbols and write that information (roots in bass clef, chord symbols above treble.)

(14i) As above, right-hand voicings are provided for these sequences of II–V7 chords. However, I chords are not provided here, with the exception of the final sequence. Identify and write in roots and correct chord symbols.

Altered Extensions


Exercises 14g–14i and Examples 14.15–14.17

Substitute Dominant Chords as Augmented Sixth Chords Let us further examine the dominant seventh (b5) chord as a link between contemporary and centuries-old practice. This structure is identical to what in European classical harmony is called an augmented sixth chord. Augmented sixth chords are so named owing to the prominent role that interval plays in the structure and function of the chord. Because the augmented sixth interval is the enharmonic equivalent of the minor seventh, and the chords also include a major third above the lower tone of the augmented sixth/minor seventh interval, it is possible to draw correlations between these chords and the dominant seventh structure. There are three types of augmented sixth chords, named arbitrarily German, Italian, and French, which are illustrated below. A prominent feature of the augmented sixth chord is the way the augmented sixth interval resolves. The notes of the augmented sixth interval typically resolve outward, in opposite directions, by a half-step to form an octave, as illustrated in Example 14.18, where a German augmented sixth chord is shown. The chord is spelled to reflect the above-described voice-leading movement; the G# is not spelled as Ab, which would suggest a Bb7 chord, but rather as the top note of an augmented sixth interval that is clearly directed toward the note a half-step above. When sounding against the similarly strong movement in the bass to resolve downward to A—an octave below the upper target note—a powerful sense of motion and arrival results. One can nonetheless see the correlation with the German augmented sixth chord and the dominant seventh chord; the Gr6 may just as readily be analyzed as a subV7/V.


Altered Extensions


Find the German augmented sixth chord in the musical passage below (Example 14.19). Example 14.20 illustrates the very similar Italian augmented sixth chord, which differs from the German only in that the fifth of the chord is absent. Example 14.21 illustrates the French augmented sixth chord, which as it turns out may be seen as identical to the subV7(b5)/V seen above in the context of contemporary harmonic practice.

EXAMPLE 14.19 Beethoven, Thirty-two Variations


Altered Extensions



Analysis Analyze using Roman numerals and find the French sixth in this passage from Mendelssohn’s Song Without Words for solo cello and piano.

Exercise 14j and Examples 14.22 Felix Mendelssohn, Song Without Words and 14.23

Recommended listening: Yo Yo Ma, Appassionata, “Song Without Words” (Sony 2007)


Altered Extensions

Notice that even within the broken chord texture, the outward resolution of the augmented sixth interval to the octave is evident, as seen in the last full measure where the Bb in the bass resolves down to the A and the G#—an augmented sixth above Bb—resolves up to the A as the top note of the right-hand arpeggiated figure. One beat later the A sounds prominently in the cello part, further emphasizing that half-step resolution. Here is where the use of the augmented sixth chord usually differs from the subV7(b5) chord in jazz, even if the structures are identical. In jazz, the seventh of the subV7(b5) chord will more commonly resolve downward or serve as a common tone (e.g. Db7 to Cmaj7; the B remains the top note on both chords). Let us examine how altered harmonies impact upon the chord scales that we can use when we improvise on jazz chord progressions.

Improvising on Altered Harmonies Whereas chords with diatonic extensions may be paired with the chord scales that are typically associated with a given chord function, chords with non-diatonic extensions require that we utilize new chord scales in improvising. For instance, we can improvise on an F Mixolydian mode whether an F7 or F7(9, 13) sounds, but if an F7(#9, b13) chord sounds, we need a scale that includes the chromatically altered tones. Table 14.1 presents scales that are commonly associated with altered chords. TABLE 14.1 Scales commonly associated with altered chords Chord type

Chord scale for improvising purposes

Dominant7(#9, b13)

Diminished whole-tone


Lydian b7; Whole-tone


Diminished whole-tone; Octatonic (half–whole)

Minor7(b5, 11)

Locrian; Superlocrian




Octatonic (whole-half )


Lydian #5

EXAMPLE 14.24 Diminished whole-tone scale

Altered Extensions


Notice that, as the name of the scale indicates, it combines a diminished tetrachord— which is the first four notes of a scale—and a whole-tone tetrachord. This scale is commonly used on the V7(#9, b13) chord. It may also be helpful to think of this scale as melodic minor ascending starting on scale degree 7. In other words, the F# diminished wholetone scale listed above is the same as a G melodic minor scale ascending starting on F#. Comparable to the chord-superimposition strategy for deriving extended and altered extended chord voicings, where the major7(b5) chord placed on different chord tones produced several different kinds of voicings, the melodic minor ascending scale serves in the same capacity when it comes to altered scales. Among the following scales are several more cases that are versions of the melodic minor ascending scale.


EXAMPLE 14.25 Lydian 7 (or Lydian dominant) scale

The Lydian b7 or Lydian dominant scale is a Lydian mode with a lowered seventh. One could also think of it as Mixolydian with a raised fourth degree, which is helpful in that this scale may be used even on unaltered dominant seventh chords; the raised fourth degree adds color to what otherwise would be strictly diatonic playing. This scale may also be derived by playing an ascending melodic minor scale starting on scale degree 4; the F# Lydian b7 is C# melodic minor ascending.

EXAMPLE 14.26 Octatonic (half-step, whole-step) scale

Octatonic scales are categorized as symmetric scales because their intervallic structure follows an evenly distributed pattern of whole- and half-steps. The half-step, whole-step octatonic scale, as in Example 14.26, begins with a half-step interval and then alternates with whole steps. This scale may be played on an altered dominant chord. The whole-step, half-step octatonic scale which follows may be played on a diminished seventh chord.

EXAMPLE 14.27 Octatonic (whole-step, half-step) scale


Altered Extensions

EXAMPLE 14.28 Whole-tone scale

The whole-tone scale, consisting of only whole tones, is another symmetrical scale. It may be played on the V7(b5) chord or even the diatonic V7 chord to produce a denser harmonic texture.

EXAMPLE 14.29 Locrian scale

The Locrian mode is a diatonic mode that may be played on the minor7(b5) chord. The Superlocrian mode, Locrian with a raised second degree, may also be played on this chord with a somewhat more colorful effect. The Superlocrian is identical to a melodic minor scale starting on scale degree 6; F# Superlocrian—which follows—consists of the notes of A melodic minor ascending.

EXAMPLE 14.30 Superlocrian (Locrian #2) scale

EXAMPLE 14.31 Lydian #5 scale

The Lydian #5 scale may be played on a major7(#5) chord, which is found much more in jazz after the “common practice” era, from the 1960s on. This scale is identical to the melodic minor scale ascending starting on the third degree. Thus, the F Lydian #5 scale is a D melodic minor scale ascending, beginning on F.

Altered Extensions


Integrating the Scales into your Melodic-Harmonic Palette Through Improvising and Composing Let us examine some ways we can make these scales more than theoretical possibilities but actually realize them in our creative work as improvisers and composers. In fact, here is another instance where improvisation and composition activities work synergistically to enhance assimilation of knowledge.

Improvising with Altered Scales From an improvisatory standpoint, the first step is to be able to sing and play each scale in the customary stepwise manner. The next step is to begin to improvise and explore the different permutations that are possible. You might begin with stepwise playing, and then once you begin to feel more comfortable, explore intervals of thirds and possibly triadic shapes, and then progressively larger intervals. However, you will find playing intervals of larger than thirds to be much more challenging on many of the above scales than with diatonic modes, and it is recommended that you establish a solid foundation with stepwise playing. Here the melodic cells will be of particular value in helping you get core shapes under your fingers. Example 14.32 provides several possibilities.


These make excellent exercises for aural transposition, and the alternation of highly focused aural transposition and more free-flowing improvisatory work on a given scale provides an ideal framework for developing formidable mastery. Once you begin to feel comfortable getting around on a given scale, place it within a context in which you can connect it with familiar scales, such as those of a II–V7–I progression. Here you will begin with the diatonic parent scale or Dorian scale of the II chord and then move to the altered scale—which you can play on the V7 chord whether or not alterations are indicated—and then back to the diatonic scale of I. Strive to create lines that move smoothly from the diatonic to the non-diatonic areas. Taking time to compose lines of this nature will be an excellent complement to this work.


Altered Extensions

Composing Lines with the Scales As recommended above in your improvising work with these scales, it is similarly advisable to place the corresponding chords within a functional sequence—e.g. II–V7–I—and compose lines that outline the diatonic to non-diatonic to diatonic movement in these progressions. Example 14.33 depicts a line that moves from Dorian on the II to diminished whole tone on the V7(#9, b13). Notice the smooth motion that connects the chromaticism of the altered dominant sonority and melody back to the diatonic target note on the I chord.


Composition Compose three melodic lines on each of the following chord sequences, making sure to use notes from the corresponding scales for the altered harmonies: Gmin  C7(#9, 13)  Fmaj7(9)



Emin7(9)  A7( 5)  Dmaj7(9)



Amin7( 5,11)  D7( 9)  Gmaj7(9) Cmaj7 C#07  Dmin7(9)  D#07  Emin7

Exercise 14k

Reharmonization The ability to harmonize a given melody in multiple ways indicates a high level of harmonic fluency and is essential for the contemporary creative musician. This skill allows composers and arrangers to broaden their palette of harmonic colors, and enables improvisers to find new creative possibilities for playing over standard repertory. The next examples show a melodic line harmonized in six different ways. Example 14.34 shows the line harmonized first with only two II–V–I sequences, and then with two common variations of those functions. As shown in harmonization 2 (Harm. 2), a IIImin7 chord substitutes for the Imaj7 in bar 2; and a VImin7 chord substitutes for Imaj7 in the final bar. Because these chords share two notes in common, these substitutions both sustain the harmonic flow and the subdominant-dominant function, while adding

Altered Extensions



variety. As you play through the progression, notice how the two harmonizations—both using entirely diatonic chords—bring out the melody, yet with subtle differences. When you create your own harmonization an important priority is that the melody stands out when played over the harmony. In other words, the harmony should not obscure the melody. In Example 14.35, extensive use of non-diatonic harmonies, and particularly altered dominant chords, yields a dense texture that still allows the melody to assume the forefront. Regarding the Roman numeral functions assigned to the second harmonization, other possibilities must be acknowledged as well. For instance, while the opening Ab7(#9) chord may be analyzed as a subV7, whether or not it is heard this way is questionable since nothing resembling its ordinary target follows soon thereafter. As harmonic richness increases, so do the ways different chords may be heard and thus analyzed. In Example 14.36, no dominant chords are used in either harmonization. This approach is sometimes categorized as “modal” in nature, not because all the chords and melody are derived from a single mode—which is clearly not the case—but because the absence of dominant chords and prevalence of major and minor quality chords (with extensions) undermines the dominant-to-tonic relationship that is characteristic of tonal music. In the so-called modal approach, chords are heard more as structurally equal and independent sonic “islands” than as part of a hierarchical, tonal spectrum. Notice the simplicity of the thinner harmonic rhythm used in harmonization 1. In harmonization 2, a stepwise descending bass line provides an effective counterpoint to the melody, in which the “B” is prominent for most of the passage.



Altered Extensions


Keyboard exercise Play the above four harmonizations at the keyboard, voicing the chords, as usual, below the melody. Sing the melody while you play the chords.

Exercise 14l Harmonization exercise Harmonize the following melody using these approaches: A II–V–I with diatonic extensions (the melody may be harmonized in at least two different II–V–I sequences). B Freely tonicizing II–V sequences; may use altered dominants. C Only altered dominant chords. D Modal: only major and minor quality chords, extensions encouraged, stepwise root movement. E Modal: only major and minor quality chords, extensions encouraged, roots moving by thirds. Sing the melody while you play the different harmonies.

Exercise 14m and Example 14.37

Rhythm Changes As the above examples illustrate, altered chords may be used in standard harmonic frameworks as well as in less conventional progressions that move feely between distantly related key areas. We close this chapter with a composition by Sonny Rollins that is written

Altered Extensions


on “Rhythm Changes,” a standard jazz progression already encountered in Chapter 12 and which has been varied in many different ways while retaining its basic character. In the following version, altered chords are used on the bridge, maintaining harmonic interest through their rich colors even as the harmonic rhythm shifts from two chords per bar to two bars per chord.

EXAMPLE 14.38 Sonny Rollins, Oleo © 1963 Prestige Music. Copyright renewed. This arrangement Copyright 2008 Prestige Music. International copyright secured. All rights reserved.


Altered Extensions

Recommended listening: Sonny Rollins, The Complete RCA Victor Recordings, “Oleo” (BMG 1972).

SUMMARY QUESTIONS 1 What common threads might be identified when comparing creating natural extensions to altered extensions? 2 What chord type supports the greatest number of altered extensions? Why? 3 Name the different extended chords (natural and altered extensions) that may be derived by superimposing the maj7( 5) structure on a given chord tone.


4 The French augmented sixth chord in European classical harmony is the same structure as what altered jazz chord? How would the application of these chords differ in terms of voice leading?

chapter 15

Diverse Approaches to Analysis

In this chapter, we: • Pursue contrasting lines of analysis through selections from jazz and European classical repertory. • Review the distinctions between tonicization and modulation, application of Roman numerals, criteria for determining chord-scale identification, and the ramifications of these concerns for the improviser. • Examine how localized parts of compositions relate to the whole.

Much of our focus thus far has been on localized harmonic structures, functions, and sequences in order to develop hands-on access to these materials when we create. Another important skill area for creative musicians is an awareness of how localized elements relate to each other and to the overall form of a piece or section. Looking at entire pieces and examining these parts-to-whole relationships develops this skill. This chapter will provide a brief introduction to this process using examples from jazz and European classical repertory. We will see that different kinds of repertory and corresponding modes of performance and creation (e.g. jazz repertory as a vehicle for improvisation as opposed to European classical repertory as a vehicle for interpretive performance) call for different analytical approaches. These contrasting analytical paradigms reflect different, culturally mediated views about the nature and purpose of music and musicianship training. The crosstraditional melding that defines today’s musical world makes this ability to investigate music through multiple lenses an important part of the diverse skill set of contemporary musicians.

Tonicization and Modulation Revisited An important aspect of our look at jazz will be a focus on harmonic structure due to the role of jazz compositions as vehicles for improvisation. In no way is this to suggest that


Diverse Approaches to Analysis

jazz compositions do not stand on their own, as do European classical compositions. They are self-contained works, whether or not improvisatory development is involved. Such an analytical track is entirely viable, but this is not the angle we will pursue in this chapter. Since improvisation is an important aspect of jazz, our emphasis will be on understanding the harmonic forms of pieces—to grasp how the parts relate to each other and to the wholes—in order to enhance our capacity to spontaneously create atop these forms. The more sophisticated our conception of the form, the more creative options we will have at any given moment and the less constrained we will be by the idiosyncrasies of the structure. Our examination of European classical repertory will take further considerations into account. Before proceeding with the musical selections, let us return to two harmonic strategies broached previously: tonicization and modulation. Tonicization refers to temporary movement to a new key area. Modulation refers to a more permanent shift, whereby the ear hears a new chord as I. As we will see in the selections below, the lines between tonicization and modulation are not always clear, and determining which strategy prevails may be a matter of judgment. Nonetheless, the distinctions are not insignificant and a primary criterion for making the determination may also shed light on its importance. Modulation indicates structural boundary in a form. It delineates a structural section, whereas tonicization generally serves more as an embellishment to a structural area. Modulation can occur between closely related keys, as in the movement from major to relative minor, or minor to relative major, or between keys that differ only by one or two accidentals. In these cases, modulation usually occurs gradually through the use of one or more pivot chords—chords that are diatonic to both the original key and the new key. For instance, in the key of F major a G minor chord will be II and in the relative minor key— D minor—the same chord will be IV. In a piece modulating from F major to D minor, the G minor chord would thus be considered a pivot chord. Indeed, the tonic chord in the new key—D minor—would be VI in the original key, foreshadowing even more directly the shift to the new I. Modulation can occur between closely related and distant keys. Closely related keys are those differing by two accidentals or fewer, with movement from major to relative minor or minor to relative major as primary examples. In both instances, the key signatures remain unchanged. Distant keys differ by more than two accidentals, as in the shift from C major to Eb major. Modulation may also occur gradually, through hints at the new key in moments of tonicization, or abruptly, with little or no preparation. The following selections involve this range of movement from a tonic key to closely related and distant key areas. While distinctions between tonicization and modulation are not always clear, an understanding of the criteria by which these distinctions might be made will enhance the improviser’s command of the harmonic structure being used (e.g. knowledge that a piece has modulated enables the improviser to shift to a new parent scale).

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EXAMPLE 15.1 Tadd Dameron, “Lady Bird”

Tadd Dameron, “Lady Bird” Recommended listening: Tadd Dameron, The Complete Blue Note and Capital Recordings of Fats Navarro and Tadd Dameron, “Lady Bird” (Blue Note 1995).

Let us begin by looking at at some of the larger structural patterns of this piece. It may be analyzed as a two-part, AB form, in C major, with movement toward three other keys. Recognition of these simple facts vastly facilitates internalization of a form and is highly recommended as an initial step when learning any kind of new repertory. The next question is: What are the three keys toward which movement occurs and how do they relate to the two formal sections? Here a useful pattern emerges. Tonicization to Ab defines the beginning of the B section, and temporary movement toward Eb major (measures 3–4) and G major (measures 11–12)—in both cases II–V7s of those keys without landing on the respective I chords—occurs at precisely the same places (the third and fourth bars) in both the A and B sections.


Diverse Approaches to Analysis

EXAMPLE 15.2 Jerome Kern, “All the Things You Are”

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Attending to further detail, yet still within the overall structural realm, we can see that the last four bars of the piece return to C major via a common II–V7–I progression followed by an interesting turnaround that leads back to the top of the form. The prominent feature of the turnaround is the minor-third root movement that begins on the bIII (Ebmaj7) and proceeds by a cycle of fifths to the subV7 (Db7) that leads back to the top of the form. Moving toward Roman numeral analysis and chord-scale analysis, it is important to see the II–V7 chords as related to their respective tonics and to think both in terms of parent scale and individual chord scales for improvising purposes. The most simple way to approach this piece is to think in terms of four major scales: C, Eb, Ab, and G and apply them to the respective sections in the form. From here, more nuanced strategies are possible at various points. For instance, owing to the overarching C major backdrop for the entire piece, one can play a Lydian b7 scale instead of Mixolydian on the Bb7 in bar 4. And let us not forget that this scale and other scales are, like altered extensions, viable options even in strictly diatonic progressions.

Jerome Kern’s “All the Things You Are” Recommended listening: Many recordings of this piece are available, including Chet Baker, The Best of Chet Baker Plays; Keith Jarrett, Setting Standards (Standards I and II, Changes, ECM 2008); Ella Fitzgerald, The Jerome Kern Songbook (Verve 1963); Brad Mehldau, The Art of the Trio, vol IV (Warner Bros 2005); and Charlie Parker, Bird After Dark (Savoy 1952).

Whereas “Lady Bird” could be analyzable within the key of C, with three instances of tonicization, “All the Things You Are” provides a good illustration of a piece that uses both tonicization and modulation. The piece is an AABA form, in Ab major, with movement to four other key areas. Section A is largely in Ab and ends with a tonicization in C major (III major). Section A1 is in Eb and follows the same pattern, ends with a tonicization in G major (again III, but this time of Eb), setting up what might be seen as a modulation to G in the first four bars of the B section. Hence, the effect is of a first phrase (A) implying movement to III but not fully or permanently establishing that as the new tonic, and then a second phrase, a fifth away, similarly moving to III, but this time III is established as the new key at the bridge. The second four bars of the B section shift to E major; whereas sections A and A1 move toward III, B moves toward VI. The final A section begins just like the initial A, but is extended by an extra four bars. An important moment here is the IVmaj to IVmin7 sequence—an instance of passing modal mixture—that represents a break from the harmonic sequence established strongly in the ear by this point. Whereas IV previously (the first A section) led to tonicization in III major, now being followed by IV minor allows the harmony to lead to III minor and


Diverse Approaches to Analysis

the cycle of II–V7s that lead back to I (e.g. IIImin7–V7/II-IImin7–V7–Imaj6). Notice the use of the maj6, 9 chord instead of the major seventh due to the root in the melody. In summary, this relatively long form is easily graspable when we proceed from the whole-to-the-parts perspective: Form: AABA. Key: Ab. Key areas: Section A is in Ab and tonicizes to III major (C). Section A1 is in Eb and tonicizes to III (G). Section B stays in G for four bars, and then tonicizes in E for four bars. Section A is identical to A1 except that IVmaj is followed by IVmin and leads back to I via two cycles of II–V7s.

John Coltrane’s “Moment’s Notice” Recommended listening: John Coltrane, Blue Trane, “Moment’s Notice” (Blue Note 2003, original release 1957).

John Coltrane’s “Moment’s Notice” is outstanding among his several prominent compositions exemplifying rapid movement between distant key areas. Again, we proceed from whole to parts. The piece is in Eb major. The form is AB which repeats, with an extended B section on the second ending. Within these large sections, the A section may be divided into two four-bar phrases, as may the B section. Hence, a predominant aspect of the framework is the use of four four-bar phrases the first time through the form. On the repeat, the last four-bar phrase is extended in length to eight bars. Let us now seek patterns and relationships between the many chords and tonicization activities that characterize this piece. At first glance the tempo of the piece, the sheer number of chords, and the seemingly random way in which they move may seem daunting, to say the least, when it comes to improvising on this framework. At closer inspection, however, significant patterns are evident that will greatly facilitate this task and reveal that every single chord upholds a function within this tightly knit, coherent, and anything-butrandom structure. Most evident is that the tonal centers of the four-bar phrases move in a readily identifiable pattern prior to the repeat: Eb–Db–Ab–Gb. In other words, they move down a step, up a fifth (or IV of the original key) and down another step. On the repeat, a slight modification is found—Eb–Db–Ab–Eb—yielding a highly manageable way of conceptualizing this framework. Needless to say, what happens within these tonal centers presents a more formidable set of challenges to the improviser, for Coltrane does not just frame these areas with corresponding diatonic chords but in fact makes use of extensive non-diatonicism. Nonetheless, prominent patterns are evident that help us navigate this non-diatonic movement. First, at the heart of each four-bar phrase—the middle two bars—are II–V7–I sequences that affirm the respective tonal centers. Second, the II chords of the first two phrases are preceded by II–V sequences from a key center a half-step above. In the first four bars, the Emin7–A7 sequence in the first bar is from D, which precedes the

Diverse Approaches to Analysis

EXAMPLE 15.3 Coltrane, “Moment’s Notice” © Jowcol Music/RKM Music. Used by permission.



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Fmin–Bb7–Ebmaj7 sequence from Eb. In the second four bars, the Dmin7–G7 sequence in the first bar is from C, which precedes the Ebmin7–Ab7–Dbmaj7 sequence from Db. Hence, we now have a handy way of thinking about the first three bars of the opening two fourbar phrases. We will deal with the fourth bar of these phrases below. While the third four-bar phrase deviates from this pattern (although the fourth phrase returns to it), this deviation involves the use of a harmonic practice so common that it scarcely contradicts our pattern-seeking efforts. Here a cycle of two II–V7 sequences (the second involving a subV7) begins in the first bar that smoothly sets up the third tonal center: Cmin7–B7–Bbmin7–Eb7–Abmaj7. The third phrase returns to the pattern evident in the first two where the II of the tonal area is preceded by a II–V7 from a tonal center a half-step above: Amin7 D7  Abmin7 Db7  Gbmaj7  Now let us look at the fourth bar of each of the four-bar phrases. At first glance it may appear difficult to account for the Abmin7–Db7 sequence, except to label it perhaps as II–V7 of bIII, or alternatively as a II–V that begins on IVmin. However, we can think of this II–V as a kind of foreshadowing of the later arrival, albeit temporary, of Gb, which we have seen is the fourth of the four tonal centers of the piece. To be sure, it may be a stretch to suggest that the ear, perhaps upon the second iteration of the form, retains this longdistance relationship. But a closer look may give reason for pause, since the Db7 chord, V of Gb, returns in the fourth bar of the third phrase. Realizing this provides yet another piece of the puzzle in finding a place for this sequence. In the second four-bar phrase, the last bar is identical to the first, which greatly facilitates conceptualization: Dmin7 G7  Ebmin7 Ab7  Dbmaj7  Dmin7(b5) G7  Moreover, this bar propels movement to the first bar of the third phrase by extending, on the front end, the cycle of II–V7s that characterizes this passage: (Dmin7 G7)  Cmin7 F7  Bbmin7 Eb7  Abmaj7  Db9  As stated above, the fourth bar of this third phrase involves movement similar to that which we have already seen, where a V7 (or in this case V9) from a distant key area sounds yet whose resolution is temporality delayed. This only serves to magnify its arrival at its I, Gb, in the next phrase. We see this exact pattern occurring in the last bar of the last phrase, where the II–V7 of the opening key area (and overarching key of the piece) sounds. Then, when the music repeats back to the top, the same delayed resolution to its I is caused by the opening II–V7 sequence a half-step above. The second ending of the piece involves a rather conventional use of diatonic chords atop a Bb pedal in Eb and requires no further commentary. It should be evident from this analysis that every chord in this piece upholds a precise and intricate role in both its localized harmonic group, and because each group forms a network of subwholes, sustains a relationship to the whole.

Diverse Approaches to Analysis


In summary, we can grasp “Moment’s Notice” through these structural components. Form: AB. Key: Eb. Key areas: Eb, Db, Ab, Gb, and on the repeat Eb, Db, Ab, Eb. Patterns within sections: Each key area lasts for four bars and is framed by its corresponding II–V in the middle two bars. The first and last bar of each four-bar key area includes a II–V7 sequence (or just V) that is non-diatonic to that particular key area but which may be related to other II–V7 sequences or tonal centers in the form. Analysis This Coltrane-inspired piece moves through several distantly related key areas but, unlike “Moment’s Notice,” the key areas are not analyzable in relationship to a tonic key. Instead, the harmonic structure is to be analyzed in terms of relationships between key areas, reminiscent of our early free-tonicization work. How many key areas can you identify in the piece? What patterns can you identify in terms of the movement between chords and key areas?

Exercise 15a and Example 15.4 Ed Sarath, Counting Up. © 2009 Ed Sarath

Jazz musicians typically have significant amounts of repertory committed to memory. The ability to recognize patterns is invaluable to learning pieces quickly and being able to improvise on even the most intricate forms without being encumbered by their idiosyncrasies. Other pieces by John Coltrane that embody the above principles include Giant Steps, Countdown, Lazy Bird, and his lovely ballad Central Park West, which we will use as a vehicle for expanding our improvisatory conception in Chapter 16. As stated above,


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our focus with this repertory has been on harmonic structure given its direct relevance to improvisers. A variety of other analytical angles—melody, form, rhythm, texture—might have also been pursued were the focus of this book a study in jazz composition. It must be emphasized, however, that ultimately the essential role of improvisation and the overall structural intricacies of jazz works cannot be separated from one another, and thus the above considerations would factor prominently in any such analysis. Let us now look at some examples of European classical repertory to gain a glimpse of some analytical considerations that might come to the fore in music that is not intended as an improvisatory vehicle.

EXAMPLE 15.5 Chopin, Prelude, Op. 28, No. 4

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Chopin, Prelude, No. 4 Recommended listening: Claudio Arrau, Ultimate Chopin (Decca Music Group 2006).


This piece might be thought of as jazz-like in its use of a melody in the right hand, chords in the left, and occasional use of extensions. Its harmonic rhythm varies from one measure to the next, sometimes involving one chord per bar, other times two per bar. Analyze the harmonies and write down the contemporary chord symbols for each chord, making sure to indicate the proper inversion; you will find an interesting sequence. However, what is most prominent in this piece is the horizontal—and here is where our analytical inquiry begins to change course—melodic movement in multiple voices, in which stepwise descending lines, often involving half-step resolutions, define the tonal flow. Vertical chord structures are by-products of this melodic movement, within which four discrete lines might be identified. The first is the treble clef melody itself, which might be reduced to the following skeletal sequence of pitches:


Diverse Approaches to Analysis


The next melodic line is the top voice in the bass clef/left hand, which might be reduced as follows:


The two underlying lines may be reduced as follows:



In essence, analysis entails apprehending a piece of music as a kind of character in a play, requiring us to penetrate to what it is that makes this particular piece unique. Just as every individual is unique, every piece of music is different and calls us to try to figure out what makes it so. In this Chopin Prelude, the horizontal flow of its multiple voices stands out as an essential aspect. The harmonies are by-products of this flow, reminding us of a principle that was introduced early on regarding the interchangeability of chords and scales/melodies: chords are vertical manifestations of pitch regions, scales and melodies are horizontal manifestations. This piece could be analyzed either in terms of its vertical, harmonic structures or its horizontal, melodic structure. We have focused on the latter in that it exemplifies an angle not so readily evident in jazz literature, particularly given the approach we have taken to that literature. Keyboard exercise Improvise at the keyboard a piece that roughly emulates the gesture (or basic shape) of the above Chopin Prelude. Play or sing a melody consisting primarily of sustained notes and play chords beneath it that move smoothly, with only one or two notes changing between chords. Do not be concerned with the names of the chords or whether or not

Diverse Approaches to Analysis


they may even be labeled in a conventional manner. Rather, let your fingers and ears guide the movement. The intent is not to replicate the harmonic language of the Chopin piece but rather the texture. It is entirely acceptable if your improvised emulation makes use of extended jazz-like harmonies or even atonal structures.

Exercise 15b

Schubert, Waltz Let us now turn to another European classical selection, this time a Schubert Waltz. After listening to the piece a number of times, attempt to identify its salient elements. The following questions serve as a guide. Analysis Identify key, provide Roman numerals, and contemporary chord symbols. Analyze the melody in terms of antecedent-consequent phrases, motivic development, and sequence. Identify the sections of the piece that make it AABA, and explain how the harmonies support these sections. Does the piece involve modulation or tonicization? What are the highest melody notes and the lowest bass notes and their possible significance in upholding the formal structure? What kind of chord is found on the last beat of bars 6 and 14 and what role does this chord play in shaping the phrase? Compare this chord to that found in bar 23. Can you find examples of the kind of voice-leading movement noted in the Chopin piece? Compare the rhythmic aspects of this piece to the Chopin piece.


Diverse Approaches to Analysis

Exercise 15c and Example 15.11 Franz Schubert, “Waltz”

Recommended listening: Paolo Bordoni, Schubert: Complete Waltzes (EMI 2006).

Analysis is a tool for delving more deeply into a given piece or kind of music and understanding the relationship between its structural features, purpose/s, and the experience it might elicit. Different kinds of music call for different analytical approaches, and as musical practice draws increasingly from diverse repertories, it is equally important for corresponding models of theoretical investigation to also emerge that enable musicians to penetrate the inner workings of diverse musical forms. In this chapter we have gained a small glimpse of the contrasting approaches to analysis that are possible. In our examination of jazz repertory, we focused on harmonic structure in that the more we understand how the parts relate to the whole, the greater our capacities to create atop the form when we improvise. From this standpoint, interpretive performers—even if not having the option to alter or invent harmonies, melodies, and rhythms—will also benefit from a grasp of the overall architecture of the music they play. At the same time, important questions are raised about looking at improvised music through a notation-based lens. While notation-based analysis can reveal much about a fully composed notated piece, how much can it tell us about music that involves a significant improvisatory component? In jazz, up to 90 percent of a given performance may be improvised. Even if we transcribe an improvised piece, to what extent can notation convey the kinds of interactions and creative decisions that were made on a moment-to-moment basis? Or the possible influence of the audience on the creative process? Whereas with composed notated music, the analytical process roughly resembles the composition process in that we can pause, examine a moment at length, proceed to what came before or what

Diverse Approaches to Analysis


follows, just as could the composer; if we examine a transcribed improvised piece from this standpoint, we depart fundamentally from the kind of engagement that was available to the improviser. These questions point to even more underlying ones that are related to the confluence of improvised and composed music. What are the unique expressive results that are possible when music is made up on the spot, particularly through collective interaction? What are the unique expressive results that are possible when a single composer fashions a work over a period of weeks or months? What are the socio-cultural or other extramusical factors that may have given rise to these contrasting musical paradigms? What are some of the interesting ways in which improvised and composed music have merged? What frontiers remain to be explored? What are the ramifications of these issues for musical study?

SUMMARY QUESTIONS 1 Name a common purpose in the analysis of jazz and European classical repertory when it comes to understanding harmonic structures. In other words, what kind of insight can analysis reveal about harmonic form that is useful to both jazz improvisers and interpretive performers? 2 What is the difference between tonicization and modulation? 3 Modulation can only occur between closely related keys. True or false? 4 How many key areas does the harmonic structure of “Moment’s Notice” move through? 5 What are some of the limitations in notation-based analysis when it comes to music with a significant improvisation component?

chapter 16

Fine-tuning and Expanding the Jazz Palette

In this chapter, we: • Explore ways of fine-tuning and expanding our creative horizons as improvisers. • Improvise on John Coltrane’s Central Park West using rhythmic, intervallic, motivic, and non-syntactic parameters as creative catalysts. • Look at jazz repertory that uses new harmonic and rhythmic elements.

The ability to play over contemporary chord changes with authentic time-feel conception may be the single most valuable skill area for today’s musicians when it comes to the broader musical pathways this skill set opens up. Between the formidable technical prowess on one’s instrument, strong aural skills, harmonic fluency, creative instincts, and the rhythmic foundations—with their ample global connections—that jazz requires, this idiom holds a special place in the training of contemporary, creative musicians. In this chapter, we explore approaches to improvising on jazz chord changes that are not commonly addressed in conventional jazz instruction in order to promote more individualized and inventive music making. We will also look at harmonic and compositional techniques that move beyond the tonal harmonic formats with which we have been working. We begin with methods for fine-tuning our improvising in chord-change formats and then explore new approaches to playing over changes. We will use John Coltrane’s Central Park West as a vehicle for these purposes.

Recommended listening: John Coltrane, Coltrane’s Sound, Central Park West, (Atlantic 1960).

Fine-tuning and Expanding the Jazz Palette


EXAMPLE 16.1 Coltrane, Central Park West. © Jowcol Music/RKM Music. Used by permission.

Rhythmic Layers for Melodic Clarity After listening to a recording of the piece, proceed to the following exercises. Our initial focus will be to simplify the rhythmic dimensions of our improvising in order to enhance the clarity of our melodic lines and their relationship to the underlying harmonies. Collective chorale improvisation Play the head as it is conventionally notated and played. After repeating the head, improvise collectively in the style of the head, creating a kind of chorale texture—an illustration of which is provided in Example 16.2—that is based in a rhythmic template derived from the head. Be sure to derive notes from the chord changes and related scales. This exercise may be played on any number of instruments.

Exercise 16a and Example 16.2


Fine-tuning and Expanding the Jazz Palette

Chorale-style solos Now play individual solos in the chorale-style format, with rhythm section background (this could be just piano or guitar or bass, depending on instrumentation in the class). This is not the place for reeling off stock II–V–I lines, which the rhythmic constraints of the chorale format will in any case not permit. Rather, play the simplest, clearest lines that are as locked into the chord changes as possible.

Exercise 16b

For some musicians—including those who have achieved a certain degree of dexterity— this may be a challenge, as they may not be accustomed to playing so rhythmically, simply and lyrically. In this first series of drills we will use only diatonic melody tones—notes that are within the diatonic chord scales; altered tones will follow. This process may be likened to applying species principles to jazz chord changes. Just as in our species improvising, where despite its rhythmically simplified nature we placed rhythmic integrity at a high premium, it is similarly important to maintain strong rhythmic integrity while improvising with the clear and simple rhythmic values of the template. Here it may help to conceive of subdivisions at this slow tempo to aid in the process. As with the first three species, we will halve the rhythmic values in the next few exercises—moving from the quarter notes of the above choral format to eighth notes, then sixteenths, then thirty-second notes. We will also incorporate two more strategies: one is that each soloist plays unaccompanied the first time through the chord sequence, and then the accompaniment comes in the second time; and second is where we will use a modified version of the form that allows us to focus on the opening sequence of chords. C#min7 F#7 : Bmaj7/Emin7 A7  Dmaj7/Bbmin7 Eb7  C#min7 F#7 : Rhythmic template solos Take turns soloing using the rhythmic template below (four eighth notes and a halfnote). First time through the sequence the soloist plays unaccompanied, second time through with accompaniment. The same goals of clarity and lyricism apply.

Exercise 16c and Example 16.3

Fine-tuning and Expanding the Jazz Palette


Rhythmic template solos A next round of solos follows, and again a new rhythmic template is introduced, this one involving eight sixteenth notes that land on the half-note target note as shown here. First time unaccompanied, second time with accompaniment.

Exercise 16d and Example 16.4

If you are able to consistently play strong sixteenth-note lines, you may proceed to the next exercise that uses thirty-second notes. If not, you may still attempt the drill as a kind of experiment, but it is recommended to spend the bulk of your practicing on the previous one until you are consistently able to play lines that clearly align with the harmonies as well as being grounded in solid rhythm. Thirty-second note solos Improvise as above but now use sixteen thirty-second notes that begin a phrase which lands on a half-note. First time unaccompanied, second time accompanied.

Exercise 16e

At this point, you may return to the previous exercises and use altered scales as discussed in the previous chapter, or you may continue and return to the above formats later.

Registral, Density, and Contour Variety Now let us apply further constraints. One is to use different intervallic sizes in improvising on this framework (Exercises 16f–16h). Improvisation Improvise on the above sequence using registral variety (your highest and lowest notes).

Exercise 16f


Fine-tuning and Expanding the Jazz Palette

Improvisation Improvise on the above sequence using density variety.

Exercise 16g Improvisation Improvise on the above sequence using ascending lines the first time through, then descending lines the second time.

Exercise 16h

Intervallic Variety Improvisation Improvise on the sequence using fourths and fifths as much as possible; a sample line is shown. Same format as above: unaccompanied first time through, then accompanied second time.

Exercise 16i and Example 16.5

You may also experiment with sixths, sevenths, and larger intervals. Improvisation Improvise using seventh chord arpeggio shapes as illustrated.

Fine-tuning and Expanding the Jazz Palette


Exercise 16j and Example 16.6

Whereas the seventh chord arpeggio shapes in Exercise 16j largely used intervals of thirds (e.g. 1, 3, 5, 7, or 3, 5, 7, 9), exercise 16k illustrates the use of dominant seventh chord shapes that are derived from extended voicings on those chords (diatonic extensions).

Improvisation Improvise using seventh chord arpeggio shapes on the II chords and shapes based on the V7(9, 13) voicing (review Chapter 13) on the dominant chords (Example 16.7).

Exercise 16k and Example 16.7 Improvisation Improvise using altered dominant voicings (review Chapter 14) melodically on the V chords, as demonstrated in Example 16.8.

Exercise 16l and Example 16.8


Fine-tuning and Expanding the Jazz Palette

Motivic and Multi-motivic Development In this section, we improvise with motivic development, first taking a single motive and developing it sequentially on the chord changes, and then using the process of multimotivic development introduced in Chapter 1, now applied in a chord changes context. One of the biggest challenges in these kinds of drills is establishing motivic clarity and not allowing stock patterns to clutter the melodic tapestry and obfuscate the sense of identity we want to establish with each motive. A good litmus test for the degree of clarity being established is to stop the music mid-solo and ask classmates to sing the motive being developed. If the motive is clear, the response will be immediate from the entire class. If the motive is unclear, the response will either be silence or lengthy debates about whether or not some aspect of what had been played might be considered motivic. Keep in mind that any idea can serve as a motive, but it is only when it is reiterated on a new pitch level or altered in some way (but not to the extent where its relationship to the first iteration is obliterated) that it becomes a sequence. The multi-motivic development exercises are particularly challenging in that they require the improviser to sustain awareness both of the chord changes as well as a linear, horizontal conception whereby not just one but multiple ideas are developed. Improvisation Improvise using motivic development The sequence in Example 16.9 illustrates one possibility.

Exercise 16m and Example 16.9 Improvisation Begins exactly as above with a first motive (A) introduced and then reiterated sequentially. But now a new motive B is to be introduced, followed by a fragment from A, and then another iteration of B. There are no rules as to how long you must wait until a second motive is introduced, or what part of the beat it must come on, or its length. What is most important is the clarity of the ideas and that the two (or more) motives are as contrasting as possible from one another. Improvise and sequentially develop the two contrasting motives.

Exercise 16n

Fine-tuning and Expanding the Jazz Palette


As discussed above, one of the biggest challenges in this exercise will be the tendency to fall back on stock phrases either in between or in place of the motives, thereby resorting to conventional conception and rendering this exercise unproductive. Think of the different motives as unique characters in a play, each with very diverse identities. There should be no question regarding the different motives: when A sounds, that identity should be crystal clear, and when B comes in, that contrasting identity should also be crystal clear. Even when the motives begin to be mixed, the use of fragments from each should be clear. Vigilance with this aspect of this exercise will go a long way toward taking you out of your familiar mode of playing and expanding your horizons. In no way is this to suggest that the phrases and concepts that are deeply lodged in your fingers and ears, acquired through much hard work, are all for naught. In fact, they represent a creative foundation to be built upon, not annihilated. When we engage with exercises such as these that expand our horizons, our goal is to both expand upon what already exists, as well as help us free up from the binding attachments inherent in mastery of any kind of knowledge or technique. But freeing up from attachments is not to obliterate the content that has been internalized. Rather, we want to access that content in new and more fluid ways. Artistic development is an additive process whereby we want access to the totality of everything we have studied and been exposed to. Improvisation Now play Central Park West using the full form, as shown in Example 16.1, using this format for solos: each soloist plays one chorus apiece, playing unaccompanied for the first six measures, with accompaniment entering on bar 7.

Exercise 16o

Integrating Strategies The above strategies can greatly expand the improviser’s creative palette as well as bring clarity and depth to our playing. It is one thing to reel off idiomatic lines that align with changes; it is quite another to consistently invent and develop ideas on a moment-tomoment basis, driven by perception of the possibilities inherent in a given idea. This involves an entirely new kind of concept, a new level of being in the moment, to be able to fathom an idea as a generator of subsequent ideas as opposed to serving as yet another link in a chain of events. The above exercises will help cultivate this kind of awareness. Several questions arise at this point: How does one integrate these strategies into one’s playing? Does this require conscious attention to a particular approach every time one improvises? If so, will not this distract the improviser from the interactive focus that is necessary when playing in groups? By taking some time to work on these inventive strategies on a regular basis, they will naturally inform one’s playing. In this sense, they are very much like aural transposition and other kinds of technical practice; one invests the time in these areas and then, when it comes time to play, the focus should be on the music rather than on the technique. Indeed, it would


Fine-tuning and Expanding the Jazz Palette

be difficult if not impossible to keep in mind all the strategies at once. As you work with these kinds of ideas, however, one or another may spontaneously come to mind in the middle of a solo and thus serve as an organizational catalyst at that moment should the improviser choose to use that idea. The ultimate purpose of the above kind of practice is to cultivate profundity by taking one outside of ordinary patterns. Improvisation Play Central Park West from beginning to end, with the option of either consciously using one or more of the above strategies, or simply the intention of allowing a newfound clarity and depth to manifest in your playing.

Exercise 16p

Expanding the Harmonic Palette Let us now begin to expand our harmonic spectrum by moving beyond the functional tonal contexts that have been our focus beginning with Chapter 5. Today’s musical landscape, involving tonal, modal, and post-tonal elements, offers musicians a wide variety of creative possibilities, and the grounding we have gained so far in tonal practices provides us with formidable tools to partake of this landscape. Musicians often think of this landscape in terms of a continuum that extends from “inside” to “outside” sonorities. To generalize, inside sounds are more consonant, outside more dissonant. Viewing this in terms of extremes, strictly diatonic, triadic passages or perhaps those created according to strict species counterpoint principles might be considered to be the most inside sonorities. The atonal, serial music of Arnold Schoenberg, Anton Webern, Milton Babitt, and Pierre Boulez might be placed at the most outside end of the continuum. Most of the music made falls within the infinite range of possibilities that exist between these extremes. Although more than a few musicians in the early to mid-twentieth century believed that tonality would fall by the wayside as a result of the emergent atonal practices, the opposite has proven to be the case. The infusion of the pitch and rhythmic aspects of world musics in contemporary Euroclassical and jazz (from early on) has played an important role in this affirmation and enrichment, rather than dissolution, of tonal-modal and post-tonal-modal practices. Nonetheless, an inside-to-outside trajectory of pitch practice is clearly evident in the musical world and provides a helpful context for understanding salient principles that prevail today. While it is beyond the scope of this book to delve extensively into these possibilities, here are a few key structures and strategies that will begin to bridge our tonal foundations with the broader range of options. Several kinds of harmonies outline this continuum: Major 7 chord with ninth in the bass Major 7(b5) chord in root position or inverted

Fine-tuning and Expanding the Jazz Palette


Major 7(#5) chord Polytonal harmonies


In addition, a relational principle comes into play that is prevalent in post-tonal music, where the hierarchy of subdominant–dominant–tonic chord functions prevalent in tonality gives way to more non-linear, non-hierarchical functions in which chords are often quasiindependent “islands.” Example 16.11 shows a passage that utilizes several of the new chord types and principles. The E pedal in the first four bars underlies and unifies the overlying changing harmonies, creating a sense of tension that is resolved when the E moves to Eb in bar 5. The Fmaj7(b5)/E and Bbmaj7(b5)/E, structures in bars 2 and 4 are structures that have been used extensively since the 1970s and are often associated with the music put out by the ECM jazz record label. The maj7(b5) chord retains its distinctively colorful sonority whether in root position or when inverted; the two inversions seen here, one with the seventh in the bass, the other with b5 in the bass, are common. In bar 5, the Gbmaj7/Ab is another addition to our chord palette, this involving a major seventh chord with the ninth in the bass. Since the ninth is part of the diatonic chord scale, the added tension does not detract from the characteristic resonance and stability of the major seventh chord sonority. Notice the use of inversion in bars 5 and 6 to create contrary motion between the descending bass line (Ab–Gb–E–D–C#) and the ascending melody line. Also notice the sustained melody note in bars 7 and 8, against which are two distantly related chords (defined by the use of two or more accidentals). What is important to recognize here, however, is that the chords share two common tones, one of which is the melody note, and thus the co-existence of strong unifying features as well as diversifying features define this moment.



Fine-tuning and Expanding the Jazz Palette

While the chords in Example 16.11 move significantly between a number of key areas, because all the sonorities are diatonic within themselves, the overall impact is heard as relatively “inside.” This point is illuminated if we look at the chord scales to be used in improvising on these harmonies; they are all among the diatonic modes. Emin7(9) takes E Dorian; Fmaj7(b5)/E takes F Lydian (or E Phrygian); Amaj7/E takes A Ionian or Lydian; Bbmaj7(b5)/E takes Bb Lydian or E Locrian, etc. Accordingly, if we think of each chord as part of a pitch region—which manifests vertically as chords and horizontally as scales—the passage moves from one diatonic pitch region to another. Chromatic richness is created by the range of movement from one region to another rather than the structures within each region. The passage thus falls toward the inside portion of the post-tonal-modal portion of the inside–outside continuum. The passage shown in Example 16.12 involves chords that begin to move toward the outside portion. First is the major7(#5) chord, which as the symbol indicates is the major seventh chord with a raised fifth degree. This chord is not a diatonic chord and thus requires a non-diatonic chord scale—the Lydian#5 scale—for improvising purposes. A bit more outside sounding is the Fmaj7/Gb chord in bar 5, which in consisting of a major seventh chord atop a non-diatonic bass note hints at polytonality—the co-existence of more than one tonal area.


Improvising over polytonal harmonies presents interesting challenges when it comes to identifying chord scales. In the case of the Fmaj7/Gb, we have a couple of options. We can simply add the Gb to the diatonic chord scale, thus resulting in an additional half-step movement (e.g. F-Gb–G) in the F Lydian (or Ionian) scale. Here it is also possible to construct a scale with two tetrachords that align with the chord structure, as Example 16.13 shows. The G/Eb chord is similar to the previous chord except that it consists of only a triad rather than a seventh chord atop the non-diatonic bass note. Here two chord scale possibilities may be identified. The first is the Lydian(#5) scale. The second is the augmented scale.

Fine-tuning and Expanding the Jazz Palette




Example 16.15 takes us even further to the outside range of the post-tonal-modal spectrum. Here we find highly dense sonorities that derive from the superimposition of two or more chords atop one another. The saxophonist David Liebman is known for his innovative use of such harmonies. Here fully notated voicings are provided in addition to the chord symbols.


Fine-tuning and Expanding the Jazz Palette

Fine-tuning and Expanding the Jazz Palette


EXAMPLE 16.15 David Liebman, Le Roi Du Monde. © David Liebman. Used by permission.

Recommended listening: David Liebman, with Jean-Paul Celea and Wolfgang Reisinger, Missing a Page, “Le Roi de Monde” (Label Blue 1998).

Cross-stylistic Melding The following are two compositions of mine that illustrate the merging of styles and influences that is prevalent in today’s musical world. The first is Quiet Mind, which draws from jazz, popular music, and European classical sources and combines several harmonic strategies discussed in the book as well as new ones. Look at the solo section; for example, the first 16 bars are modal in nature given the relatively long stretches on each chord. However, unlike conventional modal approaches, which tend to use diatonic modes, here the Ebmaj7(#5) and Dbmaj7(#5) chords call for lydian (#5) chord scales. When the harmonic rhythm speeds up on the second 16 bars of the solo form (which are the exact chord changes from the B section of the main theme), we find glimpses of tonal harmony, particularly with the Bbmin(M7) to Eb7(b9, b5) sequence, which is a II–V. But there is no I chord to be found here. Instead, a C triad with b9 in the bass, followed by B, A, Bb, and Ab triads over a G pedal, hint at a kind of polytonality that, as occurs in the main theme of the piece, links the lyricism and harmonic simplicity of the first 16 bars of the main theme with somewhat more dense sonorities. Turkish Tihai (Example 16.17) makes use of Arabic melodic and rhythmic inflections, and also an Indian cadential rhythmic device called “tihai.” Tihai translates from Hindi as “three times,” with the basic idea involving the use of a repeated pattern at the end of a passage in order to accentuate the return to the first beat of the rhythmic cycle. What makes the tihai pattern exciting is the precise mathematical placement of the idea, where the last note of the pattern becomes the first note of the beat cycle. The effect is very exciting, as it leaves the listener in a state of intense suspension, only to resolve the suspension with an unanticipated arrival at the central point of the beat cycle: sam, or 1. Examine bars 58–62


Fine-tuning and Expanding the Jazz Palette

and notice that the tihai pattern consists of a six-beat phrase that repeats three times over a seven-beat cycle and that, on the last repetition, the last beat of the pattern lines up to sound on beat 1 of the cycle to bring the phase to a powerful close. It should be noted that while in this context the tihai is composed, Indian musicians actually improvise these patterns, which requires an extraordinary command of rhythmic cycles and awareness of exactly where they are in the cycle at all times.


Fine-tuning and Expanding the Jazz Palette



Fine-tuning and Expanding the Jazz Palette

EXAMPLE 16.16 Ed Sarath, Quiet Mind. © 2000 Ed Sarath.


Fine-tuning and Expanding the Jazz Palette



Fine-tuning and Expanding the Jazz Palette

EXAMPLE 16.17 Ed Sarath, Turkish Tihai. © 1999 Ed Sarath.

Final Composition Project Composition Compose a piece that uses as many of the new harmonic structures that we have encountered in this and recent chapters as possible, as well as odd or mixed meters. Harmonic possibilities include: extended and altered chords (e.g. min7(9), V7(9,13), maj7(9), min7(11), major seventh chords with ninth in the bass, maj7( 5) chords in various inversions, maj7(#5), and polytonal harmonies.


Exercise 16q

Final Creative Synthesis The following exercises involve a return to the trans-stylistic approach introduced in Chapter 1 and the integration of these strategies with style-based approaches. It may be helpful to review Chapter 1 and return to some of the exercises presented there (e.g. wheel of duets, use of non-syntactic catalysts). As you do so, you will likely marvel at the skills you are now able to bring to those formats. Moreover, you may find that engaging in transstylistic improvisation after extensive style-specific immersion expands your creative capacities in the latter area. In other words, the formidable tonal, modal, harmonic, melodic, and rhythmic skills that now comprise your inner reservoir, in addition to serving as expanded resources for creative expression, may also be expanded through trans-stylistic creative application. Style-specific immersion and trans-stylistic exploration are not conflicting but rather highly complementary aspects of artistic development, and most of the major innovators exemplify this principle.

Fine-tuning and Expanding the Jazz Palette


Creative project In your small group, prepare a multi-movement piece that includes trans-stylistic improvisation (where no stylistic constraints are specified, so that the resultant music may draw from wide-ranging style influences) as well as style-based improvisation and composition. The movements of the piece may be continuous, each unfolding organically from the one preceding with no break, or they may be discrete sections with their own beginnings and endings.

Exercise 16r Collective free improvisation Divide the class into random configurations and improvise with nothing planned in advance. Then play a collective improvisation with the entire class as the ensemble. The importance of listening, clarity of ideas, laying out when appropriate, attention to endings, and other principles of collective improvising cannot be emphasized too strongly in this challenging and exciting approach to music-making.

Exercise 16s

Concluding Thoughts Artistic development is a lifelong endeavor in which the totality of our experience, in and beyond our particular disciplines, shapes our creative expressions. At every stage of this development, robust creative engagement and rigorous study of craft need to occur in close relationship with one another. When the creativity–craft interaction is in place, depth of expression, assimilation of skills and knowledge, the levels of meaning and fulfillment derived from our work, and the capacity to transcend boundaries—whereby we see our particular terrain as part of a broader, cross-stylistic, cross-cultural expanse—are optimal. When the creativity–craft interplay is lacking, which often manifests in an over-emphasis on craft at the expense of creative application, this range of development will most likely be limited. Thus, while learning, models and resources are often assessed in terms of the content they cover; without corresponding creative processes through which content is genuinely internalized, any claims toward efficacy are without firm basis. Given the diverse nature of today’s musical world, where the sheer volume of knowledge far exceeds what can be covered in any given curricular model, there is no more important goal in musical study than to establish grounding in this creativity–craft interaction. This lays the groundwork for a newfound self-sufficiency, where acquisition of skills becomes driven not primarily by external, institutional incentives but by the very inner spark that has been central to the innovations of artists and thinkers through the ages. If Music Theory Through Improvisation has been able to provide even a glimpse of this, it will have achieved


Fine-tuning and Expanding the Jazz Palette

a significant purpose since, once lit, the spark of artistic creativity only increases in intensity and has the capacity to propel a lifelong, self-driven quest for growth.

SUMMARY QUESTIONS 1 The harmonic progression to Central Park West covers how many key areas? 2 What is meant by pedal point and what is its musical effect? 3 Name an instance in which one might choose to create a solo form that is different from the form of the head? 4 Define “tihai.” What musical tradition does this device come from?

appendix 1

Introduction to Species Counterpoint

In 1725, J.J. Fux codified basic principles of contrapuntal writing, inspired by the music of the sixteenth-century master Palestrina, in a treatise called Gradus ad Parnassum. The system of “species counterpoint” presented in Gradus has been used as a foundational tool by composers through the ages. Counterpoint means “point against point” or note against note, and refers to the art of creating multiple simultaneously sounding melodic lines that both stand on their own and yet also complement one another. It is one thing to create a single strong melody—no small feat—and quite another to create two or more melodic lines that both uphold interest as independent entities and work together when played simultaneously to produce a coherent melodic and harmonic fabric. This requires attention to horizontal and vertical considerations. Horizontal considerations are those pertaining to individual melodic integrity—clarity of ideas, contour, distribution of stepwise motion and leaps, etc. Vertical considerations involve the alignment of simultaneously sounding notes—in other words, which intervals are acceptable in a given context and which are not. At first, the numerous constraints that guide species practice may seem somewhat excessive and perhaps minimally relevant to contemporary tonal-modal concerns. There is no denying that these guidelines confine our work to sonorities that have given way over the centuries to much more expansive approaches, even within the realm of diatonic textures. However, closer inspection reveals potentially significant benefits. In essence, species work takes our hearing and thinking to the most foundational realms of melodic and rhythmic conception. Through the use of whole, half, and quarter notes, we must deal with melody in its purest form, which lays aural and theoretical groundwork for a variety of applications. Indeed, the very 2:1 melodic lines (e.g. eighth-note melodies atop walking bass lines or even-eighth grooves) we have emphasized in jazz and other time-feel-based improvising may be seen as directly related in species practice. We will use a somewhat modified version of species principles in order to fit our particular needs. First, we will improvise as well as compose within three of the species frameworks (first through third species). While naturally we will have to relax our adherence to the full scope of constraints while improvising (e.g. it is not possible, unlike with composition, to stop, backtrack, and pursue alternative contrapuntal pathways), considerable benefits in terms of melodic and rhythmic clarity will nonetheless result from


Appendix 1

these improvisations. Moreover, the interplay of improvising and writing in the species frameworks will provide a level of fluency that may be applied broadly in our overall work. Second, whereas species practice is traditionally done in major and minor keys, with the seventh raised in minor, we will work primarily with modal species formats—thus Aeolian or natural minor without raising the seventh degree—in that this is more conducive to our particular improvisational concerns. Finally, also due to our improvisatory thrust, we will extend third species to include more florid lines than the 4:1 ratios traditionally associated with third species. This will provide a connecting link between species work and contemporary, time-feel improvising.

Overview of Species Principles Species practice is centered in creating counterpoint lines atop a pre-ordained cantus firmus line. Cantus firmus (CF) means “fixed voice,” and we will write and improvise against CF lines created by others as well as create our own. Cantus firmus lines consist entirely of whole notes and may be considered as a kind of skeletal form of melody whose integrity and interest, due to the lack of rhythmic variety, must derive solely from the horizontal flow of its tones. Against the CF may be created five general types, or species, of melodic lines, each of which is based in different rhythmic relationships to the CF and is selected to isolate and thus help musicians attend to particular kinds of horizontal and vertical considerations. As we will consider below, certain intervals produce consonant sounds against the CF, others dissonant sounds, and the art of contrapuntal writing involves the ability to balance the two aspects. As we have considered previously with the interplay of unity and variety, or repose and tension, too much consonance (corresponding to unity and repose) compromises interest, and too much dissonance (variety, tension) undermines the sense of coherence in the music. Needless to say, what characterizes consonance and dissonance from one era to another will change, but the basic principles may be seen to largely hold over several centuries of tonal and modal music. Example A1.1 illustrates the first three species and the way their respective contrapuntal lines divide note values of the previous species in half. First species uses whole-note values in both CF (which consists of whole notes in all species) and contrapuntal lines, and thus forms a 1:1 ratio between contrapuntal line and CF. The CF used in the exercises below is from Fux himself. Second species uses half notes, yielding a 2:1 ratio. Third species uses quarter notes, yielding a 3:1 ratio. Note that all exercises end with whole notes. Note also that in the second species exercise, a whole note is used in the second-to-last measure—this is permissible in instances where no more suitable ending is available. Prior to further analysis, let us play and improvise on this framework in order to directly experience the kinds of musical textures we will be working with.

Appendix 1



Here are examples of the three species from Example A1.1 but now with the more conventional raised seventh degree that leads to the final tonic note. Notice in second and third species the use of the raised sixth degree as well in order to avoid the awkward augmented second interval; at this point the original natural minor or Aeolian mode gives way to the ascending form of the melodic minor. When we improvise on CF lines, as in Exercise A1a, we will use natural minor throughout.


Appendix 1

Cantus Firmus improvisation Two or more players. Everyone sings or plays the CF one or more times to internalize its sound. Then alternate playing the CF and the various species lines in Example A1.1 and improvising on them according to this format: Player A plays the CF while Player B plays the first species melody, and then as Player A repeats the CF, Player B improvises using the same rhythmic values of the melody (half notes—2:1 against CF—in second species; quarter notes—4:1 against CF—in third). Try closing your eyes when improvising and let your ears be the guide. Switch roles.

Exercise A1a

Creating Contrapuntal Lines: General Principles Pertaining to Writing Species Melodies As we prepare to do written work in the particular species frameworks, let us begin with an overview of principles that pertain to all species, followed by species-specific considerations. 1 Confine intervals between melody and cantus firmus to a tenth or less. In other words, if too much space separates melodic lines, their relationship and interdependence is obscured. Occasional twelfths are possible if no other solution appears evident. 2 Crossing of voices—where a voice that begins lower than the CF moves above the CF—is to be avoided as it obscures the integrity of the line.

Appendix 1


3 Successive skips of more than a third are to be avoided in any given melodic passage, whether in the same or in opposite directions. Such skips create a disjointed texture. 4 Contrary motion yields optimal independence between voices, oblique motion yields the next degree of independence, similar motion the next, and parallel motion the next. Independence of lines is most obscured with parallel perfect intervals (fourths, fifths, unisons, octaves) and these intervals should be avoided (see accompanying textbox).

Voice leading Example A1.3 provides the different kinds of voice-leading motions, which are also found in Chapter 6 in relation to chords (here voice leading is shown in relationship to the CF, with Arabic numerals provided to show exact intervals).

5 Similar motion into perfect fifths and octaves is to be avoided. While not as problematic as parallel perfect intervals, these “hidden” fifths or octaves weaken the sense of melodic interdependence. 6 Dissonant intervals—seconds, fourths, diminished fifths, and sevenths—that are approached by leap are to be followed by stepwise movement in the opposite direction. Consonant intervals—unisons, perfect fifths, and octaves—may be approached by leap. Passing tones, neighboring tones, and suspensions (fourth and fifth species) are three types of dissonant tones that are common in species counterpoint (see textbox below).


Appendix 1

Types of dissonance

7 Avoid simultaneous leaps in CF and contrapuntal lines. 8 The last measure of each exercise, regardless of what species is being used, should consist of only a whole note. 9 Contrapuntal lines should maintain their own integrity as self-standing melodies. In addition, here are some important recommendations regarding procedure. Species work, with all the constraints it involves, is ultimately a kind of aural training. It is thus advisable to not use the keyboard to work out the exercises, but rather only to check the sounds you have written. This will force you to hear the lines internally. At first this may seem daunting. A good way to proceed prior to writing contrapuntal lines is to sing the CF several times, getting a clear sense of its melodic shape. Then sing the CF and try to hear sounds that work against the CF within the rhythmic constraint of the species you are working with. Or you may hear internally both the CF and the contrapuntal line. While at first you may just hear single tones as you create your melodies, strive to hear groups of tones and longer phrases. As you begin to create melodic phrases, you can notate them and then check them against the general constraints indicated above and those pertaining to the particular species that follow. Do not be discouraged if what may have sounded perfectly viable turns out to violate one constraint or another; by alternating the internal hearing and creating of lines with analytical examination, you are training the ear and mind to work together in the creative process. As you proceed, you will increasingly hear and generate lines that conform to the constraints.

Appendix 1


It is also important to realize that in order to rectify an error, it may be necessary to change measures that precede and follow that point in the exercise. At times, the best strategy may be to simply begin the exercise again. It is also advisable to determine your ending as well as the possible climactic point in your contrapuntal line prior to creating the line. You are always free to alter these plans (mainly climactic point; usually only one or two options are available for endings) once you begin creating the line, the delineation of these features in advance may help provide initial direction. We now turn to written work in the particular species frameworks. Example A1.5 presents several cantus firmus melodies atop which counterpoint melodies may be written. Later we will compose our own CFs.


First Species 1:1 In first species, the counterpoint line (as does the cantus firmus) consists only of whole notes, creating a 1:1 relationship between the two lines. In addition to the above principles that pertain to contrapuntal lines in all species, the following are specific to first species. Only consonant intervals are permitted; first species is the only species in which dissonance will be absent. It is permissible in first species to tie notes between successive measures. Since the cantus firmus is always changing notes, this will create oblique motion between CF and counterpoint line. Unisons are only permissible in the first and last measures, as these are the most stable and final sounding intervals; a unison occurring in the middle of a succession of thirds and sixths will create a gap in the melodic flow. Octaves and fifths, though to a lesser extent, will create the same effect, and thus may be used only sparingly in the middle of an exercise.


Appendix 1

Composition Compose first species lines above and below one or more of the above cantus firmus lines.

Exercise A1b and Example A1.6

Second Species 2:1 Second species involves half notes against the whole notes of the cantus firmus. Second species allows the use of dissonance, which is not only inevitable, but is an effective expressive device when used properly. However, dissonance may only be used on the second half of the measure in second species and is to be prepared and followed by stepwise motion. Therefore, successive dissonances are not possible in second species, although successive consonances are. The use of unisons is possible in the middle of the exercise, but only on weak beats, and they must be followed by stepwise motion in the opposite direction.

Composition Compose second species lines above and below one or more of the above cantus firmus lines.

Exercise A1c and Example A1.7

Appendix 1


Second species exercises begin with a half-note rest in the first half of the first measure in order to establish a sense of independent voices at the outset. Second species, as do all species, ends with a whole note. It is also acceptable to use a whole note in the penultimate measure, as Example A1.1 shows, if this helps avoid unwanted parallel intervals or otherwise enhances voice leading.

Third Species 4:1 Third species contrapuntal lines will employ four quarter notes against each of the whole notes of the cantus firmus (except in the first bar, which begins with a quarter-note rest, and the last bar which is a whole note). As with second species, the first beat of each measure must be a consonant tone, and care must be taken to sustain balance between consonant and dissonant tones and to adhere to proper resolution of dissonances (via stepwise movement into consonances). The dissonant neighboring tone is possible in third species, as is, of course, the consonant neighboring tone. Third species also permits the double neighboring tone figure, where both upper and lower neighbors are present and involve the use of two consecutive dissonances. Even with the consecutive dissonances—and the interval of a third between them—this kind of motion is acceptable, as it is heard as an embellishment of the note that sounds both on the first and fourth beat of the measure.

Composition Write a third species melody above and below one or more of the CF lines.

Exercise A1d and Example A1.8

Now let us improvise once more using second and third species principles, this time with our hearing and conception informed by the written work done above.


Appendix 1

Composition Select a cantus firmus melody and improvise in second and third species according to the following procedure. Each musician enters by playing the cantus firmus, then improvises according to the rhythmic ratio of second and third species (first species is not highly conducive to improvisation) while the next player plays the CF. There will always be one person playing the CF and one person improvising; the CF in this sense functions just like a jazz chord progression when it is repeated indefinitely as a backdrop for improvised solos. In a group of at least two players, the format is as follows: 1 Player A plays CF alone. 2 Then Player B enters with CF, and Player A improvises a second species melody. 3 If three players, Player C enters with CF, Player B improvises a second species melody, and Player A rests. 4 If four players, Player D enters with CF, Player A improvises, and Players B and C rest. 5 Player B plays CF, Player D improvises, and Players A and B rest. Continue as desired. In essence, each player plays the CF once and then improvises and then rests before coming in again with the CF and starting the cycle anew. The following variation, which requires at least three group members, involves two players improvising at a time, one in second species and one in third species. 1 Player A plays CF alone. 2 Player B enters with CF, Player A improvises second species line. 3 Player C enters with CF, Player B improvises second species line, Player A improvises third species line. If just a trio, Player A then plays CF, Player B improvises third species, and Player C second species. 4 If a quartet, Player D enters with CF, Player C improvises second species line, Player B improvises third species line, and Player A rests. Continue as desired, with each group member entering or (re-entering) after rest by playing CF, and then improvising first on second, and then on third species, and then, if a quartet or larger, resting until next CF entrance.

Exercise A1e

Now; it is obviously not possible to adhere as closely to voice-leading and other species constraints while improvising, since there are no provisions to go back and rework contrapuntal pathways as there are in written formats. At first this may appear to be a rather frivolous, “anything goes” approach to species work. What could be the value in such an approach? In fact, even if improvising in these formats may inevitably yield “errors,” it still calls upon musicians to aurally engage and make melodic decisions on a moment-to-

Appendix 1


moment basis. This is an ideal format to cultivate hearing-in-advance capacities, where each moment will suggest subsequent moves to the sensitive improviser. Moreover, if improvisers adhere strictly to the specified mode or scale of the CF and the rhythmic ratios—two constraints that are easily accommodated and absolutely essential—a kind of contemporary diatonicism will result that, even if extending beyond species principles, will yield sonorities that resonate with even the most conservative contemporary ears. Again, our written work allows us to attend to a much greater level of detail, and the interplay of improvised and written creativity in these formats will significantly enhance our melodic hearing and conception.

Improvising with More Florid Lines Improvisation Now return to the above formats and add a new rhythmic layer—this involving 8:1 lines. Therefore, with staggered entrances as proscribed, each player will play the CF, then improvise second species (2:1), third species (4:1), followed by 8:1 lines.

Exercise A1f

Written exercise Write a contrapuntal line atop one or more of the cantus firmus melodies that makes prominent if not exclusive use of 8:1 note values (eight note lines atop the whole note CF). All voice-leading principles apply. With regard to the use of dissonance, no more than two dissonant tones in a row are permissible, and they must be approached and resolved stepwise.

Exercise A1g and Example A1.9


Appendix 1

Fourth and Fifth Species Let us now turn to the remaining two species, using both the cantus firmus melodies provided as well as creating our own. The following principles will serve as a guide to the creation of CF lines. Construction of Cantus Firmus

These principles will underlie the construction of the cantus firmus. 1 Consists entirely of whole notes. 2 Generally 8–16 measures, and thus notes, in length. 3 Begins and ends on the tonic note of the mode, thus clearly establishing the sonority of the mode and a sense of finality. 4 Ends usually with 2 to 1 motion (second degree of mode to tonic) or, less frequently but acceptable, 7 to 1 motion. In other words, the cantus firmus approaches its final note with stepwise motion, with the penultimate (second to last) tone being either a step above or a step below the final tone. 5 Spans no more than an interval of an octave between its lowest and highest tones (a fifth or sixth will often suffice), thereby providing a melodic framework that supports additional lines without obscuring their integrity through excessive registral movement. 6 Does not employ successive repeated tones, as this undermines the sense of melodic direction, particularly given the long duration of the cantus firmus notes. Care should also be taken to avoid excessively recurring tones even if they are not successive (e.g. the same pitch occurring three times in five measures), as this can be monotonous and undermine the sense of melodic direction. 7 Avoid melodic intervals larger than a sixth, as well as tritones, or augmented intervals. 8 Predominantly stepwise, but not exclusively: two to three leaps of more than a third are ideal. 9 Leaps of more than a third are to be followed by a change of direction. 10 While CF lines are naturally limited in their melodic potential by their rhythmic constraints, they can still be thought to have a beginning, climactic point—indicated by the highest note—and ending. 11 For present purposes, we will confine our cantus firmus melodies to Dorian or Aeolian modes. 12 Take care not to sing or play the CF too slowly—at least MM quarter note = 70—as this compromises the melodic flow of both the CF and contrapuntal lines.

Fourth Species: Suspensions In fourth species, as shown in Example A1.10, the prevalent rhythm is the half note that is tied—or suspended—over the bar line, thus producing a syncopated texture where the

Appendix 1



cantus firmus notes change on the strong beat of the measure and the counterpoint line changes on the weak beat of the measure. The technique of suspension involves three parts: preparation, suspension, and resolution. The preparation occurs on the second half of the measure, the suspension on the first half of the next measure, and the resolution on the second half of that measure. The preparation and resolution of the suspension must involve consonant tones. The suspension itself may be either consonant or dissonant. If the suspension is dissonant, it will generally resolve down a step (half or whole) to a consonant tone. If the suspension is consonant, it can resolve upward or downward. The most common and desirable suspensions in upper counterpoint lines are the 4-3 and 7-6 suspensions. The 9-8 suspension is possible but must be used sparingly in that the resolution of the dissonant ninth to the highly stable octave produces a strong impression of finality that distracts from the melodic flow. The 2-1 suspension in the upper counterpoint creates an even stronger impression of finality and is thus to be avoided. In lower counterpoint lines, the 2-3 and 9-10 are most desirable. The 4-5 suspension must be used sparingly for similar reasons cited for 9-8 and 2-1 suspensions in upper counterpoint lines; to reiterate—the resolution to the open fifth undermines melodic flow—and along these same lines, the 7-8 suspension, with its resolution to the octave, is also to be avoided. Chains of suspensions may also be used to good effect, creating another form of sequential relationship in a contrapuntal setting. In the upper voice, chains or series of 4-3 and 7-6 suspensions are ideal. Sequences of 9-8 and 6-5 suspensions are to be avoided because they involve forms of parallel perfect intervals. Even if the parallel perfect intervals (8 and 5) are separated by one note, they are in close enough proximity to undermine independence of voices, as though they were consecutive. In the lower voice, 2-3 and 9-10 suspensions are ideal, and 7-8 and 4-5 suspensions are to be avoided.


Appendix 1

Composition Compose a CF and fourth species lines above and below it.

Exercise A1.1h and Example A1.11

Fifth Species: Integration of the Previous Four Species Fifth species, illustrated in Example A1.12, involves the combination of the rhythmic values of the prior four species, with the exception of the whole note of first species, which is allowable only on the last measure. Fifth species also allows the use of eighth notes to provide occasional instances of a more florid texture. Fifth species begins with either a quarter- or half-note rest. The rules that apply to the rhythmic values of the prior species are in effect whenever those rhythmic values are used in fifth species. Hence, there are no new voice-leading principles of ways of using consonance and dissonance in fifth species.


Appendix 1

Composition Compose a CF and fifth species lines above and below it.

Exercise A1i and Example A1.13

SUMMARY QUESTIONS 1 Define cantus firmus. 2 Correlate consonance and dissonance with the concepts of tension, repose, stability, and motion discussed in Chapter 1 (e.g. consonance equates with___). 3 In which species are only consonant intervals allowed? 4 What purposes might be served by species counterpoint study for contemporary improvisers? 5 Dissonant tones should be avoided as much as possible. True or False? 6 Leaps of more than a third should be followed by what kind of melodic motion? 7 If dissonant tones are used, it is preferable to approach and resolve them by leap. True or False? Defend your answer. 8 Two simultaneously sounding voices best retain their independence when moving by __________ motion, and independence is most compromised when they move by __________ motion. 9 Why are parallel perfect intervals between two voices to be avoided?


appendix 2

Overtone Series and Equal Temperament When a note sounds, which we call the fundamental, it generates a series of additional tones, called overtones, which are generally not consciously perceived by listeners. Usually only the fundamental is heard. Example A2.1 shows a portion of the series of overtones generated by the fundamental tone C that is three octaves below middle C. The overtones are the basis for musical pitch systems, and it is not insignificant that the first two overtones are the octave and the fifth above the fundamental note, and that these intervals are prominent in much of the world’s music. For example, Hindustani musicians play for hours against the backdrop of a drone alternating between the fundamental tone of the raga and a fifth above it. And as is evident in this book, the V to I relationship has been central in Western music for centuries. Play a tone at the piano and depress the sustain pedal, the furthest foot pedal to the right. Then press your ear close to the sounding board and listen closely for overtones, as faint and subtle as they may be. Often it is the fifth that is the most discernible, suggesting further support for the significance of this partial in much of the world’s music. Another exercise for hearing overtones is to depress and hold the low C without the sustain pedal, and to then play the overtones staccato and fortissimo in succession. Notice how the low C string continues to vibrate with each pitch. Different musical traditions make different use of the tunings inherent in the overtone system. In Western music, the natural tuning of the overtones is altered—or tempered—in order to allow for the octave to be divided into 12 equal intervals. This system of 12 chromatic notes that we often take for granted makes possible the harmonic richness that is unique to Western music. Rapid movement between distantly related key areas and chord extensions and alterations is possible owing to equal temperament. Other musical traditions

EXAMPLE A2.1 Overtone series

Appendix 2


divide the octave differently, sometimes into fewer than 12 subdivisions, and often into many more subdivisions, thus making use of what Westerners might consider microtonal increments that open up extraordinary expressive possibilities. In this sense, the harmonic richness of Western music resulting from tempered tuning and the microtonal richness of many other musical cultures may be seen as two divergent evolutionary streams, each of which contributes uniquely to the overall musical landscape. In terms of the crossfertilization between traditions that prevail in our times, the reason that this has manifested more in the rhythmic domain (e.g. time feels, odd meters) may be that instrumental design is not as conducive to cross-traditional pitch practices.

appendix 3

Rhythmic Exercises

The following exercises are a continuation of principles presented in Chapter 4. To review: chant the syllables and clap the accents. Groupings of two: Ta Ka; three: Ta Ki (kee) Ta; four: Ta Ka Di (dee) Mi (mee); five: Ta Di Ki (kee) Na Ta. Each line of accent patterns should be repeated eight times. In other words, in Example A3.1, the first line consisting of three accents should be repeated eight times before moving to the next line of accents. The eight repetitions enable us to internalize each line before moving on to the next.


8 beats: 2-3-2

> > > > > > > > T K | T K T | T K T :|| > > EXAMPLE A3.1


7 beats: 4-3

> > > T K > >


> > > > > D M | T K T :|| > > > > >

Appendix 3


9 beats: 5-4

> > > > > > > > T D K N T|T K > > > > > > > > > > > >


> > D M :|| > > > >



> >

10 beats: 3-4-3

> >

> > > > T K T|T K D M > > > > > > > >

> >

> > | T K T:|| > > >



11 beats: 5-4-2

> >> > T D > > >





> >

> > > K N T|T K D > > > > > > > >




> > M | T K :|| > > > > >


12 beats: 5-5-2

> > > > > > > > > > > > > T D K N T | T D K N T | T K:|| > > > > > > > > > > > > EXAMPLE A3.6

7. 13 beats: 3-4-3-3

> > >

> >



> > > >


> > > > > >

> >

T K T | T K D M | T K T | T K T:|| > > > > > > > > > > > EXAMPLE A3.7

8. 14 beats: 4-3-5-2

> > >




> >



> > >


> > > > >

T K D M | T K T | T D K N T | T K:||

> > > > > > > > >


> > >

> > > > >


Reminder: Each line of accents should be repeated eight times.

> > >

appendix 4

Jazz Etudes

The Jazz Etudes are excellent vehicles for individual practice, partner work, and small group work. They progress gradually in difficulty and embody many of the principles discussed in this book. The format presented here will help you gain optimal benefits from the Etudes. • Analyze the chord progressions for each of the Etudes. Identify key area; provide Roman numerals, parent scales, and individual chord scales for improvising purposes. • Apply on your principal instrument the above chord scale (Ex. 7b) and arpeggio (Ex. 7c) from the end of Chapter 7 (p. 135) to each Etude. • Learn to comp the changes at the keyboard so that you can play them in steady time (comping formats recommended from Chapter 5) and comp for a partner. • Be able to sing the melodies and comp the changes at the same time. After you sing the head, improvise vocally over the changes while you comp. • Compose solo lines over the chord changes that embody the techniques discussed in this and earlier chapters, including: melodic cells, 2:1 and 4:1 lines, melodic contour (steps and leaps), arpeggio shapes, approach tones, embellishments. • Accompany at the keyboard your partner on his or her principal instrument. Switch roles. • Transposed parts for Bb and Eb instruments are provided later in the Appendix.



EXAMPLE A4.1 Ed Sarath, Jazz Etudes 1–17. © 1998 Ed Sarath.


EXAMPLE A4.2 © 1998 Ed Sarath.

EXAMPLE A4.3 © 1998 Ed Sarath.



EXAMPLE A4.4 © 1998 Ed Sarath.

Appendix 4

Appendix 4

EXAMPLE A4.5 © 1998 Ed Sarath.

EXAMPLE A4.6 © 1998 Ed Sarath.




EXAMPLE A4.7 © 1998 Ed Sarath.

EXAMPLE A4.8 © 1998 Ed Sarath.


Appendix 4

Appendix 4



EXAMPLE A4.10 © 1998 Ed Sarath.



EXAMPLE A4.11 © 1998 Ed Sarath.

EXAMPLE A4.12 © 1998 Ed Sarath.



EXAMPLE A4.13 © 1998 Ed Sarath.


EXAMPLE A4.14 © 1998 Ed Sarath.

Appendix 4

Appendix 4




EXAMPLE A4.15 © 1998 Ed Sarath.

EXAMPLE A4.16 © 1998 Ed Sarath.




EXAMPLE A4.17 © 1998 Ed Sarath.

Bb Parts

EXAMPLE A4.18 © 1998 Ed Sarath.

EXAMPLE A4.19 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Bb Parts

EXAMPLE A4.20 © 1998 Ed Sarath.

EXAMPLE A4.21 © 1998 Ed Sarath.

EXAMPLE A4.22 © 1998 Ed Sarath.



Bb Parts

EXAMPLE A4.23 © 1998 Ed Sarath.

EXAMPLE A4.24 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Bb Parts

EXAMPLE A4.25 © 1998 Ed Sarath.

EXAMPLE A4.26 © 1998 Ed Sarath.

EXAMPLE A4.27 © 1998 Ed Sarath.



Bb Parts

EXAMPLE A4.28 © 1998 Ed Sarath.

EXAMPLE A4.29 © 1998 Ed Sarath.

EXAMPLE A4.30 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Bb Parts

EXAMPLE A4.31 © 1998 Ed Sarath.

EXAMPLE A4.32 © 1998 Ed Sarath.



Bb Parts

EXAMPLE A4.33 © 1998 Ed Sarath.

EXAMPLE A4.34 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Eb Parts

EXAMPLE A4.35 © 1998 Ed Sarath.

EXAMPLE A4.36 © 1998 Ed Sarath.

EXAMPLE A4.37 © 1998 Ed Sarath.



Eb Parts

EXAMPLE A4.38 © 1998 Ed Sarath.

EXAMPLE A4.39 © 1998 Ed Sarath.

EXAMPLE A4.40 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Eb Parts

EXAMPLE A4.41 © 1998 Ed Sarath.

EXAMPLE A4.42 © 1998 Ed Sarath.

EXAMPLE A4.43 © 1998 Ed Sarath.



Eb Parts

EXAMPLE A4.44 © 1998 Ed Sarath.

EXAMPLE A4.45 © 1998 Ed Sarath.

EXAMPLE A4.46 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Eb Parts

EXAMPLE A4.47 © 1998 Ed Sarath.

EXAMPLE A4.48 © 1998 Ed Sarath.



Eb Parts

EXAMPLE A4.49 © 1998 Ed Sarath.

EXAMPLE A4.50 © 1998 Ed Sarath.

Appendix 4

Appendix 4

Eb Parts

EXAMPLE A4.51 © 1998 Ed Sarath.


appendix 5

Additional Keyboard Exercises

Seminal Keyboard Projects A summary of the eight Seminal Keyboard Projects and their locations in the book is presented below. These projects provide a coherent keyboard skills base for additional study. In this Appendix, advanced keyboard voicings drills are offered to expand your abilities even further.

Location of Seminal Keyboard Projects by chapter: SEMINAL KEYBOARD PROJECTS

1 Chapter 5, Exercise 5m, cycle major sevenths, with voice (p. 95). 2 Chapter 6, Exercise 6a–6b, II–V–I with voice (p. 109). 3 Chapter 6, Exercise 6w (p. 126). (a) I–V7/II–IImin7–V7–I–V7/IV IV (IV becomes new I, continue around cycle). (b) Play own progression from free-tonicization Exercise 6v. 4 Chapter 10, Exercise 10q (p. 184). (a) I–IV–III–V7/II–II–V7–I–V7/IV–IV(new I) (b) Create and realize progression by chord symbols from free-tonicization 2 strategies. 5 Chapter 12, Exercise 12c, figured bass realization, with composed melody (p. 210). 6 Chapter 13, Exercise 13a, extended II–V–I progression (p. 219). 7 Chapter 14, Exercise 14b, altered/extended II–V–I (p. 237). 8 Chapter 14, Exercise 14c, II–V–I–V7alt/II–II–subValt–Imin–IIm7( 5,11)–V7( 9)–Imin–V7( 5)/ II–i6/4–V7–i (p. 239).




Advanced Guide Tone Exercise Recall from Chapter 7 that guide tones are the thirds and sevenths of chords and are the essential tones defining harmonic movement. When played atop the roots in II–V–I sequences, the resultant three-note texture produces a notable fullness. The guide tone exercise that follows moves through the 12 keys by descending half-steps. The guide tones

Appendix 5


on each I chord are retained and the half-step movement in the bass is what shifts to the next key area. Keyboard exercise Continue this sequence at the keyboard in all keys, proceeding by descending half-steps.

Exercise A5a and Example A5.1

Advanced Two-hand, Non-tertial Open Voicings While the following voicings, like the ones we used throughout the book, consist of five notes, they differ in the way they distribute these notes. Instead of a single note in the left hand and four in the right hand, these voicings have us play two notes in the left hand and three in the right hand. They are derived from two strategies. One is dropping the secondto-highest voice in the treble clef down an octave; this is sometimes called the “drop-two” technique and is commonly used in big band writing. Second is replacing the fifth on the I chord with the sixth (or thirteenth). These open structures produce a new kind of resonance. Instead of tertial structures on the II and I chords we now have a greater intervallic variety, including the quartal structure (voicing in fourths) in the right hand for added richness. Keyboard exercise Continue this sequence at the keyboard in all keys, proceeding by key centers that move in descending whole steps (e.g. C–B –A –G ).

b b b

Exercise A5b and Example A5.2


Appendix 5

In the next exercise, we apply the above principles to create open voicings for the IImin7(9)–V7(#9, b13)–Imaj7(6, 9) progression. Again, notice the similarities with the voicings we have used previously for this progression, except with the second voice from the top dropped down an octave to create the more open sound and the 6-5 replacement on the I chord. Keyboard exercise Continue the sequence in all keys.

Exercise A5c and Example A5.3

Superimposing triads atop the root and third in the left hand creates other types of altered dominant chords in the next voicings. Exercise A5d involves a V7(#11) chord, which is created by simply playing a major triad a step above the root of the V7. Keyboard exercise Continue the sequence in all keys.

Exercise A5d and Example A5.4

Appendix 5


This exercise shows a V79(b9, b13) voicing, created by playing a minor triad a half-step above the root of the V7. Keyboard exercise Continue the sequence in all keys.

Exercise A5e and Example A5.5

Exercise A5f shows an alternative V7(#9, b13) voicing to the one shown above in exercise A5c. Here we play a major triad on the b13 of the V7 (e.g. in bar 1, Eb major triad on the altered G7 chord). Although the voicing omits the seventh, the root and third in the left hand, it more than adequately upholds the V7 sound and function. Keyboard exercise Continue the sequence in all keys.

Exercise A5f and Example A5.6


Appendix 5

Exercise A5g shows a V7(b5, b9) voicing that is created by playing a major triad a tritone above the root of the V7 chord (e.g. in bar 1, the Db major triad on the altered G7 chord). Keyboard exercise Continue the sequence in all keys.

Exercise A5g and Example A5.7

appendix 6

Instrument Ranges, Transposition, and Score Excerpts Most improvisers also compose, and one of the most fulfilling experiences for any musician is to hear one’s music come to life when performed by an ensemble of instruments or voices. Three things are essential in learning to write for large bodies of instruments. One is, naturally, to listen to much large ensemble music. Second is to study scores. Third is to do piano reductions of full scores in order to have hands-on access to the sounds of works in their pre-orchestrated forms. This Appendix provides a brief introduction to this kind of study. It begins with instrument ranges and transpositions for most symphonic and jazz instruments, and then shows piano reductions of several European classical and jazz works. While one does not make the leap from small group to large ensemble writing overnight (and it is wise to build up a significant portfolio of small group music prior to attempting to write for larger forces), an early glimpse of what large ensemble writing entails may enhance later efforts in this direction. A word about transposition. Some instruments, due to their design, are pitched in such a way that concert pitches—the notes that sound at the piano—need to be transposed to the key of these instruments. For instance, the concert pitch C needs to be written as D for the Bb trumpet and Bb clarinet. Writing the note up a whole step compensates for the fact that Bb is a whole step below C. The French horn in F is transposed up a perfect fifth from concert pitch, the Eb alto saxophone up a major sixth, the Eb baritone saxophone up a major thirteenth (an octave and a sixth) due to these principles. Instruments such as flute, oboe, bassoon, trombone, violin, viola, and cello are non-transposing instruments; music for these instruments is notated exactly where the music sounds in concert pitch. The excerpts from the full scores that follow the section on instrument ranges and transposition have been selected to provide a snapshot of the rich diversity of large ensemble music in today’s world. The big band in jazz, in fact, may be thought of as a counterpart to the symphony orchestra in European classical music and in recent years is increasingly referred to as the “jazz orchestra.” The juxtaposition of a passage from Beethoven’s Third Symphony with excerpts from music of jazz composers Maria Schneider and Thad Jones provides a small snapshot of the breadth of today’s musical world and the creative opportunities that await musicians who gain commensurate training.



Appendix 6

Appendix 6




Appendix 6

This selection may be found on many recordings, including: Beethoven, Symphony No. 3 Eroica, Philadelphia Orchestra and Riccardo Muti (Angel Records 1999).

EXAMPLE A6.3 Beethoven, Symphony No. 3 in Eb Major, Op. 55 (Eroica)

Appendix 6




Appendix 6

This celebratory moment in Beethoven’s Third Symphony illustrates what is possible when basic melodic and harmonic material is framed within a large ensemble format. Identify the basic thematic and accompanying material and then observe what it looks like in the piano reduction that follows.

EXAMPLE A6.5 Piano reduction

Maria Schneider’s Gumba Blue makes use of multiple themes sounding simultaneously as well as rich harmonic structures and movement. Notice beginning at the third measure the sequence of augmented triads, voiced in alto saxophones I and II and trombones I, II, and III, that moves by an ascending half-step. This is an example of a technique called planing, where a harmonic structure is shifted up or down, often by a half-step, while its internal intervallic make-up (in this case augmented chords) remains unchanged. Notice also the drum part, where slash marks instruct the drummer to play the basic time feel with occasional rhythmic patterns added that lend support to those patterns played by the ensemble. Notice too that the guitarist and pianist are given both chord changes and written melodic parts to play. This selection may be found on the following recording: Maria Schneider, Evanescence (Enja 1994).

Appendix 6

EXAMPLE A6.6 Maria Schneider, Gumba Blue. Maria Schneider, Gumba Blue. © 1989 Maria Schneider. Used by permission.




Appendix 6

Appendix 6


EXAMPLE A6.8 Piano reduction

It goes without saying that it can be challenging to fit everything that is written for a large ensemble into a two-stave piano reduction, particularly with pieces such as the above. Here the rhythm section parts are omitted, except when (as with the bass part), they double other parts. Compare, as you did with the Beethoven excerpt, the full score and the piano reduction to get a sense of how a relatively few ideas can be orchestrated for large ensemble.


Appendix 6

EXAMPLE A6.9 Thad Jones, Fingers.

This selection may be found on the following recording: Thad Jones Legacy, Vanguard Jazz Orchestra (New World Records 1999). In this example, only the winds and brass are shown above in order to illustrate a fullensemble tutti passage where all instruments are playing the same rhythm but different melodic lines. As the ensuing piano reduction shows, each eighth note is harmonized by a different chord structure while the chord changes indicated move at a slower harmonic rhythm. Closer observation will reveal that some of the eighth notes are harmonized with structures that are directly related to the chord listed (e.g. the harmonization of the eighth

Appendix 6



note on the second half of beat 1 in bar 1 uses tones diatonic to Bb major) while some (e.g. the very next chord, which uses a C#min11 structure) clearly stretch the sonority of the chord change indicated. Generally, notes at strategic points (strong beats within a measure, and of longer duration) will be harmonized with structures that align more directly with the underlying harmony, while passing notes may be harmonized with more distantly related structures that make extensive use of chromaticism. These are heard as motion and do not distract from the overarching harmonic progression, which in this case is a very straightforward chord sequence. Thad Jones is known for his extensive use of altered structures in his harmonization of ensemble passages in order to get rich and dense sounds


Appendix 6

from the ensemble. Notice in bar 4 the superimposition of distantly related major chords atop the underlying harmonies: on the Eb7 (voiced in bass clef ) an A major chord (treble clef ) is superimposed, on the E7 a C major chord is superimposed, on the A7—where an altered voicing containing the #9 and b13 is used in the bass clef—an Eb major chord is superimposed.

EXAMPLE A6.11 Piano reduction

appendix 7

Aural Transposition

This Appendix includes additional aural transposition exercises to complement those offered in the text. It outlines three main components of a comprehensive program in melodic aural transposition: technical exercises (scale and arpeggio patterns), idiomatic patterns (II–V–I lines), and repertory (complete melodies). As always, be able to sing the pattern before working it out in a single key on your instrument, and then use the voice as a guide when you work the patterns out by ear in the 12 keys.

Triads We begin with triads. Do not be constrained by the register in which the exercises are written; take the patterns throughout the entire range of your instrument.

EXAMPLE A7.1 continued overleaf


Appendix 7


Seventh Chords As with triads, a couple of patterns already encountered in Chapter 3 are shown, followed by various seventh chord permutations that spawn a wide variety of intervals. While these intervals will certainly pose challenges to most instrumentalists, they are grounded in a kind of melodic coherence that, once the basic pattern is set in motion, guides the ear through the rest of the sequence. Even in the notated version provided, it should not be necessary to read the notes after a few iterations of the pattern; you are encouraged therefore to try to get through the pattern even in the first key without reading the entire exercise. Again, the ability to sing the patterns is essential.


The above seventh chord patterns were based on 1–3–5–7 and 1–5–7–3 permutations. The following seventh chord patterns are based on 7–3–5–1 permutations and give rise to an interesting mix of thirds, fourths, sixths, and sevenths. Again, they follow a melodic logic that makes it surprisingly easy to hear the continuation of the sequence once it is established through a few iterations. Remember that you are not confined to the range in which the sequence is given here and are encouraged to take the sequence throughout the range of your instrument. Also remember that it is of minimal importance whether or not you reverse direction (e.g. reach the top of your range and then begin taking the sequence down)

Appendix 7


or end the exercise in precisely the manner indicated. What is of greatest importance is hearing, singing, and playing the sequences accurately in their ascending and descending forms. In that these involve larger intervals, it is important to play them slowly at first, taking care to build a solid aural and technical foundation prior. Velocity will develop naturally once this foundation is securely in place.


Pentatonic Scales Chapters 2 and 3 provided several excellent preliminary pentatonic scale exercises. After reviewing them, proceed with the more advanced permutations that follow in Example A7.4.



Appendix 7

The following pentatonic scale exercises make use of a technique commonly employed by jazz musicians. This involves creating an “inside–outside” effect by alternating pentatonic scales from distantly related key areas. In Example A7.5, exercises 18 and 19 patterns use pentatonic scales a tritone apart. As you examine the patterns you will notice that each iteration of a scale is consistent within itself—in other words, the C pentatonic patterns ascend precisely as they do in the basic exercise (from Chapter 3) shown above, as do their distant Gb partner patterns. The pattern in exercise 19 is particularly useful in that the shift to the distant pentatonic occurs on the fourth of every four eighth notes. This sets up a kind of counterpoint that enhances the inside–outside effect. From a rhythmic standpoint, the ear hears four-note groupings as intact units, yet from a melodic standpoint, the shift to the distant key area, instead of occurring as it does in exercise 18 with the beginning of a new four-note rhythmic pattern, now occurs on the fourth of the four notes, creating a highly colorful shift in sonority.


Idiomatic Lines As you likely found even with the aural transposition exercises in the body of the text, this is an intensive kind of practice. From this standpoint alone, it can be beneficial to balance your technical aural transposition work with lines of a more melodic nature. In addition, practicing melodies helps us internalize strong melodic shapes. The following are some idiomatic melodic lines that may be used for this purpose. These are particularly good for singing.

Appendix 7



Additional idiomatic lines are found in the text: Diatonic lines are found in Chapter 7, in Example 7.8. Chromatic lines are found in Chapter 7, in Examples 7.9, 7.10, and 7.11. The Jazz Etudes in Appendix 4 are also good sources of aural transposition lines. For instance, in Jazz Etude 7, you might continue the four-bar motive through all keys.

Repertory Playing complete melodies that you like can be highly beneficial not just for your ear but also for your sound and melodic conception. You might begin with more lyrical, stepwise, largely diatonic melodies from European classical, jazz, and popular music. Then you might proceed to jazz standards, ballads and bossa novas that involve more chromaticism and wider intervals. A few examples: Invitation, Round Midnight, Pensativa, Nica’s Dream, and Bluesette. There are many others that could be placed in this category. Finally, you can tackle virtuosic bebop heads such as Donna Lee and Four Brothers.

appendix 8

Sample Syllabus

For application in a two-semester (each consisting of 15 weeks) course sequence. Music Theory Through Improvisation includes a wide scope of activities, ranging from improvisation, composition, aural transposition and other ear-training activities, to keyboard realization, rhythm, and various kinds of written work. The following syllabus provides a framework for integrating this into a coherent and manageable system. Much of the work in improvisation, composition, aural transposition, rhythm, melody, and harmony is structured within regular class meetings, with occasional outside appointments scheduled for the purpose of monitoring proficiency in keyboard, and optionally other areas. The framework, which has evolved over the past 15 years in classes whose enrollment has ranged from 20 to 40, leaves ample room for creative adaptation on the part of individual instructors. Additional recommendations are found in the Preface as well as in the Suggestions for Instructors link on the website.

First semester Week Course material


Cover: Chapter 1. Trans-stylistic improvisation exercises 1a–1f (long tones, wheel of duets, dynamics, density, and tessitura). Discuss syntactic and non-syntactic elements, tension and repose, unity and variety, silence, and importance of engaged listening. Discuss creation of personal listening library. Assign: Two-part improvisation project (Ex. 1g), to be done with two players.


Due: Perform duet improvisations (Ex. 1g) in class. Cover: Pulse-based improvising, pitch-based improvising, formbased improvising exercises; play in class via ad hoc small groups. Assign: Small group project (Ex. 1ee) for next week.

Proficiency exams (outside of class)

Appendix 8


Due: Small group project (Ex. 1ee) perform in class. Cover: Introduce/review basic elements in Chapter 2: clefs, key signatures, intervals, scales; written (2a–d, j) and aural (2e, f) exercises. Major and minor pentatonic scales, modes, aural transposition, and melodic cells. Assign: Written exercises—2a–d, h–j. Aural transposition (Ex. 2g). In addition, choose a melodic cell pattern from Exercises 2k–p; learn in all keys.


Cover: Importance of aural immersion (via recordings in infusing time-feel concepts. Perform Modal Etude 1 (Chapter 3, Example 3.1); students take turns soloing; rhythm section players comp. Discuss constituent minor pentatonic scales within Dorian mode, rhythmic templates, initial keyboard exploration Exercise (3n). Chapter 4: Do Call and Response patterns with minor pentatonic scales. Assign: Exemplar project (Ex. 3c). Write out Dorian modes with constituent minor pentatonic scales (Ex. 3g). Call and Response (Ex. 4a); each student as caller.


Due: Call and Response (Ex. 4a). Spot-check random students re exemplar project (Ex. 3c). Written (Ex. 3g). Cover: Perform Modal Etude 2. Perform minor blues (Ex. 4g). Begin Indian rhythm exercises (Ex. 4j). Discuss parameters of small group performance format as outlined in Chapter 4: (a) group rhythmic exercise, (b) group aural transposition (recommend Ex. 2q to begin), (c) mode-rhythmics piece: create two-chord, minor pentatonic ostinato pattern, compose melody, improvise, compose tutti section. Introduction to tonality (Chapter 5). Cover/review triads and seventh chords. Introduce keyboard realization principles. Assign: Written: 5b, c (triads), g, i, j, k, l (seventh chords). Establish small group performance schedule (one or two groups to play each class session). Seminal Keyboard Project 1 (Ex. 5m) for week 7.


Due: Small group performances (one or two groups). Cover: Modemaster drills (Chapter 5) to fortify knowledge of triads, seventh chords, and modes.



Appendix 8

Assign: Modemaster drills (Ex. 5u, v). 7

Due: Small group performances cont. (next one or two groups).

Due: Seminal Keyboard Project 1 (Ex. 5m), by individual appointments (3–5 min. each).

Cover: Chapter 6, Harmonic functions. Roman numeral analysis. Key-defining features of V7 chord. Commonalities and distinctions between jazz and Euroclassical cadential sequences. IImin7–V7–I sequence. Chord–scale relationships. Keyboard application. Improvise over II–V–I progression in class. II–V–I in minor. Assign: Seminal Keyboard Project 2 (Ex. 6a, 6b) for week 9. Written exercises, 6e, h–k. 8

Due: Small group performances cont. (next one or two groups). Cover: Chapter 6 cont.: Free-tonicization strategies. Assign: Modemaster drills (Ex. 5u, v).


Due: Small group performances cont. (may begin Jazz Etudes, Appendix 4, if two cycles of small group performances with mode-rhythmics has been completed). Written exercises, 6e, h–k. Cover: Chapter 7, Swing. Chapter 8, Melodic Line Construction and Harmonization. Passing notes and target notes, guide tones, approach tones, surround tones, composing song-form melodies and quasiimprovised melodies. Assign: Written Ex. 8e–g. Seminal Keyboard Project 3 (Ex. 6w), for week 11.


Due: Small group performances cont. (select from Jazz Etudes, Appendix 4; be sure to include the composition of tutti lines on changes as part of project). Modemaster drills (Ex. 5u,v). Cover: Chapter 8, cont. Harmonic Rhythm. Top–down harmonization techniques. Chapter 9, Chord Inversion. Review types of inversion. Discuss differences in jazz and European classical harmony re inversion (prevalent in Euro) and chord extension (prevalent in jazz). Non-harmonic tones in European classical. Roman numeral analysis of Bach chorales (Ex. 8b–e).

Due: Seminal Keyboard Project 2 (Ex. 6a, b).

Appendix 8


Assign: Ex. 8k, original melody and harmonization, can be played with small group. 11

Due: Small group performances cont. (select from Jazz Etudes, Appendix 4).

Seminal keyboard Project #3 (Ex. 6w).

Written (Ex. 8e–g). Cover: Chapter 10, Non-diatonic Harmony; introduce applied chords (secondary dominant and secondary VII) chords (Ex. 10g, h, i, j). Passing diminished seventh chords. Assign: Seminal Keyboard Project 4 (Ex. 10q), for final week. Written (Ex. 8g, i, k). 12

Due: Small group performances cont. (select from Jazz Etudes, Appendix 4). Written (Ex. 8g, i, k). Cover: Chapter 10 cont. Substitute Dominant Chords. Free tonicization strategies, level II. Chapter 11, Modal Mixture. Passing and structural modal mixture functions, corresponding Roman numeral analysis. Assign: Written (Ex. 10m–p).


Due: Small group performances cont. (select from Jazz Etudes, Appendix 4). Written (Ex. 10m–p). Cover: Chapter 11, Modal Mixture cont. Assign: Written (Ex. 11e–h).


Due: Small group performances cont. (select from Jazz Etudes, Appendix 4). Written (Ex. 11e–h). Cover: Review.


Review and final exam.

Due: Seminal Keyboard Project 4, Ex. 10q.


Appendix 8

Second semester Week Course material 1

Proficiency exams

Cover: Chapter 12, Figured Bass Realization at the Keyboard; basic principles, keyboard style realization and writing. Chapter 11, Creative Synthesis (Ex. 11k). Assign: Seminal Keyboard Project 5 (Ex. 12c), for week 4 (Ex. 11k).


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover: Chapter 12, Figured Bass Realization cont. Assign: Written (Ex. 12d).


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover: Chapter 12, Figured Bass Realization cont.


Due: Small group performances cont; Jazz Etudes (Appendix 4) or original compositions. Written (Ex..12d). Ex 11k, Creative Synthesis Projects, perform in class.

Due: Seminal Keyboard Project 5 (Ex. 12c), figured bass realization.

Cover: Chapter 13, Chord Extension; basic principles, extended chords on II–V–I sequence. Keyboard voicings, replacement tones (9–1, 13–5), chord superimposition techniques using maj7(b5) structure, A and B voicings. Written exercises 13b–d, i, Assign: Seminal Keyboard Project 6, Ex. 13a. Written (Ex. 13k). 5

Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover: Chapter 13 cont. Extended chords on minor II–V–I sequence. Assign: Written (Ex. 13m, n).


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Written (13k, m, n). Cover: Chapter 14, Altered extensions. V7(#9, b13). Chord superimposition using maj7(bb5) chord. Augmented sixth chords in European classical harmony as subV7 chords. Top–down harmonization techniques (Ex. 14a, d).

Seminal Keyboard Project 6 (Ex. 13a).

Appendix 8


Assign: Transcription project, Ex. 7 for week 8. Written (Ex. 14g, h, i). 7

Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Written (Ex. 14g). Cover: Chapter 14, Altered Extensions cont. Extended subV7 chords. Chord-scale analysis with altered harmonies. Assign: Seminal Keyboard Project 7 (Ex. 13a), for week 9. Written exercises (14h, i).


Due: Transcription day; present transcriptions in class (play along with recording). Cover: Chapter 14 cont. Top–down harmonization. Assign: Seminal Keyboard Project 7 (Ex. 13a), for week 10. Written (Ex. 14l).


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Written (Ex. 14l). Cover: Chapter 15, Analysis. Assign: Seminal Keyboard Project 8 (Ex. 14b), for week 11.


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover: Chapter15, cont. Assign: Seminal Keyboard Project 8 (Ex. 14c) Written (Ex. 15a, c).


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Written (Ex. 15a, c) Cover: Chapter 16, Further Creative Horizons. Improvise with Coltrane’s Central Park West as specified in Ex. a–o.


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover: Chapter 16 cont. New harmonic structures (e.g. maj7(#5)) and corresponding chord scales. Assign: Composition project (Ex. 16q).


Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover and assign: Creative Synthesis (Ex. 16r).

Due: Seminal Keyboard Project 7 (Ex. 14b).



Appendix 8

Due: Small group performances cont. Jazz Etudes (Appendix 4) or original compositions. Cover: Creative synthesis cont.


Review. Creative synthesis projects in class.

Seminal Keyboard Project 8 (Ex. 14c).

appendix 9

CD and Web Audio Tracks Music examples that correspond to the play-along CD are indicated by the CD icon. Listening examples on the website are indicated by the website icon. To access the website, log on to: CD Program for improvisation practice (CD in book jacket) CD track


Corresponding web track

Location in book


Modal Etude 1


Chapter 3, Example 3.1


Modal Etude 2


Chapter 4, Example 4.6


Minor Blues


Jazz Etude 1


Appendix 4


Jazz Etude 4


Appendix 4


Jazz Etude 7

Appendix 4


Jazz Etude 10

Appendix 4


Jazz Etude 11


Jazz Etude 13

Appendix 4


Jazz Etude 14

Appendix 4


Jazz Etude 15


Appendix 4


Jazz Etude 17


Appendix 4


Minor II–V–I sequences in A minor, C minor, D minor, E minor, two repetitions in each key

Chapter 6, Exercise 6g


Turnaround pattern

Chapter 6

Chapter 4, Example 4.14


Appendix 4


Appendix 9

Web audio tracks Web track


Corresponding CD track

Location in book



Chapter 1, Example 1.5


Strings Improvisation 1

Chapter 1, Exercise 1dd


Strings Improvisation 2

Chapter 1, Exercise 1dd


Modal Etude 1


Chapter 3, Example 3.1


Modal Etude 2


Chapter 4, Example 4.6


Rhythmic exercise

Chapter 4, Exercise 4k Appendix 3, Exercise 2


Minor pentatonic bass line with rhythmic chanting

Chapter 4, Example 4.15


Rhythmic templates

Chapter 4, Exercise 4c


Call and Response 1

Chapter 4, Exercise 4a


Call and Response 2

Chapter 4, Exercise 4b


3:4 polyrhythm

Chapter 7, Example 7.2


Jazz Etude 1


Appendix 4


Jazz Etude 4


Appendix 4


Jazz Etude 11


Appendix 4


Jazz Etude 15


Appendix 4


Jazz Etude 17


Appendix 4


Quiet Mind

Chapter 16, Example 16.16


Turkish Tihai

Chapter 16, Example 16.17

Modal Etudes 1, 2; Minor Blues and Jazz Etudes 1, 4, 11, 15, 17, composed by Ed Sarath. (Copyright Ed Sarath) Performers for Modal Etude 1, 2; Minor Blues, and Jazz Etudes 1, 15, 17: Andrew Bishop, saxophones; Ellen Rowe, piano; Kurt Krahnke, bass; Pete Siers; drums. Performers for Jazz Etudes 4, 11: Andrew Haefner, saxophone; Michael Malis, piano; Doug Stuart, bass; Colin Campbell, drums.


accents (see articulation) accidentals, 30, 85, 235 Aeolian mode, 38, 55, 182 All the Things You Are, 261 altered chords, 212, 233, 242, 248 altered scales, 248–251 alto, 32, 52, 211–214 antecedent-consequent phrase, 9, 150–151 anticipation (see non-harmonic tones) anticipatory hearing, 15, 16 applied chords, 168–169 approach tones, 149, 313 applied leading tone chords, 173 secondary dominants, 169–175 secondary subV7, 177 Arabic music, 24, 38, 285 Arabic numerals, 39, 142, 212, Armstrong, Louis, 63 arpeggio, aural transposition patterns, 113, 135, 149 Art Ensemble of Chicago, 25 articulation, accents, 44, 80–81, 128, 310–312 swing and even-eighth phrasing, 47, 128–129, 148–151 augmented intervals, 35–36, 47 augmented sixth chords, 233–245 augmented triad, 85, 87 aural immersion, 48 (see also listening) aural transposition, 28, 39–47, 51, 97, 351 A voicings/B voicings, 221 Bach chorales, 162–163 Bach, Johann Sebastian, 52, 85, 138, 163 baroque period, 190, 205

bass, 92, 96, 238 bass clef, 31, 76, 92 bass lines, 52, 76–79, 81–82 beat cycle, 81 Bebop scale, 148 Beethoven, Ludwig von, 246, 340, 342 Bloom, Jane Ira, 63 blues, 48, 52, 65, 77–81, 131–133 minor blues, 84, 95–99 Blues scale, 131–133 borrowed chords, 186–188 (see also modal mixture) Brahms, Johannes, 10, 188, 190 bridge, 234, 255, 261, 280 cadence, 103–105, 126, 145, 198, 240 authentic, 105 deceptive, 105 half, 105 plagal, 105 cadential 6/4 chord, 105 call and response, 66–70 Central Park West, 273 Chopin, Frederic, 195, 266–267 chord identification, 92–94, 174, 215, 280–281, chord movement, 119, 193, 197 major sixth chord, 141 minor-major seventh, 160 seventh chords, 87–91, 95–100, 104 triads, 34, 59, 84–91, 97–99 chord-scale analysis, 102, 111, 112, 118, 126, 155, 181, 192 individual chord-scale approach, 111 parent scale approach, 111


chord substitution, 177, 211 chord superimposition, 213, 216–225, 229, 232–235, 237, 240, 242, 249 circle of fifths (see cycle of fifths) clarity of ideas, 20 clef, 28–34 close position voicings, 92–94 closely related keys, 258 Coltrane, Alice, 25–26 Coltrane, John, 20, 24, 25, 26, 62, 235, 262–263, 265–266, 272–273 common practice periods, European classical and jazz, 96, 162, 205, 214 common tones, 78, 103, 105, 196–198, 206, 281 comping patterns, 108, 110, 116, 152, 156, 313 composition, 70, 76–80, 83, 111, 132, 138, 156, 197, 294 consonance, 102, 138, 140, 244, 300, 301 contour, melodic, 7–10, 147–148, 152, 313 contrary motion, 117, 122, 155, 160, 165, 188, 281, 297 counterpoint, 158, 161 (see also species counterpoint) cycle of fifths, 31, 39, 43, 45–46, 68, 70, 170 d’Rivera, Pachito, 63 Dameron, Tadd, 259 Davis, Miles, 63 delayed resolution, 173, 264 diatonic, 35, 38, 41, 47, 55, 274, 281, 303 definition of, 85, 99 diminished seventh chords, 87, 88, 168, 175, 177 passing diminished seventh chord, 175, 183 dissonance, 139, 162, 298, 300–307 dominant seventh chord, 104, 105, 110, 111 Dorian mode, 38, 54, 57–65, 95–100, 140 double flats, 236 double sharps, 236 doubling, 205–206 drone, 10, 27, 56, 61 eleventh chords, 191 Ellington, Duke, 63, 85 endings (see improvisation) enharmonic spelling, 30, 145, 177, 244–245 even eighth note feel, 49, 62, 108, 128–129


extensions, 105, 139–140, 191, 211, 237–256 F clef, 29 figured bass realization, 201–212 Fitzgerald, Ella, 27, 63 florid texture, 3, 54, 76, 210 French augmented sixths, 245–247 fundamental tone, 11 German augmented sixth, 245–246 Gillespie, Dizzy, 63 grooves, 11, 19, 21, 48, 77 guide tones, 143–148, 334–335 half cadence, 105 half-diminished seventh chord, 87, 114, 174, 181 half step, 30–32, 35 approach tones, 149 octatonic scales, 249 resolution of augmented sixth chords, 245 resolution of guide tones, 144 surround tones, 149 top of voicing, 141 Hancock, Herbie, 63 harmonic and non-harmonic tones, 139, 158–163 harmonic functions, 102–128 harmonic rhythm, 133–134, 155, 161 harmonization, 151–156 head, 52–54, 75, 79, 131, 150 outhead, 75, 76, 79 implication-realization, 15 improvisation, collective, 19 endings, 20 form-based, 12 open, 19 pitch-based, 10 pulse-based, 11 solo pieces, 17 trans-stylistic, 1–28 Indian rhythmic principles, 80 inner dimensions, creative process, 13–15 intervals, 9, 28, 35–47, 61, 91–92 inversions, 36 inversion, triads and seventh chords, 91 Invitation, 235 Ionian mode, 38, 98, 191 Italian sixth, 245–247


Jarrett, Keith, 26 jazz, commonalities and differences with Euroclassical, 104, 106 harmony, 90, 96–97, 103 Jobim, Antonio Carlos, 189 Jones, Thad, 63, 348–349 Kern, Jarome, 261 keyboard, fingerings, 86, 88 realization, 84, 95–96, 106–109 seminal keyboard projects, 334 keyboard style realization, 206 key signatures, 31 Lady Bird, 258 lead sheet, 90, 167, 219 leading tone, 102, 104, 114–116, 168, 174, 180, 203, 206 leaps, intervallic, 10, 61, 76, 152 ledger lines, 29 Liebman, David, 134, 283–284 listening, heightened awareness, 13 recorded resources, 24, 61 Locrian mode, 38, 98–100, 181 Lydian mode, 38, 980100, 112, 191–192 major keys, 31 major scale, 29, 31 major seventh chords, 95, 105, 190, 141, 162, 215 major sixth chord, 141 mediant, 102 meditation, 13–15 melodic cells, 41–61 melody, melodic analysis, 142–143, 151, 156 melodic contour, 7–10, 152 melodic minor, 33 as basis for altered scales, 249–251 Mendelssohn, Felix, 247 Metheny, Pat, 63 Meyer, Leonard, 4, 15, 28 middle C, 29–31, 86 Mingus, Charles, 63 minor scale, 11, 33 harmonic, 33 melodic, 33 natural, 33


minor seventh chord, 59, 107, 125, 140, 157, 197 minor triad, 59, 98–100 Mixolydian mode, 38, 98–100, 157 modal composition, 70, 197–198 mode-master drills, 98–100 mode-rhythmic exercises, 76–77, 83 modes, 38 Modal Etude #1, 52–53 Bb part, 54 Eb part, 54 Modal Etude #2, 71–72 Bb part, 73–74 Eb part, 74–75 modal mixture, 186 modal interchange, 186 modulation, 124, 168, 183 distinguished from tonicization, 168, 183 Moment’s Notice, 262 Monk, Thelonious, 132 motive, 7, 9, 18, 42, 61, 68, 150 Mozart, Wolfgang, 164 My Funny Valentine, 158–160 Narmour, Eugene, 16, 27 Neapolitan sixth chord, 195 ninth chords, 211, 216 non-harmonic tones, 158–163 anticipation, 162 neighboring tone, 162 passing tone, 162 suspension, 162 non-syntactic elements, 16–20, 24 oblique motion, 117–118, 205 octatonic scale, 248–249 octave, 30 Oleo, 255 open fifth, 56–59 open voicings, 94 overtone series, 308–309 parallel motion, 118, 205 Parker, Charlie, 63 passing notes, 42, 138–40, 155 passing tones, 42, 139, 162–163 pedal point, 166–167, 190, 198 pentatonic scale, 40–41 minor pentatonic, 40, 55–57, 59–62, 77–78 pivot chord, 258


planing, 344 polyrhythm, 80, 129–130 popular music, 85, 89, 90, 96, 105–118, 131, 165, 172, 213 pulse, 6, 8, 11, 24, 56, 80 quartal harmony, 59 range, 3, 20 replacement tones, 216–217 resolution, 17, 85, 105 delayed, 173 half-step voice-leading in extended II-V sequence, 227 indicated with arrow, 119 non-harmonic tones, 161 problematic, 141, rhythm, Indian rhythmic principles, 80 layers, 273 time-feel, 61, 62, 70, 76–77, 80, 83, 128 (see even-eighth note feel and swing time feel) rhythm changes, 155, 211 rhythm section, 52, 54, 77, 107 rhythmic ratios, 50, 211 rhythmic templates, 48, 50, 57–60, 66, 68–69 ride cymbal, 129 Rollins, Sonny, 255 Roman numerals, 38, 78, 88–91, 98, 103, 121, 164, 182 root movements, 95, 103, 143, 175, 187, 195 root position, 84, 90, 91, 93–94, 96 scale, Blues, 132–133 Chromatic, 30 scale degrees, 38 scale superimposition, 203 Schneider, Maria, 63, 345 Schubert, Franz, 269 seminal keyboard projects, 95, 109, 126, 184, 210, 219, 237, 239 sequence, harmonic, 111–126, 156–197 motivic (see motive) secondary dominant (also see applied chords), 160–176 seventh chords, 87


silence, 17 similar motion, 118 solo improvisation, (unaccompanied), 17 soprano-alto-tenor-bass format, 210 species counterpoint, 293 first species, 299 fourth and fifth species, 304 improvising in modified species formats, 303 second species, 300 third species, 301 spread voicing, 93 Strayhorn, Billy, 9 structural function, 187 subdominant, 103, 177 submediant, 103 substitute dominant, 177 subV7 chord, 177 superimposition (see chord superimposition) superlocrian, 249, 250 Supertonic, 102 surround tones, 136 sus 4 chord (or sus chord), 141 suspension, 144, 162 Swallow, Steve, 160 swing (time feel), 49, 108, 128–129 symmetric scale, 249 syntactic parameters, 4 Take The A Train, 9 target note, 42, 155, 143–149, 156 tendency tone, 146, 203 tenor, 32, 210 tenor clef, 32 tessitura, 4, 5, 16 tetrachords, 249, 282 third, 33, thirteenth chords, 191 tihai, 290 time feels (see rhythm) tonality, 84, 95, 169, 201, 205 tonic, 102, 112, 114, 115, 119, 125, 159, 168 tonicization, 124, 168, distinguished from modulation, 168 free tonicization, 124–126, 183–185 top-down harmonization, 151–154 transcription, 133 transparency, 21 transposition, 41, 349 triads, 85 Triste, 189


tritone substitution, 177 turn-arounds, 123 tutti lines, 76, 150, 155 voice leading, 106, 116–122, 1456–150, 205, 218, 234

walking bass line, 108, 129–131 weak beat, 130 writing approaches, four-part writing, 164–166 keyboard style (five part), 96, 116–124