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Harmony 3by Barrie Nettles

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Harmony 3by Barrie Nettles

Spring 2007 Edition

Joe Mulholland

Chair, Harmony Department

© Copyright 2007 Berklee College of Music All rights reserved

Printed on recycled paper.

harmony 3 Spring 2007 Edition

CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

A Word to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii

part 1 Diatonic Functioning Chord Scales . . . . . . . . . . . . . . . . . 1

Secondary Dominant Chord Scales . . . . . . . . . . . . . . . . . . . . . 4

Optional Chord Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Other Major Key Chord Scales. . . . . . . . . . . . . . . . . . . . . . . . 10

Minor Key Chord Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Blues Chord Scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

part 2 Dominant Chord Functions . . . . . . . . . . . . . . . . . . . . . . . 22

V7—Standard Deceptive Resolutions . . . . . . . . . . . . . . . . . . 22

Substitute Dominant Chords . . . . . . . . . . . . . . . . . . . . . . . . . 27

Related II–7 Chords for Substitute Dominants . . . . . . . . . . 33

Extended Substitute Dominants . . . . . . . . . . . . . . . . . . . . . . 35

Substitute Dominant Chord Scales . . . . . . . . . . . . . . . . . . . . 37

Dominant Functions in Minor Keys . . . . . . . . . . . . . . . . . . . 41

part 3 Diminished Chord Patterns . . . . . . . . . . . . . . . . . . . . . . . 45

Ascending Diminished Chords . . . . . . . . . . . . . . . . . . . . . . . 48

Descending Diminished Chords . . . . . . . . . . . . . . . . . . . . . . 49

Auxiliary Diminished Chords . . . . . . . . . . . . . . . . . . . . . . . . 50

Alternate Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Available Tensions for Diminished Chords. . . . . . . . . . . . . . 53

Diminished 7th Chord Scales . . . . . . . . . . . . . . . . . . . . . . . . . 56

Symmetric Diminished. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

part 4 Modulation Considerations . . . . . . . . . . . . . . . . . . . . . . . 61

Direct Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Pivot Chord Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Dominant Chord Modulation . . . . . . . . . . . . . . . . . . . . . . . . 70

Transitional Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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Introduction

This revision of the Harmony 3 book takes place during an important transitional period in Berklee’s history. The college is engaged in its first comprehensive curriculum review, and all aspects of content, pacing and pedagogy are open to examination and change where needed.

The fundamental design of this book will follow the same formula that has served Berklee students well for some 30 years: a reference outline of material that is examined and explained in much greater depth in the classroom. The concepts introduced in this book are presented in straightforward, relatively simple form; teacher and student work to-gether to achieve a meaningful grasp of the material. Regular homework, aural comprehension of the ideas, and application of the techniques to written and recorded projects are indispensable. Nuanced understanding and deep ownership of the ideas will take a lifetime to achieve.

The Berklee Harmony curriculum is uniquely flexible and inclusive. It was originally designed to codify the rich harmonic vocabulary of the popular music of its day — primarily, the Great American Songbook and the innovations of the great jazz composers, arrangers and performers. From the late 1960’s to the present, American music became a kaleido-scope of coexisting and competing styles, with each generation and style choosing from the ever-expanding palette of chord progressions and melodic practices. The Berklee Harmony program has consistently given students the tools to navigate this vast array of musical possibilities and to understand the essential features of their chosen style. A simple, pas-sive reading of this book will never foster that understanding; only active application of the ideas to one’s area of interest (and areas beyond) will yield meaningful, creative results.

Thanks are due to several colleagues in the Professional Writing Division who gave valuable advice on content and style for this revision; in par-ticular, Suzanne Clark, Matthew Nicholl, Steve Rochinski and Daniel Ian Smith made detailed suggestions and had insights on the overall structure that resulted in a much better book. Special thanks go to Bill Brinkley for providing essential feedback on innumerable musical and style issues. His contribution went well beyond providing design and music typesetting.

The Harmony Department looks forward to continued development and improvement of materials which will serve the students’ needs, especially in light of the ongoing Curriculum Review Initiative.

Joe Mulholland Chair, Harmony Department

viii harmony 3 ix

A Word to the Student

The purpose of this book is to give you the tools to expand your creative horizons. The chord scale analyses presented apply to any music, no mat-ter how simple or complex the harmonic or melodic content. Rock, pop, Latin, Jazz, indeed any tonal music, can be better understood using a chord scale approach.

Because contemporary music is so broad in its scope, a working musi-cian must know as much as possible in order to meet the demands of the evolving marketplace. That is why this book has detailed examinations of many musical situations.

Essentially, much of Harmony 3 is a review of Harmony 2, with a slightly different emphasis. Major key, minor key, secondary dominants, modal interchange and available tensions are all re-examined in terms of chord scale theory. Therefore, your knowledge of these fundamentals needs to be very secure. In particular, fluent chord-spelling and scale construc-tion are absolutely crucial to making creative use of the concepts in this course.

The chord scale descriptions in this book are not meant to be merely memorized — that is only a first step — they need to be understood and used.Therefore…n Sing Everythingn Play Everythingn Question Everythingn Use Everything

A chord scale can be defined many ways:n As the “sound picture” of a musical moment.n As the combination of horizontal (melodic) and

vertical (harmonic) musical components.n As a palette of potential notes for a given harmonic situation.n As an organized rendering of the stated or implied tonal context.n As a linear representation of a vertical structure.

These are all good definitions. As you apply chord scale theory to the mu-sic you make, see which definitions bring the creative issues into focus.

There are two basic categories of chord scales:1. The diatonic result of melodic/harmonic activity in a clearly

defined key.2. Variations, alterations and alternate choices for those situations.

ix

In tonal (diatonic, key-related) music, chord scales are implied even in the simplest two-part passage comprised of melody and bass. This is true even if not all seven notes of a scale are sounded. Context, harmonic stress, melodic cadences and much more combine to create a context that allows our ears to “fill in” the missing notes. The choice of chord scale reflects the writer’s conscious or unconscious choice about coloring a voicing or shaping a melody: light/dark, thick/thin, predictable/surprising, subtle/intense, etc. It’s your music: take control of what you already know, and then discover new possibilities.

Chord scale nomenclature is derived from the tertian (“built in 3rds”) construction of chords and tensions. The basic labeling conventions are:1. Chord Tones: 1, 3 (or b3, or sus4), 5 (or b5 or #5), 6, 7 (or b7 or °7)2. Available Tensions: T9 (or T b 9 or T#9), T11 (or T#11 or b5),

T13 (or T b13).3. Harmonic Avoid Notes: tensions that are not “available” harmonically

on a given chord. Use “S” for “scale” plus the scale degree from the root of the chord, e.g., S b2 and S b6 in Phrygian, S4 in Mixolydian.

Thus, a major scale is labeled: 1 T9 3 S4 5 T13 7 1

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#

w w w w w w w w

1 T9 3 S4 5 T13 7 1

The Phrygian mode is labeled: 1 S b2 b3 T11 5 S b6 b7. III–7 in D major = F # Phrygian:

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w œ w w w œ w w

1 S b2 b3 S4 5 Sb6 b7 1

A Mixolydian b9, #9, b13 scale is labeled: 1 Tb9 T#9 3 S4 (5 Tb13) b7 V7 b9, #9, b13 in D minor:

&b

w w w w# œ w w w w

1 T b9 T#9 3 S4 5 T b13 b7 1

The concept of available tensions should be familiar from Harmony 2, but more review and explanation will follow in the text. To use this material musically, you need to know the notes in the scales, the names of the scales and the numbers associated with the notes.

part 1 Diatonic Functioning Chords 1

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part 1 Diatonic Functioning Chord Scales

Chord Scale Chord scales are used to identify the available melodic and harmonic pitches for a chord in a functional and stylistic context. They are an ex-tremely useful tool when harmonizing a melody line, but they have many other applications as well.

Chord scales may be described as extended chord structures, with ten-sions and other non-chord tones displaced down an octave to create a scale. A chord scale organizes the musical palette available to the writer or player in a given musical situation; it can be fully sounded in the melody and chords, or implied by a few notes and a key signature.

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w œw œ#

w œw

ww#

w

1 3 5 T7 T9 T#11 T13

Chord Scale Terminology The above extended maj7 chord may be identified either as Cmaj7(#11) or as a Lydian chord scale. It could be heard as IVmaj7 in the key of G, bIImaj7 in B major or in a number of other ways. Modal terminology (“Lydian,” for example) is used to identify the intervallic relationships between adjacent pitches.

Available tensions are diatonic non-chord tones which are a whole-step above a chord tone (a major ninth reduced by an octave). They are called “available” because they are diatonic, and they work well in a voicing or as sustained melodic pitches.

Harmonic avoid notes, also called avoid notes, are avoided harmonically but available melodically as approach notes or passing tones. If an avoid note is used in a chord voicing, or as a sustained melody note, it causes an unacceptable clash with the chord tones. In this book, avoid notes are indicated by filled note heads (œ); chord tones and available tensions are written as whole notes (w). Because there are no avoid notes in a Lydian scale, all of the notes of the scale above are available for use in a chord voicing or melody.

2 harmony 3

Diatonic Functioning Chord Scales


&

w w w œ w w w w

The modal name for the chord scale above is C Ionian. The chord symbol for this scale would be Cmaj7. It is Imaj7 in the key of C. Both the chord symbol and the chord scale refer to the same structure, but the chord scale is more complete and shows all the diatonic pitches.

The fourth degree (F) is an avoid note. It is usable only as an approach note, passing tone or neighbor tone. If it were used in a voicing as a ten-sion above a chord, it would clash with the major 3rd of the chord, creat-ing an unacceptable dissonance. In addition, since it is a melodically unstable tone, it is inconsistent with the stable nature of a tonic chord. (Of course, anything is possible as a special effect, but the focus in this course is on contemporary common practice.)

Modal Progressions It is important to distinguish modal terminology when used solely for labels to identify chord scales, from modal harmony. Modal progressions are extremely common in contemporary music, and were popularized by jazz innovators of the 1950’s and 1960’s. Music that has a mode other than Ionian as its tonal center and harmonic source will be covered in much more depth in Harmony 4.

Purely diatonic music uses diatonic chord scales . That is, if the melody and chords, or melody and bass, are all diatonic, then the chord scale for each harmonic event — each chord change — will be a familiar mode of the major or minor key that governs the whole piece. The available ten-sions will be a whole-step above a chord tone: diatonic pitches a half-step above a chord tone are avoid notes. (The examples below are in a major key; minor key music naturally yields different results. Minor key is ex-plored later in Part One.)

Ionian A diatonic melody accompanied by a I chord, or by the tonic of the key in the bass, produces an Ionian chord scale; the 4th degree is avoided. The I chord can have 9 and/or 13 in the melody or added as tensions to a voic-ing.

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#

#

w w w œ w w w w

1 T9 3 S4 5 T13 7 1


Dorian A diatonic melody accompanied by a II– chord, or by the 2nd degree of the key in the bass, produces a Dorian chord scale. The 6th degree is avoided, even though it is a whole-step above the 5th, because it creates a tritone with the 3rd of the chord. This creates a texture that suggests a dominant function rather than subdominant. The II– chord can have 9 and/or 11 in the melody or added as tensions to a voicing.

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#

#

w w w w w œ w w

1 T9 b3 T11 5 S6 b7 1

Phrygian A diatonic melody accompanied by a III– chord, or by the 3rd degree of the key in the bass, produces a Phrygian chord scale; the b2nd and b6th degrees are avoided. A III– chord can have 11 in the melody or added as a tension to a voicing.

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#

#

w œ w w w œ w w

1 S b2 b3 T11 5 S b6 b7 1

Lydian A diatonic melody accompanied by a IV chord, or by the 4th degree of the key in the bass, produces a Lydian chord scale has no avoid notes. A IV chord can have 9, #11, and/or 13 in the melody or added as tensions to a voicing.

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#

w w w w w w w w

1 T9 3 T#11 5 T13 7 1

Mixolydian A diatonic melody accompanied by a V chord, or by the 5th degree of the key in the bass, produces a Mixolydian chord scale; the 4th degree is avoided. A V chord can have 9 and/or 13 in the melody or added as ten-sions to a voicing.

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#

#w w w œ w w w w

1 T9 3 S4 5 T13 b7 1

Sus4 V7sus4 often precedes a V7 chord and sometimes replaces it in contem-porary practice. The chord scale sounded by V7sus4 remains Mixolydian, but the 3rd degree is avoided. 9 and/or 13 are still the available tensions.

4 harmony 3

Secondary Dominant Chord Scales

part 1 Diatonic Functioning Chords

Aeolian A diatonic melody accompanied by a VI– chord, or by the 6th degree of the key in the bass, produces an Aeolian chord scale; the b6th degree is avoided. A VI– chord can have 9 and/or 11 in the melody or added as ten-sions to a voicing.

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#

# w w w w w œ w w

1 T9 b3 T11 5 S b6 b7 1

Locrian A diatonic melody accompanied by a VII–7b5 chord, or by the 7th degree of the key in the bass, produces a Locrian chord scale; the 2nd degree is avoided. A VII–7b5 chord can have 11 and/or b13 in the melody or added as tensions to a voicing.

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#

# w œ w w w w w w

1 S b2 b3 T11 b5 Tb13 b7 1

Secondary Dominant Chord Scales

Chord Scales for secondary dominants typically reflect their diatonic context, for example:

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?

#

#

#

#

#

#

˙

.œ j

œ

w

w

w

œ œœ œœ œ

œ œ

w

ww#

w

ww

w

w

N

Œ

œ œ .œ

J

œ

ww

ww#

.œ

J

œ œœ

www

w

A C #7 F# –7 B7 E7sus4

In a major key, secondary dominants create a strong expectation of resolution, with root motion down a perfect fifth (or up a perfect fourth) to a diatonic chord. Therefore, the chord scale for a secondary dominant will contain the chord tones of the dominant chord and tensions that are diatonic to the key. The result, in all cases, will be some form of Mixolyd-ian scale. Minor key is somewhat more complex, but these basic elements remain the same. Minor key secondary dominants will be discussed in Part 2.

The avoid note rule for secondary dominants is simple: avoid scale tone 4. (It is the root of the expected chord of resolution.) All other diatonic tensions are available, whether 9, b9 or #9, 13 or b13.

etc.


(The following examples appear in G major.)

V7/IV, V7/V The chord scale for V7/IV and V7/V is Mixolydian ; the 4th degree (the root of the expected chord of resolution) is avoided:

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w w w œ w w wn w

1 T9 3 S4 5 T13 b7 1

V7/IV G7

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w w w# œ w w w w

1 T9 3 S4 5 T 13 b7 1

V7/V A7

V7/II Conditional Avoid Notes The chord scale for V7/II is Mixolydian b13 ; the 4th degree is avoided, and there is also a conditional avoid note, b13. Although it is a half-step above a chord tone, it still sounds appropriate in this context. (It is a common tone with the minor third of the expected chord of resolution.)

In a chord voicing, the 5th is generally omitted if T b13 is used. Condi-tional avoid notes are enclosed in parentheses because, although they are both available, they are generally not used together.

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w w w# œ w w w w

1 T9 3 S4 5 T b13 b7 1

V7/II E7

( )

V7/III and V7/VI The chord scale for V7/III and V7/VI is Mixolydian b9, b13 ; (The diatonic pitch #9 is usually included to remove the awkward augmented 2nd be-tween b9 and 3). The 4th degree is avoided; 5 and b13 are conditional avoid notes:

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w w w# œ w# w w w

1 T b9 3 S4 5 T b13 b7 1

V7/III F#7

( )

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w w w w# œ w w w w

1 T b9 T#9 3 S4 5 T b13 b7 1

V7/VI B7

( )

In a chord voicing, the 5th is generally omitted if b13 is used. Conditional avoid notes are enclosed in parentheses to remind the writer or player to use them with care in voicings or melodies.

harmony 3 part 1 Diatonic Functioning Chords

Optional Chord Scales

Any secondary dominant chord scale may be altered for arranging, stylis-tic or melodic reasons. These scales all function as dominant scales (since all have 3 and b7), but each has a unique character or color that affects the listener’s experience. Specifically, they each contain tension(s) that are not diatonic to their function. This results in a subtle ambiguity about their expected resolution. Their appropriate use requires experience and awareness of the harmonic/melodic context being created.

The following examples are in the key of G major.

V7 V7 may utilize the typical, diatonically-derived Mixolydian scale, or any of the following alterations:

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#

#

#

w wb w œ w w w w

w wb w œ w wb w w

w wb wn w# œ w wb w w

w wb wn w#wb wb w w

Mixolydian ( b9, b13)

Mixolydian ( b9, #9, b13)

Altered

Mixolydian ( b9)

1 Tb9 3 S4 5 T b13 b7 1

1 Tb9 T#9 3 S4 5 T b13 b7 1

1 Tb9 3 S4 5 T13 b7 1

1 Tb9 T#9 3 b5 T b13 b7 1

Altered Scale An altered scale contains a root, the 3rd and 7th, with the 9th, 5th and 13th altered to create tensions b9, #9, b5 ( b5 is enharmonically the same as #11), and b13. It does not contain a 4th degree, and has no avoid notes. Its ab-breviation in a chord symbol is “alt,” for example, D7alt.

The altered scale is also known as “diminished wholetone” (the bottom half is alternating half- and whole-steps and the top half is whole steps), or “super Locrian.”


V7/IV and V7/V Similar to V7, V7/IV andV7/V may use the following options instead of the diatonically-derived Mixolydian. V7/V is shown here:

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&

&

#

#

#

#

w wb w# œ w w w w

w w w# œ w wn w w

w wb w w# œ w wn w w

w wb w w#wb wn w w

Mixolydian (b9)

Mixolydian ( b13)


Altered

V7/II V7/II may use any of the following alterations instead of the diatonically-derived Mixolydian b13 chord scale.

&

&

&

#

#

#

w wn w# œ w w w w

w wn w w# œ w w w w

w wn w w#wb w w w

Mixolydian ( b9, b13)


Altered

V7/III and V7/VI V7/III and V7/VI may use altered instead of the diatonically-derived Mixolydian ( b9, b13) or Mixolydian ( b9, #9, b13):

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w w w w#w w w w

Altered

V7/III

F#7

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w w w w#wn w w w

Altered

V7/VI

B7

1 Tb9 3 S4 5 T13 b7 1

1 T9 3 S4 5 Tb13 b7 1

1 Tb9 T#9 3 S4 5 T b13 b7 1

1 Tb9 T#9 3 S4 5 T b13 b7 1

1 Tb9 T#9 3 b5 T b13 b7 1

1 Tb9 T#9 3 b5 T b13 b7 1

1 Tb9 T#9 3 b5 T b13 b7 1

1 Tb9 T#9 3 b5 T b13 b7 1

1 Tb9 3 S4 5 T b13 b7 1

harmony 3

Optional Chord Scales


Sus4 Before a secondary dominant If a secondary dominant is preceded by a sus4, the tensions for the sus4 chord will be the same as for the secondary dominant. This reinforces the connection between the suspension and the dominant sound. Note the differences in tensions on these two chords:

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w w œ w w w wn w

1 T9 S3 4 5 T13 b7 1

V7sus4⁄IV #G7sus4

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#

w w œ# w w# w w w

1 T b9 S3 4 5 Tb13 b7 1

V7sus4⁄III

#F#7sus4

Related II–7 Chord Scale A related II–7 chord of a secondary dominant or an extended dominant typically has a Dorian sound that reflects its subdominant function. If it is a dual function chord, the player/writer can choose to emphasize its diatonic function (Phrygian for III–7 or Aeolian for VI–7) or its related II–7 (Dorian) function. This emphasis can be obvious, as in a sustained chord voicing, or subtle, as in a passing tone in a melody. Again, this is a choice that will affect the musical context and create a slightly different experience for the listener.

Aug 7th Chord Whole Tone Scale Another option on dominant chords is the whole tone scale. It is com-monly used for +7th chords. It is used infrequently, generally as a special effect, and it has a unique character that can be useful in a particular context. The whole tone scale is symmetrical: it has 6 notes in whole steps, and therefore does not contain any avoid notes.

&

#

w w w w# w#w w

1 T9 3 T#11 #5 b7 1

V7sus4/III

#D+7

Symmetric Dominant Scale A final option is the symmetric dominant scale. It is built using a repeat-ing sequence of half-steps and whole-steps. This results in a dominant-sounding scale due to the presence of 1, 3, 5, and b7. Because of its mix-ture of natural and altered tensions, it is not diatonic to any key. As with any “optional” scale, it is used when some tonal ambiguity is desired, or when its unique color is appropriate.

Secondary Dominant


&

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w wn w‹ w# w# w w# w w

1 T b9 T#9 3 T#11 5 T13 b7 1

V7/II

E7 Symmetric Dominant Scale

Extended Dominants The basic chord scale for extended dominant chords is Mixolydian, but the writer or player may instead choose to use any of the options de-scribed above. The use of Mixolydian reinforces the expectation that the progression will ultimately resolve in a major key, since the tensions (9 and 13) are from major.

The unaltered Mixolydian is commonly used in folk, pop or rock music; Mixolydian scales with alterations are more typical in jazz. Once the chord pattern has begun, the initial scale choice usually continues, but variations are possible, depending on stylistic and melodic consider-ations.

Summary of Diatonic Function Chord Scales

The information in this chapter describes chord scale derivation in dia-tonic music. Much contemporary music, especially pop and rock, uses familiar diatonic major and minor key chord patterns and scales to estab-lish a tonal context. It is essential to become familiar with these patterns and scales through attentive listening and playing. They may be played as chords on a guitar or keyboard, or they may be the result of simple melody/bass activity. In any case, the collection of tones at work during a musical passage comprise the chord scale for that harmonic/melodic area. It is up to you, the player or writer, to explore the common, more basic relationships as well as the creative options.

With that in mind, here is a summary of fundamentals in major keys:

n Diatonic chords and melody combine to create diatonic chord scales.n Secondary dominants create Mixolydian chord scales with diatonic

tensions.n Extended dominants use Mixolydian chord scales (the same as V7/V).n Dominant chords using any form of Mixolydian scale are expected

to resolve down a perfect 5th and may optionally contain additional alterations.

n Related II–7 chords use either Dorian or their normal diatonic chord scale. Related II–7 b5 uses Locrian.

n Avoid notes are non-chord tones a half-step above a chord tone except:n Avoid the 6th degree for II–7 chords and,n On dominant chords, b9 and/or b13 are available.

1 harmony 3

Other Major Key Chord Scales


Summary of Diatonic Function Chord Scales (cont'd)n Avoid notes are not available as harmonic tensions in a voicing, but

are available as approach notes or passing tones.n The quality of a dominant chord’s 13th degree ( b13 or natural 13) will

usually predict the quality (major or minor) of the expected chord of resolution since that pitch represents the target chord’s 3rd degree. (In C major, A7(b13) suggests resolution to D–, F is the common tone.)


Exceptions to IV Lydian The diatonic IV chord usually uses a Lydian chord scale. However, there are some instances when an Ionian scale is more appropriate:

1. If the IV chord is preceded by its secondary dominant (V7/IV), it can create the expectation to hear a IV Ionian chord scale. (The lowered 7th of V7/IV is a common tone with the 4th degree of IV Ionian).

&

w ww œw ww w

w ww œw w

wb w

w ww œb

w ww w

w ww œw ww w

I V7⁄IV IV V7

C C7 F G7

2. If the intent is to prepare the listener for the IV chord to progress to IV–, a IV Ionian chord scale helps create that expectation, since the 4th degree of IV Ionian and IV– Dorian are the same.

& w ww œb

w ww w

w wwb wb w

œ wbw

w ww œw ww w

IVmaj7 IV–7 I

Fmaj7 F–7 C G7

3. The style of music may have an effect on the choice of chord scales. For example, the scale for the IV chord in Country and Western music is almost always Ionian. (The standard pedal tuning of a pedal steel guitar allows only for natural 4ths. In many folk, rock and pop styles, a common embellishment of triadic progressions on guitar is to alter-nate any triad with it’s sus4.)

Modal Interchange Modal interchange chords derive their chord scales from their modal source . The modal source is the parallel scale that yields the modal inter-change chord. For example, in the key of E, G # –7 is diatonic to E Ionian; Gmaj7 (bIIImaj7) is diatonic to E natural minor or E Dorian. (The same is, of course, true for triads.)


&

&

#

#

#

#

#

#

œ œ

wwww

a

a œ œ œ œ œ

œ œ

wwww

N

N œ œ œ œ œ

E major: III–7

b III maj7E Dorian:

It is important to distinguish between modal source and chord scale . In the example above, the source of bIIImaj7 is the tonic E Dorian scale. The chord scale for the bIIImaj7 chord is G Lydian. If the player or writer decides to use E Aeolian as the modal source, the chord scale for G maj7 will be G Ionian.

&

#

#

œ œ

wwww

N

N œ œ œ œ œ œ œ œ œ œ œ œ b III maj7

If modal source is E Dorian…

1 T9 3 T#11 5 T13 T7 1

…the chord scale is G Lydian

&

#

œ œ

wwww œ œ œ œ œ œ œ œ œ œ œ œ b III maj7

If modal source is E Aeolian…

1 T9 b3 S4 5 T13 T7 1

…the chord scale is G Ionian

Therefore, bIII can have a slightly different sound depending on the modal source that is selected. It is only a difference of one note, but that can be a very important note if it is a crucial melodic pitch, or is used in a voicing that captures a specific mood, or is a common tone with the next chord in the progression.

To summarize, the modal source will always be a parallel scale, e.g., E major/E minor. The chord scale for a modal interchange chord will always have the same tonic as the root of the chord, e.g., in the key of E major, Gmaj7 chord = G Lydian chord scale.

The examples that follow are by far the most common; as always, other choices are possible and will create a different result. All of these scales will be explored in their minor key context in the chapter on minor keys.

12 harmony 3



Non-diatonically Rooted Triads The non-diatonically rooted major chords in a major key typically use Lydian. This is common in jazz-influenced settings, and is also widely used in triadic folk, pop or rock situations, because the raised 4th in the chord scale represents a diatonic pitch. This allows for diatonic melodic phrases to be colored by the non-diatonic chord.

Other scales can be used, such as Ionian for bVII or bIII. Context and the writer/player’s intent will determine the choice of notes in a given situa-tion.

&

#

#

#

#

wn wn ww wn

wn wwn

1 T9 3 T#11 5 T13 7 1

b IImaj7

&

#

#

#

#

wn ww w

wn ww wn

1 T9 3 T#11 5 T13 7 1

b IIImaj7

&

#

#

#

#

wn ww w

wn ww wn

1 T9 3 T#11 5 T13 7 1

bVImaj7

&

#

#

#

#

wn w ww ww w

wn

1 T9 3 T#11 5 T13 7 1

bVIImaj7

Other modal interchange chords borrowed from parallel minor keys use the following chord scales.

I–7, V–7

&

w wwb w w

w wbw

1 T9 b3 T11 5 T13 b7 1

I–7 (Dorian)

& w wwb w w

w ww

1 T9 b3 T11 5 T13 b7 1

V–7 (Dorian)

IV–6, IV–7

& w wwb wb w w

œb w

& w wwb wb w w

wb w

1 T9 b3 T11 5 T13 b7 1

IV–7 (Dorian)

1 T9 b3 T11 5 T13 Sb7 1

IV–6 (Dorian)

Note that when Dorian chord scales are used on modal interchange chords, the 6th degree is labeled T13, not S6. The difference is due to harmonic function.

As stated earlier, when Dorian is used for a II–7 chord, the tritone be-tween b3 and 6 creates a dominant quality that contradicts the subdomi-nant function of the chord. The 6th degree of the II–7 chord is the leading tone of the key, and by definition subdominant chords do not contain the leading tone. However, when Dorian is used on I–7, IV–7, or V–7, T13 is an important color note, and is available for use in voicings, especially when supported by T11.

Note that Dorian is an appropriate chord scale for either IV–7, as above, or IV–6; IV–6 has S b7 as an avoid note, because it is a half-step above the major 6th, creating an unacceptable clash with that chord tone.

IV–6 can use melodic minor as an alternative to Dorian.

and Major Sevenths


II–7 b5 This chord is seldom found as a stand-alone modal interchange chord in major; it is almost always part of a II–7 b5 to V7 progression. As such, it typically uses a Locrian chord scale, since it is the II–7 b5 chord from the parallel Aeolian.

&

w œb w w wb wb w w

1 S b2 b3 T11 b5 T b13 b7 1

II–7 b5 (Locrian)

An alternate scale for II–7 b5 when used in a major key is Locrian n9, the n9 representing the major 3rd of the key. In cases where the intent is to make II–7 b5 sound like a chord preparing a cadence to tonic major, it is the appropriate scale.

&

w w w w wb wb w w

1 T9 b3 T11 b5 T b13 b7 1

II–7 b5 [Locrian ( n9)]

Minor Key Chord Scales

Diatonic chords in minor keys still use diatonic chord scales. However, due to the different varieties of tonic minor scales (natural minor, har-monic minor, melodic minor, etc.), more chord scale options are gener-ated for diatonic minor key chords. The criteria for avoid notes remain the same as in major keys with very few exceptions.

In Harmony 2 it was shown that the different forms of tonic minor included the minor as well as the major 6th and 7th scale degrees. This results in what can be referred to as the composite minor scale :

&

#

w w w w w w w# w w# w

1 2 b3 T11 5 b6 n6 b7 n7 1 min6 maj7 min7 maj7

E composite minor

14 harmony 3



Diatonic chords from minor tonalities have chord scales based on the dif-ferent tonic scales of those minor keys. A review of the tonic minor scales and the resulting wide variety of diatonic chords indicates how much freedom is possible when choosing a chord scale for any minor key chord. The choice of exactly which scale degree to use when deriving a chord scale depends on context and the intent of the writer/player.

The information in this section describes the selection of notes most often used for specific chord functions. In general:

1. The chord scales used for the tonic I– chord may be any form of minor scale, but by far the most common are Aeolian, Dorian and melodic minor. Any pitch a half-step above a chord tone is an avoid note.

2. Most of the non-tonic chord scales in minor keys (II–7 b5, II–7, IV–7, etc.) are derived from natural minor or Dorian minor. Any non-chord tone a half-step above a chord tone is an avoid note.

3. All dominant chords similar in function to those found in major key harmony (primary dominant, secondary dominants, substitute domi-nants, extended dominants) have chord scales which are appropriate to their function:n Chords with diatonic function use diatonic tensions;n Dominant chords which have expected resolutions down a perfect

fifth (i.e, secondary dominants) use some form of Mixolydian chord scale.

The most commonly used diatonic chord scales follow.

I–6 The I–6 chord uses either a Dorian chord scale, with the 7th degree avoided, or a melodic minor chord scale:

&b

b

b

w w w w w wn œ w

1 T9 b3 T11 5 6 S b7 1

C–6

Dorian

&b

b

b

w w w w w wn wn w

1 T9 b3 T11 5 6 T7 1

C–6

Melodic minor


I–7 The I–7 chord uses either a Dorian chord scale or a natural minor (Aeolian) chord scale. Dorian tonic minor does allow for the use of ten-sion 13; it is a whole-step above a chord tone and is an acceptable color on a tonic chord. (Phrygian is also an option on I–7. It is used when a darker color is desired.)

&b

b

b

w w w w w wn w w

1 T9 b3 T11 5 T13 b7 1

C–7

Dorian

&b

b

b

w w w w w œ w w

1 T9 b3 T11 5 S b6 b7 1

C–7

Aeolian

I– maj7 The I–maj7 chord uses either a melodic minor ascending chord scale or, less often, a harmonic minor chord scale:

&b

b

b

w w w w w wn wn w

1 T9 b3 T11 5 T13 7 1

C–maj7

Melodic minor

&b

b

b

w w w w w œ wn w

1 T9 b3 T11 5 S b6 (n)7 1

C–maj7

Harmonic minor

Unlike in major keys where S4 is a half-step above the major 3rd, T11 is an available tension on the tonic minor chord scales. In numerous con-temporary rock tunes it is an important melody note on I– chords.

When used as a tension in voicing the I–, I–7 or I–6, T11 is often sup-ported by T9.

Natural 11 is seldom used on I–maj7 since a tritone will be created be-tween it and the maj7th degree. This creates an unstable dominant sound that is at odds with the tonic function of the chord.

The chord scales for the other minor key chords can be thought of as displacements of one of the tonic scales.

1 harmony 3



Chords built on the 2nd scale degree typically use either a Phrygian or Locrian chord scale. II– and II–7 are most commonly found in modal music. II–7 b5 is most often found as part of a subdominant/dominant chord pattern.

II–7 &b

b

b

w œ w w wn œ w w

1 S b2 b3 T11 5 S b6 b7 1

II–7

D–7

Phrygian

II–7 b5 &b

b

b

w œ w w w w w w

1 S b2 b3 T11 b5 T b13 b7 1

II–7 b5

D–7 b5

Locrian

bIIImaj7 Chords built on the 3rd scale degree typically use an Ionian (major) chord scale. Other options exist.

&b

b

b

w w w œ w w w w

1 T9 3 S4 5 T13 7 1

b III maj7

E b maj7

Major

Chords built on the 4th scale degree typically use either a Dorian (IV–7), Lydian b7, or Mixolydian chord scale (IV7). Other options exist.

IV–7 &b

b

bw w w w w w w w

1 T9 b3 T11 5 T13 b7 1

IV–7

F–7

Dorian

IV7 &b

b

bw w wn wn w w w w

1 T9 3 T#11 5 T13 b7 1

IV7

F7

Lydian b7

&b

b

bw w wn œ w w w w

1 T9 3 S4 5 T13 b7 1

IV7

F7

Mixolydian


V7(b9) Chords built on the 5th scale degree typically use Mixolydian b9, #9, b13 for V7, or Phrygian. Other options exist.

&b

b

b w w w wn œ w w w w

1 T b9 T#9 3 S4 5 Tb13 b7 1

V7(b9)

G7(b 9)

Mixolydian (b9, #9, b13)

V–7 &b

b

b w œ w w w œ w w

1 S b2 b3 T11 5 S b6 b7 1

V–7

G–7

Phrygian

VI–7(b5) There are two possible scale degrees in minor for VI. The VI–7 b5 chord (which has a tonic function) usually uses a Locrian chord scale. Other options exist, e.g., Locrian natural 9 creates a melodic minor texture.

&b

b

b wn œ w w w w w wn

1 S b2 b3 T11 b5 T b13 b7 1

VI–7(b5)

A–7(b5)

Locrian

bVImaj7 The bVI chord (which has subdominant function) generally uses Lydian.

&b

b

b w w w w w w w w

1 T9 3 T#11 5 T13 7 1

bVImaj7

A b7maj7

Lydian

There are also two possible scale degrees in minor for VII. The bVII chord can use either a Mixolydian ( bVII7), or Ionian chord scale ( bVIImaj7), depending on the desired musical effect and the other chords in the harmonic phrase. The VII°7 chord is much less common, but does occur, especially in Latin-influenced music. Diminished chords that function in major keys will be discussed in detail later in this book.

bVII7 &b

b

b ww w œ w w w w

1 T9 3 S4 5 T13 b7 1

bVII7

B b 7

Mixolydian

1 harmony 3

Blues Chord Scales


bVIImaj7 &b

b

b ww w œ w w wn w

1 T9 3 S4 5 T13 7 1

bVIImaj7

B bmaj7

Ionian

VIIº7

&b

b

b wnœ w œ w w w wn

1 S b2 b3 S b4 b5 T b13 °7 1

VII°7

B°7

This is the 7th mode of harmonic minor. It is identical to V7( b9, b13)/3, and shares its dominant function.

Blues Chord Scales

There is tremendous variety in blues chord progressions and the har-monic colors that can be applied to them. The possibilities range from a simple repeating melodic phrase over a triadic progression (like Son House’s “Death Letter Blues”), to extremely chromatic improvisations over highly-elaborated harmonies that were pioneered by Charlie Parker (e.g., “Blues For Alice”) and later players. The most common uses fall somewhere in the middle, but there is still a myriad of potential melodic and harmonic choices at any given moment in a blues progression. These choices are generally governed by the style (Delta, Chicago, be-bop, rock, etc.) so in reality, the possibilities can usually be clearly defined.

Nevertheless, the range of options make it nearly impossible to neatly categorize each function in a blues with a “typical” chord scale. The player or writer must sort out the appropriate palette to use in each case. With that in mind, some of the most commonly used combinations are presented here.

The chord scales common to blues harmonies are derived from chord tones in the accompaniment and melodic pitches from the blues melodic scale in use . This is often the tonic minor pentatonic scale, or a major pentatonic from the b3 above the tonic, but could be another scale. (For the purposes of this book, we will ignore the inflections and pitch-bending that can blur the distinction between 3 and b3, 5 and b5, 7 and b7. Although they are an important part of authentic blues performance, our intent here is to allow clear choices in a harmonic situation.)


The tonic I7 chord in blues can have many different chord scales:

I7( #9) &b

wwb œ w

wb w

1 T#9 S4 5 b7 1

#F7#9

&b

w w# w œ wb wn w wb w

1 T#9 3 S4 5 n5 T13 b7 1

#F7#9

&b

w w# w œ w w wb w

1 T#9 3 S4 5 T13 b7 1

#F7#9

&b

w w# w œ wwb w

1 T#9 3 S4 5 b7 1

#F7#9

&b

w œ wbw w

w

1 S9 T#9 5 T13 1

#F7#9

I7(9) &b

w w w œ w w wb w

1 T9 3 S4 5 T13 b7 1

#F7(9)

&b

w w w œ wb wn w wb w

1 T9 3 S4 b5 5 T13 b7 1

#F7(9)

The subdominant IV7 chord in blues most often uses a Mixolydian chord scale:

IV7 &b

w w w œb w w wb w

1 T9 3 S4 5 T13 b7 1

#B b7(9)

Depending on style, b9 and 9 may appear side by side in the melody (although not in a sustained voicing). This unusual pairing of tensions is the result of the melismatic inflection, or bending, between b5 and 5 of the key, and is not reflected in chord voicings or the chord scale for IV7.

2 harmony 3

Blues Chord Scales


The V7 chord (borrowed from major key harmonies) is either a Mixolyd-ian scale, Mixolydian with alterations, or an altered chord scale:

V7

&b

w w w œ w w w w

1 T9 3 S4 5 T13 b7 1

#C7(9)

&b

w wb wb wn œ w w w w

1 T b9 T#9 3 S4 5 T13 b7 1

#C7( #9)

&b

w w w œ w wb w w

1 T9 3 S4 5 T b13 b7 1

#C7( b13)

&b

w wb wb wnwb wb w w

1 T b9 T#9 3 b5 T b13 b7 1

#C7(alt)

Avoid notes Natural 11 is not normally an available tension for dominant chords. However, in blues, it is very common to find it as a stressed melodic pitch on the primary I7, IV7, and V7, since in all these cases, natural 11 is a blues pitch. Powerful repeated melodic riffs and individualized expres-sive gestures (bent notes, slides from b5 to 5, etc.) are of prime impor-tance in blues, often taking prececedence over traditional concerns about voice-leading and scale tendencies. Creative use of these possibilities allows the musician to interpret just about anything with a blues flavor. Blues melody + blues harmonies = blues style, even if the music is not in a twelve-bar form.

&b4

4 œ œ œ œ

J

œ .œ

j

œb.œ œb œ

œœ œ

j

œbœ

j

œb ˙

n11 n11 n11

#F7 B b7 F7

V7/II Other chords found in blues progressions, such as secondary dominants and modal interchange chords, function the same way they do in major or minor key harmonies, and therefore use their normal chord scales. However, V7/II usually takes a Mixolydian b9, #9, b13 chord scale. A natu-ral 9 on V7/II implies an Ionian (major scale) tonality, whereas #9 and b9 are both blues melodic pitches (1 and b7 of the key).


&b

w wb w w# œ w w w w

1 T b9 T#9 3 S4 5 T b13 b7 1

D7( #9)

III–7 b5 III–7( b5) is best understood as an inversion of I7 that sometimes occurs at the 4th measure of a blues form. Its weak harmonic stress intensifies its function as an approach chord to IV. Since it is a mode of Mixolydian, it will share the same tones, but rooted on III of the key, resulting in a Locrian chord scale:

&b w œ w w wb w w w

1 S b2 b3 T11 b5 T b13 b7 1

#A–7( b 5)

Summary of Diatonic Chord Scale Usage

Chord Scale Criterian Diatonic chords take diatonic chord scales, with the exception of IV

when it is preceded by its dominant or expected to progress to IV– .n Any dominant chord with an expected resolution down a perfect fifth

uses some form of Mixolydian chord scale.n For dominant chords, diatonic tensions are the first choice; alterations

are a creative option.n b9 and #9 may coexist in a dominant functioning Mixolydian scale

(i.e, not on a I or IV chord in blues).n Most –7 b5 chords use Locrian.n All sus4 chords use Mixolydian or Mixolydian with alterations.

The avoid note is S3.n A wholetone scale is used for dominant chords with #5.

Harmonic Avoid Note Criterian Any note appearing in a chord scale which is a half-step above a chord

tone should be avoided harmonically. b9 and b13 are the exceptions and are available on dominant chords.

n The 6th degree of the Dorian scale should be avoided on II–7 in major keys.

n The 6th degree of the Dorian scale (T13) is available in minor keys and on modal interchange chords in major.

n Either the 5th or b13th of a dominant chord should be avoided if the other pitch is used.

22 harmony 3 part 2 Dominant Chord Functions 23

part 2 Dominant Chord Functions

V7—Standard Deceptive Resolutions

Deceptive resolutions of the primary dominant are commonly used for extending the endings of arrangements and as a means for creating spontaneous extended endings in playing situations. In songwriting, they can serve to reharmonize a repeated melodic phrase or add an element of surprise to a conventional chord progression. They are also very useful in creating a pathway to a new tonal center, resulting in a modulation or just a temporary tonicization of a closely related key.

In a traditional major key context, when V7 resolves deceptively the reso-lution often occurs at both a melodic cadence and on a strong harmonic stress point, that is, at the beginning of a phrase or section. It will usu-ally sound as though the progression will eventually move to tonic. In contemporary pop and rock, which is often more triadic, the resolving tendency of the V chord is weakened by the lack of a tritone. Consequent-ly, many progressions in these idioms are not as bound by earlier conven-tions of harmonic stress or phrase structure. They are more likely to be based on free movement between diatonic chords (including the V triad) and modal interchange chords such as bII, bIII, IV–, bVI and bVII. These progressions are often derived from blues-influenced or pentatonic bass lines, and exploit the relationships between closely related keys.

The possibilities are endless, and it is beyond the scope of this book to show every nuance and variation in usage. However, it is possible to train your ears to recognize these different types of resolution and to use your analytical skills to understand how they are employed in music.

Two of the standard deceptive resolutions of the V7 chord have already been seen in diatonic harmonic analysis. V7 resolving to III–7 or VI–7 (both tonic substitute chords) are the most basic examples of deceptive resolution because the underlying functions remain the same as a resolu-tion to the I chord. The harmonic motion is diatonic progressing to dia-tonic; the functional progression is from dominant to (substitute) tonic. The variety of root motion and continuation of forward motion make this device invaluable in all styles of diatonic songwriting, from simple folk tunes to more complex styles.

part 2 Dominant Chord Functions 23

V7 to III–7

&b4

4 ..

.

.’’’’ ’’’’ ’’’’ ’’’’ ’’’’ ’’’’ ’’’’ ’’’’

Tonic Alternate Subdominant Dominant Alternate Alternate Subdominant Dominant Tonic Tonic Tonic

F D–7 G–7 C7sus4 C7 A–7 D–7 B b C7sus4 C7

V7 to VI–7&b4

4 ..

.

.’’’’ ’’’’ ’’’’ ’’’’ ’’’’ ’’’’ ’’’’ ’’’’

Tonic Alternate Subdominant Dominant Alternate Alternate Subdominant Dominant Tonic Tonic Tonic

F D–7 G–7 C7sus4 C7 D–7 A–7 B b C7sus4 C7

Notice that in the progressions above:1. 2 measures of tonic chords begin each 4-bar phrase;2. the dominant chord resolves to a different tonic chord each time;3. the tonic F would not be available as a melody pitch on A–7, although

it would on D–7;4. the position of III–7 and VI– are reversed, but,5. the essential sound of the progression is unchanged because the

functional movement is the same.

There are a number of other standard deceptive resolutions of V7. They are called “standard” because they are common in popular music. They work in several different ways, but they all progress to chords that are diatonically related, usually modal interchange chords.

The strongest melodic pitches at a cadence point are degrees 1 and 5 (“do” and “sol”) of the key. These two diatonic notes are the most stable in the key; therefore, chords that contain those two pitches will sound like at least partial resolutions from V7.

An examination of the available pitches for III–7, VI–7, # IV–7( b5), bIIImaj7, bIImaj7, bVImaj7, and bVIImaj7 shows that each deceptive reso-lution of V7 will contain scale degree 1 or 5 (or both) as a chord tone or available tension:

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4

4

4

4

˙ ˙˙b˙˙ ˙

˙˙

˙

˙

˙

w

w

w

w

III–7 E–7: (C is not available)VI–7 A–7# IV(min7 b5) F#min7( b5): (G is not available)bIIImaj7 Ebmaj7(13)bVImaj7 A bmaj7bIImaj7 D bmaj7( #11)

D–7 G7( b 9,13)

V7⁄I

24 harmony 3



V7 to # IV–7( b5) V7 may resolve deceptively to # IV–7( b5):

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A–7 C/D D7 A–7 C/D D7 A–7 C/D D7

C # (min7 b 5) C–7 G/B B b 6 A7 Ab maj7 G

# IV–7( b5) is a diatonic functioning chord (despite its # IV root) which will be explained further in the chapter about diminished seventh chords. The presence of scale degrees 1 and 3 (do and mi of the key) as chord tones account for the effect of a partial resolution. This chord is inherently very unstable and will almost always continue to progress to the primary tonic either through stepwise motion (as above) or a cycle 5 progression.

V7 may resolve deceptively to any of the non-diatonically rooted major sevenths.

V7 to bIIImaj7

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bIIImaj7

C(9) E7(#9) Eb7 D7(#9) D–7 G7 Eb maj7

The functional explanation for this deceptive resolution is that V7 (primary dominant) moves to a modal interchange tonic chord; thus, dominant to alternate tonic.


V7 to bIImaj7 V7 may also resolve deceptively to the other maj7 modal interchange chords: the functional explanation for the next two deceptive resolutions is V7 (primary dominant) moving to a modal interchange subdominant minor chord; thus, dominant to subdominant.

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œœœ

n ˙˙˙

.œb J

œb ˙

.

.

.

œ

œœ

j

œœœ

n ˙˙˙

.œb J

œb ˙

w

ww

w

w

b

b

#C7sus4 G7sus4 G Pop ballad, q=98

#C7sus4 D7sus4 D7 Abmaj7

V7 to bVImaj7

&

?

4

4

4

4

œ œ œ .œ

j

œw

˙˙#

˙˙

œ œ œ ˙˙b ˙

˙N ˙#

˙b ˙

.œ

j

œ

.œ

j

œ

œ

œ ˙

œN

œ ˙

˙

˙

w

w

w

wb

C(9) E7(#9) Eb7 D7(#9) D–7 G7 A bmaj7

2 harmony 3



V7 to bVIImaj7 Less commonly, V7 may deceptively resolve to bVIImaj7:

&

?

#

#

#

#

#

#

4

4

4

4

j

œ œ

j

œ œ œ

.œ J

œ œ

œ

j

œ œ

j

œ œ œ

.œ

J

œ œ

œ

.œ

j

œ œ œ

.œ

j

œ œ

œ

w

.œj

œ œ

œ

j

œ œ œœ

j

œ

.œ

j

œ œ

œ

&

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#

#

#

#

#

#

j

œ œ œœ

j

œ

.œj

œ œ

œ

w

.

.œœ

J

œœ˙˙

.

.

œ

œn

j

œ

œ

˙

˙

w

.

.œœ

J

œœ˙˙

.

.

œ

œn

j

œ

œ

˙

˙

w

ww

w

w

wn

n

A Dmaj7 E7

E7 Gmaj7

q=86

When V7 resolves deceptively to a maj7 chord, the progression often follows the cycle of fifths to return to tonic.

&

?

4

4

4

4

œ œ ˙

˙˙

˙

˙

˙ ˙˙

˙

w

˙

˙

˙˙˙b

˙˙b ˙

œb

œb ˙

˙b

w

wwww

w

w

w

D–7 G7 Eb6 Abmaj7 D bmaj7 C(9)

&

?

4

4

4

4

œ œ ˙

˙˙

˙

˙

˙ ˙˙

˙

w

˙˙˙b

˙˙˙

˙ ˙

˙b ˙

˙b

w

wwww

w

w

w

D–7 G7 A bmaj7 D bmaj7 C(9)

&

?

4

4

4

4

œ œ ˙

˙˙

˙

˙

˙ ˙˙

˙

w

wwwb

w

w

w

b

b

w

wwww

w

w

w

D–7 G7 D bmaj7 C(9)


Summary of V7’s Common Deceptive Resolutions

n The diatonic or diatonically related deceptive resolution chords are: III–7; VI–7; # IV–7( b5); bIIImaj7; bVImaj7; bIImaj7; bVIImaj7.

n The available tensions on these chords follow the rules appropriate to the chords’ functions.

Substitute Dominant Chords

Tritone The characteristic sound of the dominant chord is produced by the pres-ence of the tritone (3 whole steps) which exists between the third and seventh of the dominant chord:

&

?

w

w w œ œ w

w

37 (

)

Augmented 4th

G7

Tritone Resolution The characteristic of dominant resolution is the movement of the two pitches of the tritone to the 1st and 3rd degrees of the target chord. The root of the dominant chord will move down a perfect fifth:

&

?

w

w

w

w

w

w

G7 C

2 harmony 3



The two pitches of the tritone are the most unstable pitches of the key. The leading tone (7th of the key) and the 4th degree of the key have a ten-dency to resolve as shown above and below. If the fifth of the dominant chord is present, it will also move to the root of the target chord.

&

?

w

w

w

w

ww

w

w

G7 C

Movement of the 5th The tendencies of the tritone notes are unaffected if inverted (as above). Just as the notes of the tritone resolve by chromatic movement, the 5th of the dominant chord may also resolve chromatically.

&

?

w

w

˙ ˙b

w

ww

w

w

G7 C

The altered fifth (D b) may assume the root function on the dominant chord, since the tritone notes remain a tritone:

&

?

w

w

˙

˙

˙b

ww

w

G7 D b7 C


Two Related Dominants The resulting dominant chords share the same tritone (the functions for the third and seventh are reversed) and may therefore have similar func-tion.

&

?

w

w

w

w

b

w œ œ

w

w

w

w

b

wb

G7 D b7

Tritone

73

3 7( )

( )

Substitute Dominant The dominant chord and its substitute dominant chord share the same tritone and their roots are a tritone apart. (Substitute dominants are also known as tritone substitutions .)

SubV7 The substitute dominant for V7 is subV7. Just as the expected resolution of V7 to I requires an arrow showing the resolution, the resolution of the subV7 has its own analysis symbol, a dotted arrow.

&

?

4

4

4

4

˙˙

w

w

w

w

w

w

w

˙˙

w

w

wb

b

w

w

w

w

n

V7 I sub V7 IG7 C D b7 C

A solid arrow represents dominant resolution down a perfect fifth; a dotted arrow represents substitute dominant resolution (subV7) down a half-step .

The context in which either chord appears determines their function:

&

?

b

b

b

b

b

b

b

b

b

b

b

b

4

4

4

4

˙˙

w

w

w

w

ww

w

˙˙

w

w

wn

n

w

ww

wb

b

V7 I sub V7 ID b7 G b G7 G b

&

?

4

4

4

4

˙˙

w

w

w

w

w

w

w

˙˙

w

w

wb

b

w

w

w

w

V7 I sub V7 I G7 C D b7 C

3 harmony 3



Substitute dominants are often used in the composition or arrangement of jazz tunes to provide variety in bass motion, a change of chord scale color, or to trigger a modulation. They are less common in contemporary rock and pop songwriting, but regardless of style, they are still an impor-tant resource for creating rich, colorful chord progressions.

SubV7/II, SubV7/IV, SubV7/V The primary dominant and secondary dominants are chords which have an expected resolution down a perfect fifth. This expectation is created by their diatonic context. The non-diatonic tones in secondary domi-nants, and the tritones in both primary and secondary dominants, create harmonic tension that is resolved with a resolution back to a diatonic chord. Secondary dominants all have diatonic roots a perfect 5th above a diatonic chord.

The expected resolution for substitute dominants is down a half-step to a diatonic chord. Substitute secondary dominants all have non-diatonic roots a minor second above a diatonic chord.The substitute secondary dominant chords are subV7/II, subV7/IV, subV7/V:

&

?

4

4

4

4

.

.

.

.

.

.

.

.

˙ œb œb

˙

˙

˙

˙

b

b

˙

˙b

˙ œ œb

˙

˙

˙

˙

b

˙ ˙b

˙ œb œb

˙

˙

˙

˙b

˙

˙b

˙œb œb

˙

˙

˙

˙

˙

˙b

Imaj7 subV7⁄IV IVmaj7

subV7⁄II II–7 subV7⁄V V7 subV7

Cmaj7 G b7 Fmaj7 Eb7 D–7 Ab7 G7 Db7

Note that the substitute dominant or the dominant may be interpolated (as in measure 4); in that case, the dominant and it’s substitute dominant have a common resolution.

IV7 and bVII7 One characteristic of substitute dominant chords in major key contexts is that their roots are not diatonic. (The primary and secondary dominant chords by definition have diatonic roots.) Although IV7 could be heard as subV/III, it has a diatonic root and it rarely sounds as though its function will be as a substitute dominant (though it may progress down a half-step to the tonic sounding III–7). IV7 more often appears as a modal inter-change chord; functioning as a subdominant minor cadence chord:

& 4

4 ..

.

.˙œ œ ˙

œœ œ .˙

Œ

œb œ œœ œ œ œ

Cmaj7 E–7 A–7 F7

IV7 can also be used to add blues influence to an otherwise diatonic major tune.


Similarly, bVII7’s function as a modal interchange cadence chord (subdominant minor) is more common than the possibility of a subV7/VI function: although it may resolve down a half-step to the tonic sound-ing VI–7 chord it is much more commonly heard progressing back to I.

&

?

4

4

4

4

.

.

.

.

˙ œ œ

˙

˙˙

˙b

˙ ˙b

˙œ œ

˙

˙

˙

˙b

˙ ˙b

Imaj7 bVII7 VI–7 bVII7

Cmaj7 B b7 A–7 B b7

SubV7/III, SubV7/VI In unusual situations, most often influenced by harmonic stress patterns, IV7 may function as subV7/III and bVII7 may function as subV7/VI.

If either one of these chords appears interpolated between its tritone substitute chord and the target chord, it will be a subV7, as are the F7 and B b7 in this example:

& 4

4 .. ˙

œ œ ˙œœ œ .˙

Œ Ó

œ œ œœ

&

.

.

œœ œ ˙

Ó œ œ œ œ .˙Œ

j

œ œ

j

œb œ œ œ

Cmaj7 E7 B b7 A–7

D–7 B7 F7 E–7 D–7 D bmaj7

In this example, the B b7 and F7 are heard as elaborations of the second-ary dominants that preceed them. Each pair of chords shares a com-mon tritone and a common target; in addition, they occur on very weak harmonic stresses.

A more thorough examination of IV7, bVII7, and other dominant chords that don’t function in a traditional manner will be presented in Harmony 4.

As has been the case with many previous topics, the VII–7 b5 chord is not involved in the listing. V7/IV (or I7) is never subV7/VII.

32 harmony 3



Minor Key SubV7s Substitute dominant chords are also common in minor key chord pro-gressions, especially those from the Tin Pan Alley/Great American Song-book genre, or minor key songs with blues influences (e.g., “Angel Eyes”).

&b

b

b

b

4

4.˙œ

.œ

j

œ˙n

.˙ œ œ w

&b

b

b

bŒ

œ .œ

j

œ .œ

j

œ ˙ œ œ œ œ œn w

subV7⁄V

subV7⁄II subV7

F–7 D b7 C7 F– A b7 G–7b5 G b7

subV7⁄IV

subV7⁄V F–7 C b7 Bb–7 D b7 C7 F–

The differences between major and minor key scale structure results in some differences in the subV’s that are created. For example, subV7/ bIII, while theoretically possible, is extremely unusual. In minor keys, un-like major, subV7/II and subV7/V have diatonic roots; however, they still create the expectation of resolution down a half-step to a diatonic chord. The common substitute dominants in minor key are:

subV7 I–

C– D b7 C–

&

?

b

b

b

b

b

b

˙

˙˙

˙˙˙

b

˙ ˙b

w

ww

w

subV7⁄II II–(b5)

C– E b7 D–7(b5)

&

?

b

b

b

b

b

b

˙

˙˙

˙˙

˙b

˙˙

ww

w

w

subV7⁄IV IV–7

C– G b7 F–7

&

?

b

b

b

b

b

b

˙

˙˙

˙

˙˙bb

˙

˙b

w

ww

w

subV7⁄V V7

C– A b7 G7

&

?

b

b

b

b

b

b

˙

˙˙

˙

˙˙b

˙

˙

www

n

w

These chords, the way they function in progressions, and their chord scales will be examined in more detail in the section on chord scales for substitute dominants.


Related II–7 Chords for Substitute Dominants

Any dominant chord may be preceded by its related II–7. The related II–7s of substitute dominants are all non-diatonic. Because the related II–7 chords of the substitute dominants cannot have dual function, they will be analyzed simply in terms of their relationships with the substitute dominant chords: the relationship. As before, the bracket shows root motion down a perfect fifth (or up a perfect fourth).

If the related II–7 chords for primary or secondary dominants are com-bined with their substitute dominants, four possibilities for subdomi-nant/dominant resolution exist:

&

?

˙

˙

˙

˙

˙

˙

w

w

w

D–7 G7 Cmaj7

&

?

˙

˙

˙

˙

b

˙ ˙b

w

w

w

D–7 D b7 Cmaj71. 2.

Examples 1 and 2 (above) are by far the most widely used, because their root motion is consistent: all fifths or all half-steps.

Examples 3 and 4 (below) lack this consistent root motion. In addition, they lack the suspended tone (the tonic of the key and the root of the tar-get chord) that characterizes a full subdominant-dominant-tonic resolu-tion. They are more often used in an arrangement or reharmonization of an existing song.

&

?

˙

˙

b

b

˙

˙

˙b

˙b

w

w

w

A b–7 D b7 Cmaj7

&

?

˙

˙

b

b˙

˙

˙b ˙

w

w

w

A b–7 G7 Cmaj73. 4.

34 harmony 3

Related II–7 Chords for Substitute Dominants


To summarize:1. The related II–7s of the primary or secondary dominants either

progress normally, by fifths:

& 4

4 .. .œ J

œ œ œ .œb

J

œ ˙.œ J

œ œ œ w

&

.

.œ œ œœœ .œ

J

œ ˙ œ œ .˙ œb œb .˙

V7⁄IV

V7⁄II

Cmaj7 G–7 C7 Fmaj7 E–7 A7

V7⁄V V7

D–7 A–7 D7 G7sus4 D–7( b5) G7( b9)

2. And the related II–7s of the substitute dominants either progress nor-mally, by fifths:

& 4

4 .. .œ J

œ œ œ .œb

J

œb ˙n.œ J

œ œ œ wb

&

.

.œ œ œœœ .œb

J

œb ˙œ œ .˙ œb œb .˙

subV7⁄IV

subV7⁄II

Cmaj7 D b–7 G b7 Fmaj7 B b–7 E b7

subV7⁄V

subV7⁄II

D–7 Eb–7 A b7 G7sus4 A b–7 D b7

3. OR, any of the above II–7 chords may progress down a half-step to the root of the dominant or the substitute dominant chord. Since the root motion from the II–7 to the dominant or substitute dominant chord will be down a half-step, the analysis symbol used is a dotted bracket:

& 4

4 .. .œ J

œ œ œ .œb

J

œ ˙.œ J

œ œ œ wb

&

.

.œ œ œœœ .œ

J

œ ˙ œ œ .˙œb œb .˙

subV7⁄IV

V7⁄II

Cmaj7 G–7 G b7 Fmaj7 B b–7 A7(b9)

subV7⁄V V7

D–7 A–7 A b7 G7sus4 A b–7 G7(b9)


A solid arrow or bracket indicates root motion down a perfect fifth:

? ..w

˙

˙

w ˙

˙

w

˙

˙

w

˙

˙

A dotted arrow or bracket indicates root motion down a half-step:

? ..w

˙ ˙b w ˙ ˙b w

˙ ˙b w

˙ ˙b

Only dominant chords can be analyzed with an arrow; only –7 or –7(b5) chords may appear at the beginning of a bracket; only dominant chords may appear at the end of the bracket.

–7or

–7(b5) dom7

–7or

–7(b5) dom7

Extended Substitute Dominants

Extended Dominants Extended dominants are dominant chords found on strong stress points, or within a pattern or dominant resolution following the cycle of fifths with an extended dominant as the starting point for the pattern:

&

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b

b

b

b

4

4

4

4

˙

˙

n

#

˙

˙

b

n

˙

˙

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n

˙

˙n

˙

˙

b

b

˙

˙

b ˙

˙

w

w

w

w

˙

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˙#

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b

b

b

b

.

.

.

.

˙

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# ˙

˙

n

˙

˙b

b ˙

˙

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n ˙

˙

b

w

w

ww

˙

˙

˙

˙#

n

˙˙

˙

˙

( )(3) V7 Imaj7 V7⁄III

D7 G7( b9) C7 F7(#9) B bmaj7 A7( b9)

V7 Imaj7 V7⁄III

D7( b13) G7( b9) C7 F7(#9) B bmaj7 A7(#9)

( )

3 harmony 3

Extended Substitute Dominants


Extended Substitute Dominants The same characteristics apply when substitute dominant chords are involved. The root motion during extended dominant motion follows the cycle of fifths; the root motion during extended substitute dominant mo-tion is chromatic. The analysis for extended dominants is a solid arrow; the analysis for extended substitute dominants is a dotted arrow :

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b

b

b

b

4

4

4

4

˙

˙

n

#

˙

˙

b

n

˙

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˙b

b

˙

˙n

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b

b

˙

˙

b ˙

˙b

∫

w

w

w

w

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b

b

b

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b ˙

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b ˙

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b ˙

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w

w

ww

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n

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( )(3)

( ) V7 Imaj7 V7⁄III

A b7 G7 G b7 F7 B bmaj7 A7(#9)

Chromatic

Chromatic

V7 Imaj7 V7⁄III

D7 D b7 C7 C b7 B bmaj7 A7( b9)

Interpolated Extended In measures 1–2 and 5–6 of the above example, every other chord rep-resents an extended substitute dominant chord, while the remaining chords are extended dominants resolving by half-step. If the root of the first dominant chord in the pattern is not diatonic, it will sound like an extended substitute dominant. The extended substitute dominant may be interpolated prior to the resolution of an extended dominant:

&

?

b

b

b

b

4

4

4

4

w

w

w

w

w

wn

b

w

˙

˙b

˙ ˙b

wb

wn˙

˙b

˙ ˙b

w

wb

˙

˙b

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b

b

b

b

.

.

.

.

w

w

ww

˙˙n

w

wb

˙

˙n

wb

w

w

wb

w

˙b ˙

wb

˙

˙b

Imaj7 V7⁄II V7

B bmaj7 G7 D b7 C7 G b7 F7 C b7

Imaj7 V7⁄IV IVmaj7 IV–7 bVII7

B bmaj7 B b7 E7 Ebmaj7 E b–7 A b7

( )

Substitute Dominants


Related II–7 of Extended It is more common for the substitute dominant to follow the extended dominant (as above) than for the substitute to appear first. Related II–7 chords may precede their respective dominant chords:

&

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b

b

b

b

4

4

4

4

˙

œ œ

w

w

w

˙ ˙

œ.˙n

˙ œb œœ

œ œb

œb

˙ ˙b

˙b œb œ

œ.˙n

œ

œ œb

œb

˙ ˙b

˙ œ∫ œ

˙b œb œ

˙ œb

œb

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b

b

b

b

.

.

.

.

œ

˙

œ

w

ww

˙ œ œ

w

˙b œn œ#

˙ œn

œn

˙ œœ

w

wn

wb

w

˙b ˙

wb

˙

˙b

B bmaj7 D–7 G7 A b–7 D b7 G–7 C7 D b–7 G b7 F7 G b–7 C b7

B bmaj7 Bb7 B–7 E7 Ebmaj7 E b–7 A b7

Harmonic rhythm for all extended dominant motion will be increased with the addition of related II–7 chords. Further, a II–7 may itself be the target chord of resolution.

Substitute Dominant Chord Scales

Tensions for Sub V’s Since substitute dominant chords are not diatonic structures, their extended structures do not require a diatonic orientation. The tensions available on any substitute dominant are the pitches a major ninth above any chord tone (whether diatonic to the key or not).

&

# wwwwwwwb

b

n

b

b

subV7A b7

T9

T13

T#11&

# wwwwwwwb

bn

subV7⁄IIB b7

T9

T#11T13

&

#

wwwwwwwb

nbb

subV7⁄VEb7

T9

T#11T13

&

#

wwwwwwwb

b

b

n

b

b

subV7⁄IVD b7

T9

T#11

T13

In all cases, the tension #11 on a substitute dominant represents the root of the original chord (the primary dominant or secondary dominant).


Added Bb7

3 harmony 3



All substitute dominant chords have available tensions 9, #11, and 13. These pitches represent a major triad a whole-step above the root of the dominant chord, a fact that can suggest voicing possibilities when writing for piano or larger ensembles. When these voices are combined into a chord scale, the result is a scale that can be described as Lydian b7 (or Lydian dominant):

&

#

wb wb w w wb w wb wb

subV7

A b7

1 T9 3 T#11 5 T13 b7 1

Though alterations are possible to all forms of Mixolydian scales, the only alterations normally found to the Lydian b7 scale occur on the substitute dominants of I, IV, and V. This is a relatively rare usage, found mostly in Brazilian songs, especially bossa nova.

Since those chords have an expected resolution to a chord with a major third, the major third of the chord of resolution may occur in the Lydian b7(#9) chord scale as an alternative to T9:

&

wb w ww wb

wb wb wb

D b7( #9) = subV7

#9 of Db ; 3 of Cmaj7

& wb wN wb wwb wb wb wb

G b7( #9) = subV7⁄IV

#9 of Gb ; 3 of Fmaj7

& wb w ww wb

w wbwb

A b7( #9) = subV7⁄ V

#9 of Ab ; 3 of G7

Though b9 and #9 may normally coexist, b9 is not available in the above alteration to the Lydian b7 scale.

Lydian b7 Chord Scale The Lydian b7 chord scale is used for:n All substitute dominant chords (expected resolution down a half-step)n Extended substitute dominant chords (also expected to resolve down

a half-step).

It is also sometimes used for:n bVII7 in a major key (expected root motion up a whole-step),n IV7 in a major key (expected root motion down a perfect fourth)

IV7 and bVII7 can also use Mixolydian. These are modal interchange chords and the choice of chord scale is based on style (e.g., Mixolydian is a much more common choice in rock and folk progressions) and con-textual considerations, such as a desire to reinforce the original key or a parallel tonality. For example, example 1 below uses a Mixolydian chord scale with S4 on very weak beats. Example 2 uses Lydian b7; note how the C# in measure 4 continues the melodic idea from the previous measure and reinforces the A major tonality by sounding the major 3rd of the key.


&

#

#

#

4

4.œ œ œ

œ œ.œ

j

œ œœn œ œ œ

.œnw

&

#

#

#

.œ

j

œ

j

œ œ

j

œ .˙‰

j

œ

J

œ œ

J

œ œ œ œ œ œœ œ œ w

A A7sus4 A7 D G7 A

A E–7 Eb7 Dmaj7 G7 A

1.

2.

By sounding the extended structure of the substitute dominant over the root of the original dominant chord, an alternative to the normal avail-able tensions for the primary or secondary dominant chords may be found:

Substitute Dominant

&

?

wwwwwwwb

bbb

wb

wwwwwww

w

subV7 V7alt

A b7 (9, #11,13) D7alt

As illustrated in the example above, when the pitches of the substitute dominant chord (in treble clef) are sounded over the root of the original dominant chord from which it is derived, the functions for each note change to become: b5 – b7 – b9 – 3 (enharmonic) – b13 – root – #9. This is an altered dominant chord.

Although the altered dominant chord scale can be seen as a mode of Lydian b7, the altered scale is not used on substitute dominants. As was explained in the chapter on dominant functioning chord scales, the al-tered dominant is an option that is used solely on chords that will resolve down a perfect fifth.

Tensions for Related II–7s of The available tensions for the related II–7 chords of substitute dominants are drawn from the key in which the chord is the diatonic II–7:

&

#

#

œwwwwww

n

b

b

n

b

b

B b–7 subV7

&

#

#

œwwwwwwb

n

n

b

C–7 subV7⁄II

&

#

#

œwwwwww

b

b

nb

b

n

b

Eb–7 subV7⁄IV

&

#

#

œwwwwww

n

b

n

b

b

F–7 subV7⁄V

from A b from B b

from D b from E b

Over V7’s Root


4 harmony 3



Related II–7 Chord Scales Dorian, the scale for a II–7 chord, is used for any II–7 chord which is present in a progression with a or relationship. This reflects its subdominant function: it is in the progression to prepare the domi-nant chord.

In other situations involving the relationship, the chord scales used are also Dorian—Mixolydian, in order to reflect the sound of a II–7 V7, regardless of the resolution for the dominant chord.

To summarize:1. Mixolydian, Mixolydian with alterations, whole tone, and altered are

chord scales which create an expectation to resolve down a perfect fifth.

2. On substitute dominants, Lydian b7 is the chord scale that creates an expectation to resolve down a half-step.

3. On IV7 and bVII7, the choice of chord scale depends on musical context and the desires of the writer or player.

Considerations: Chord Scales For Extended Substitute Dominants

The decision to hear an extended dominant versus an extended substitute dominant is made by the listener based on the function of the dominant in the key.

n If the pattern follows the cycle of fifths (whether the roots are diatonic or not), most will hear extended dominants. This can be reinforced by the use of a straight Mixolydian scale.

n If the pattern is chromatic (whether the roots are diatonic or not), most will hear extended substitute dominants. This can be reinforced by the use of a Lydian b7 scale.

The chromaticism resulting from the inclusion of substitute dominant chords in a progression can make the tonality somewhat unclear. This allows for more freedom in the analysis and, therefore, in the choice of chord scales.

Ultimately, the choice of determining the chord function for progres-sions containing extended dominants and extended substitute dominants belongs to the writer/performer and is dictated to the listener.


Dominant Functions in Minor Keys

Since minor keys have chords built on the natural 6th and 7th scale degrees as well as the raised 6th and 7th, the root of some of the dominant chords functioning in the key may be both a perfect fifth and a half-step above different diatonic pitches; that is, a chord can simultaneously appear to be a secondary dominant and a substitute dominant.

In such situations, the intentions of the composer/arranger/improviser will dictate which scale to use. There is no hard-and-fast rule to follow, but Mixolydian chord scales generally imply resolution down a perfect fifth; Lydian b7 chord scales generally imply resolution down a half-step.

It is important to consider the tensions on the Lydian b7 scales: if tension #11 is not diatonic to the key, ambiguity about the tonality may be created. This is not necessarily a bad thing: subtle manipulation of the listener’s expectations can be achieved by creative use of tensions.

V7/II, V7/IV, V7/V The common secondary dominants in minor keys were covered briefly in an earlier chapter. To review, they are normally constructed using chord tones appropriate to the chord, plus tensions from the key signature. For example:

&

?

b

b

b

b

4

4

4

4

.

.

.

.

Medium R'n'B balladq»•º

œœœ

œœ

≈

œœœœ

˙˙˙

˙ œ

œ œ# œœ œ#

V7/IV

‰

œœœœ

≈

œ œœ

œn

œœ

œ

≈

.

.

j

œ

œ

˙ œ œ œœœ

&

?

b

b

b

b

.

.

.

.

œœœœ

œœœ

≈

œœœ

œœœ

˙˙˙

˙

≈

œ œœ œn

‰ .r

œ œ œ œ

œœ

œ

œœ

œ

˙ Ó

V7⁄IV

G–7 G–7 G7( b13)

C–7 C–7

Medium R ’n B ballad q=80

The chord scale for the G7 (V7/IV), is G Mixolydian b13; B natural from the chord, E b from the key.

42 harmony 3



The same approach is used for V7/II and V7/V, the other common sec-ondary dominants in minor: appropriate chord tones, plus tensions from the key signature. This will provide the most basic, diatonic sound for the musical passage. As in major, any alteration of the scale is possible, depending on the intentions of the player or writer.

The secondary dominant of VI–7b5 is almost never encountered; V7/ bIII and V7/ bVII will be discussed below.

SubV7, SubV7/IV, SubV7/V These three substitute dominant chords are fairly common in minor key tunes, especially those in the jazz and contemporary Gospel music tradi-tions. They resolve to diatonic targets down a half-step, and use the same chord scale, Lydian b7, as their major-key counterparts. The following example is in B minor:

&

?

#

#

#

#

www

wwwwn

b

www

w

www

www

wwwwn

bn

www

w

www

www

wwww

n

www

w

www#

subV7 I–7 subV7⁄IV IV–7

subV7⁄V V7

Tensions are: 1. 9, #11, 13 2. diatonic 3. common tones with chord of resolution (except one note on V7)Roots are a half-step above the chord of resolution.

&

?

#

#

#

#

SubV7

wn w w w w w wb

wwwwn

b

1 T9 3 T#11 5 T13 b7

subV7C7

Other Minor Key As mentioned earlier, there are three dominant chords common in minor key progressions that can be a perfect fifth above a diatonic pitch and at the same time a half-step above another diatonic pitch, for example:

In B minor, D7 can be:

&

?

#

#

#

#

˙˙˙

n ˙

˙˙

˙

˙

˙˙˙

n ˙

˙˙

#

˙ ˙

V7⁄ bVI or

subV7⁄II

Dominant Chords


The choice of chord scale, either for use in a voicing or a melodic passage will create different expectations. Compare these two examples:

&

#

#

4

4

.

.œœ

j

œ

j

œœ

j

œœ˙˙

Œ

œ œ.œ

j

œ

j

œ œ

j

œœ˙˙

Œ

œ œ

&

#

#

.

.œœ

j

œ œœœ

.

.

.

œœœ

j

œœ#œœ

œw

V7⁄ bVI

B– D7

Gmaj7 F#7sus4 F#7 B–

1.

&

#

#

4

4

.

.œœ

j

œ

j

œœ

j

œ ˙

Œ

œ œ..œœ

j

œœœœœœ

˙˙

.

.œœ#

j

œ

œ

&

#

#

w

w

˙

˙

Œ

œ œœ œ œ

‰

.œ ˙

˙˙ ˙˙#

ww

subV7⁄ II

B– E–7 B–7 B–7 D7

C # –7b5 F#7sus4 F#7sus4 F#7 B–

2.

In example 1, the G natural as a passing tone on D7 anticipates the root of the chord of resolution, bVI. In example 2, the G# is diatonic to the composite minor scale. Placing D7 on a very weak harmonic stress point strengthens the perception of its subV function.

bVII7, V7/ bIII bVII7 is a diatonic chord in minor key; it commonly progresses up a step to tonic I– . It also appears to be the secondary dominant of bIII, a perfect fifth below. However, secondary dominants by definition contain a chromatic alteration. The chord scale for either situation is Mixolydian. Lydian b7 is theoretically possible but in practice is almost never used, because #11 of the chord would be the major 3rd in a minor key.

&

?

b

b

b

b

b

b

4

4

4

4

˙

œ

œœœ

˙˙ œ œ œ

˙

˙

˙

˙

˙ œ

œœœ˙

˙˙

œn œœ

˙

˙

˙

˙

˙

˙˙

˙

˙

I– bVII7 I– bVII7 bIIImaj7

C– B b7 C– B b7 Ebmaj7

Mixolydian Lydian b7 (much less common)

44 harmony 3


part 3 Diminished Chord Patterns 4

SubV7/II, V7/ bVI SubV7/II (a chord which may progress down a half-step to II–) is also the secondary dominant of bVImaj7 (the diatonic chord a perfect fifth below). Therefore the chord scale may be either Lydian b7 or Mixolydian, although Mixolydian is much more common.

&b

b

b 4

4

œœ

Œ Ó Ó

œ œœ œ .œ

j

œ œœ œ .˙

Œ

&b

b

bœ

œŒ Ó Œ ‰

j

œ œnœ œ œ œ œ œ

j

œ œ

j

œ w

C–6 Eb7 A bmaj7G7sus4 G7

C–6 C–6 E–7b5 Eb7 D–7b5 D b7

q=155, straight 8ths

Lydian b7 is theoretically possible but is not generally used, because #11 of the chord is the major 6th of the key; S4 is the diatonic minor 6th of the key. In the example above, subV/II in measure 6 is placed on a very weak harmonic stress and is prepared by a related II–7 b5 to clarify its subV7 function.

IV7, V7/ bVII IV7 is usually associated with the I–7 chord. Together they appear to have a relationship, but it is misleading to analyze them using the bracket, since they are not a subdominant/dominant pair.

When used as a diatonic chord in minor, IV7 is a subdominant chord from tonic Dorian, and usually progresses (not resolves) back to I– ; it usually uses a Mixolydian chord scale, (Lydian b7 is an option, especially if the tonic scale is melodic minor).

IV7 is also a perfect fifth above the bVII chord, and sometimes resolves there. A Mixolydian scale is again the appropriate choice:

&

?

b

b

b

b

b

b

4

4

4

4

www

˙ œnœ œ œ

˙

˙

˙˙˙

œ

œ

œœ

˙Aœ œ œ œn

˙

˙

˙

˙

˙b

˙

I–7 IV7 I–7 V7⁄ bVII bVII7

C–7 F7 C–7 F7 B b7

Mixolydian Mixolydian


part 3 Diminished Chord Patterns

Diminished seventh chords in major keys are most often found as passing chords between neighboring diatonic chords, or as approach chords to diatonic chords.

The diminished 7th chord patterns described in this chapter are typical of progressions in major keys; they are almost never found in minor. (VII° 7, built on the 7th degree of the harmonic minor scale, functions as a dominant substitute in minor.) They are most characteristic of music that is fairly complex and often highly chromatic, such as jazz, some contemporary Gospel and classic Broadway tunes; however, they are still used effectively by contemporary pop and rock artists. In contemporary Brazilian songs, diminished chords are used in a wide variety of creative ways. These uses are outside the scope of this book, but are well worth exploring.

All diminished seventh chords contain two tritone intervals. Because of these tritones, diminished chords are extremely unstable, and have a clear tendency or “need” to resolve. Additionally, all diminished seventh chords contain non-diatonic pitches; the ascending and descending diminished seventh chords have roots that are not in the key. In almost all cases, the expected resolution is to a neighboring diatonic chord or an inversion with a diatonic bass note.

The most common patterns for diminished seventh chords are:

# I°7 # I°7 approaching II–7 or passing from Imaj7 to II–7:

&

?

˙ ˙b

˙ ˙

˙ ˙

˙ ˙#

œ.˙

w

ww

Imaj7 # I°7 II–7

Cmaj7 C#°7 D–7

This chord may or may not be a part of the pattern.

4 harmony 3

Diminished Chord Patterns


# II°7 # II°7 approaching III–7 or passing from II–7 to III–7:

&

?

˙ ˙b

˙ ˙#

˙ ˙

˙ ˙#

œ

.˙

w

ww

II–7 # II°7 III–7

D–7 D#°7 E–7

# IV°7 # IV°7 approaching V7 or passing from IVmaj7 to V7:

&

?

˙ ˙b

˙ ˙

˙ ˙

˙ ˙#

œ

.˙

w

ww

IVmaj7 # IV°7 V7

Fmaj7 F#°7 G7

#V°7 #V°7 approaching VI–7 or passing from V7 to VI–7:

&

?

˙ ˙

˙ ˙

˙ ˙

˙ ˙#

œ.˙

w

ww

V7 #V°7 VI–7

G7 G #°7 A–7

bIII°7 bIII°7 approaching II–7 or passing from III–7 to II–7:

&

?

˙ ˙

˙ ˙b

˙ ˙

˙ ˙b

w

w

w

w

III–7 bIII°7 II–7

E–7 Eb°7 D–7


bVI°7 bVI°7 approaching V7 or passing to V7 from VI–7:

&

?

˙ ˙

˙ ˙b

˙ ˙

˙ ˙b

w

w

w

w

VI–7 bVI°7 V7

A–7 A b°7 G7

I°7 I°7 as an auxiliary to the tonic Imaj7. It can be used as a chromatic decoration, or to delay the arrival of the I chord:

&

?

˙ ˙

˙ ˙b

˙ ˙b

˙ ˙

w

w

w

w

Imaj7 I°7 V7

Cmaj7 C°7 Cmaj7

V°7 V°7 as an auxiliary to the dominant V7:

&

?

˙ ˙

˙ ˙b

˙ ˙b

˙ ˙

w

w

w

w

n

V7 V°7 V7

G7 G°7 G7

The diminished chords’ root motions can be used to categorize three dif-ferent types of diminished chords:

n Ascending diminished seventh chords, have root motion up a half-step from non-diatonic to diatonic.

n Descending diminished seventh chords, whave root motion down a half-step from non-diatonic to diatonic.

n Auxiliary diminished seventh chords, have a common root with the tonic or dominant chord.

4 harmony 3

Ascending Diminished Chords


Ascending and descending diminished chords fill the need for smooth voice leading between adjacent diatonic chords a whole-step apart. The auxiliary diminished (I°7 and V°7) have common tone roots with their target chord, and can be thought of as chromatic elaborations of the basic chord.

Ascending Diminished Chords

Ascending diminished seventh chords are derived from the secondary dominants of their target chords and have smooth voice leading charac-teristics.

# I°7 is derived from an inverted V7(b9)/II:

&

?

4

4

4

4

˙

œ œ

˙˙˙˙

˙˙˙˙#

b

˙ ˙#

˙

˙˙œ œ

˙

I V7( b9)⁄II II–7

Cmaj7 A7( b9)⁄ C # D–7

#I°7

( )

# II°7 is derived from an inverted V7(b9)/III:

&

?

4

4

4

4

˙

œ œ

˙˙˙˙

˙˙˙˙#

b

˙ ˙#

˙

˙˙

œ œ

œ œ

˙˙˙˙

##

˙ ˙#

w

w

wwn

w

V7( b9)⁄III III–7

B7( b9)⁄ D# E–7

#II°7

( )


# IV°7 is derived from an inverted V7(b9)/V:

&

?

4

4

4

4

˙

˙˙

˙ ˙

˙

˙˙b

˙ ˙#

w

ww

w

w

IVmaj7 V7( b9)⁄ V V7

Fmaj7 D7( b9)⁄ F# G7

#IV°7

#V°7 is derived from an inverted V7(b9)/VI:

&

?

4

4

4

4

˙

˙˙

˙ ˙

˙

˙˙b

˙ ˙#

˙

˙˙

˙ ˙

˙

˙˙

˙ ˙#

wwww

w

w

V7( b9)⁄VI VI–7

E7( b9)⁄ G # A–7

#V°7

Descending Diminished Chords

Descending diminished seventh chords are not derived from secondary dominant chords, since they do not contain the tritone of the expected resolution chord’s dominant. The following two diminished chords ( bIII°7, bVI°7) are derived from chromatic voice leading.

bIII°7 is expected to resolve to II–7 (but does not contain the tritone of the V7/II chord):

&

?

4

4

4

4

˙œ œ

˙˙˙˙

˙˙˙˙bb

˙ ˙b

˙

˙˙˙˙

˙

III–7 bIII°7 II–7

E–7 Eb°7 D–7

Tritone of A7 is not present.

harmony 3

Auxiliary Diminished Chords


Note that bIII°7 and # II°7 are enharmonically the same chords but the expected resolutions are different; the context in which they appear de-termines the function.

bVI°7 occurs very rarely; its common resolution is to I/5.

&

?

4

4

4

4

˙œ œ

˙˙˙˙

˙˙˙˙bb

˙ ˙b

˙ œ œ

œœœœ

œœœœ

˙˙˙˙

b

œ

œ ˙b

w

w

www

w

bVI°7 I ⁄ V

A b°7 C⁄ G

Tritone of D7 is not present.

Auxiliary Diminished Chords

Tonic and dominant chords of the key may be approached or embellished by their respective auxiliary diminished seventh chords (I°7 and V°7). Like the descending diminished chords, the auxiliary diminished sev-enth chords are derived from chromatic voice leading and not secondary dominant function. They either delay the resolution to the target chord or create harmonic motion over a static bass note.

I°7 is the auxiliary to the tonic I chord (and does not contain the tritone of the V7 chord). V°7 is the auxiliary to the dominant chord (and does not contain the tritone of the V7/V chord)

The auxiliary diminished chords either delay the movement to their target chords (I and V respectively):

(Key of C)

&

?

˙

˙

˙

˙

˙

˙

˙

˙

b

b

œ

˙b œ# ˙˙n

œ#œ ˙

˙ ˙

II–7 subV7 I°7 Imaj7

D–7 D b7 C°7 Cmaj7

Delays the arrival of Imaj7;chromatic approach to 3 and 5


(Key of G)

&

?

#

#

œ œ œ œ œ œ œœ

˙˙˙˙

˙˙˙˙#

b

˙b ˙n

˙˙˙˙

b

nb

˙˙˙˙

n

#n

Imaj7 #IV°7 V°7 V7

Gmaj7 C #°7 D°7 D7

Delays the arrival of V7;chromatic approach to 3, 5 and 7

Or, they provide chromatic motion over a static bass note: (Key of C)

&

?

˙

˙

˙

˙

˙

˙

˙

˙

b

b

œ

œ

œ

œb

œ ˙

˙n

œ

œ

œ

œ

# ˙

˙

II–7 subV7 Imaj7 I°7 Imaj7

D–7 D b7 Cmaj7 C°7 Cmaj7

Elaboration

(Key of G)

&

?

#

#

œ

œ œ œ œb

˙˙˙˙

˙˙˙˙

b

nb

.œN

j

œ œ

œ

wwww

V7 V°7 V7

D7 D°7 D7

Elaboration

Unlike dominant chords, which have a potential for deceptive resolution, diminished seventh chords create an absolute expectation of resolution. It is rare for a diminished seventh chord to move deceptively. However, the ascending and descending diminished chords do have alternate chords of resolution. If an alternate resolution does occur, the chromatic bass mo-tion is still retained.

2 harmony 3

Alternate Resolutions


Alternate Resolutions

# I°7 # I°7 has an expected resolution to II–7. It has an alternate resolution to II–7’s related dominant: the V7 chord with its 5th in the bass:

&

?

œ œ

˙˙˙˙

#b

˙#

w

wwww

w

C #°7 G7⁄ D

Notice that melodic pitch “B” is not available on the normal resolution: II–7.

# II°7 # II°7 has an expected resolution to the tonic III–7 chord. It has an alter-nate resolution to the tonic I chord with its 3rd in the bass:

&

?

œ œ

˙˙˙˙

#b

˙#

w

wwww

w

D #°7 C6 ⁄ E

Notice that melodic pitch “C” is not available on the normal resolution: III–7.

# IV°7 # IV°7 has an expected resolution to the dominant V7 chord. It has an alternate resolution to the tonic I chord with its 5th in the bass:

&

?

œ œ

˙˙˙˙

#b

˙#

w

wwww

w

F#°7 C6 ⁄ E

Notice that melodic pitch “C” is not available on the normal resolution: V7.

#V°7 #V°7 has an expected resolution to VI–7. It has an alternate resolution to the secondary dominant chord built on the same root: V7/II:

&

?

œ œ

˙˙˙˙

#

˙#

w#wwww#

w

G #°7 A7


bIII°7 bIII°7 has an expected resolution to the II–7 chord. It has an alternate resolution to the II–7’s related V7/5th in the bass:

&

?

œ œ

˙˙˙˙

bb

˙b

w

www

w

w

Eb°7 G7⁄ D

Notice that melodic pitch “B” is not available on the normal resolution: II–7.

The auxiliary diminished chords do not have alternative resolutions.

Available Tensions for Diminished Chords

Tension Numbering for Diminished ChordsTension numbering for diminished chords is slightly different than for any other chord quality since there are four possible tensions, not three. Tmaj7 (technically Tb15 in the example below!) is in fact a tension and not a chord tone, since there are four chord tones already present:

&

?

wwœœ

wwww#

b

# I°7

maj7

If the target for any diminished seventh chord is diatonic, the tensions are also diatonic, just as they are for diatonic chords and secondary dom-inants. Using diatonic tensions reaffirms the home key. Diatonic pitches a major ninth above a chord tone are available tensions . The examples below illustrate tensions for the most commonly occurring diminished chords.

4 harmony 3

Available Tensions for Diminished Chords


I°7, # II°7 The available tensions for I°7, # II°7, bIII°7, and # IV°7 in the key of C major are:

&

?

wwœœ

wwww##

# II°7

D#°7maj7 (enharmonic)b13

&

?

œwwœ

wwww#

b

# IV°7

F#°7b1311&

?

wwœœ

wwwwbb

bIII°7

Eb°7maj7b13 (enharmonic)

&

?

wœœw

wwww

bb

I°7

C°7maj7 9

Note that the chord tones and available tensions for the above four di-minished chords are the same (or enharmonically the same). Inverting a diminshed chord does not change its interval structure. Therefore, the same notes are available on each chord, since all four chords are func-tioning in the same key:

&

?

wœœw

wwœœ

wwœœ

œwwœ

wwww

bb

wwwwbb

wwww##

wwww#

b

I°7 bIII°7 # II°7 # IV°7

Enharmonic equivalents (i.e., C°7 = Eb°7, etc.)

#V°7, bVI°7 The available tensions for #V°7 and bVI°7 in the key of C major are:

&

?

wwœœ

wwwwb

bVI°7

A b°7maj7b13 (enharmonic)

&

?

wwœœ

wwww#

#V°7

G #°7maj7 (enharmonic)b13

bIII°7, # IV°7


Note that all the chord tones for the above two diminished chords are the same or enharmonically the same. Therefore, the available tensions are the same, since the chords are identical in structure:

&

?

wwœœ

wwœœ

wwww#

wwwwb

#V°7 bVI°7

G #°7 A b°7

Enharmonic equivalents

# I°7, V°7 The available tensions for # I°7 and V°7 in the key of C major are:

&

?

wwœœ

wwww#

b

# I°7

C #°7

maj7Tb13

&

?

œwwœ

wwww

bb

V°7

G°7119

Note that all the chord tones for the above two diminished chords are the same or enharmonically the same. Once again, the available tensions are the same since the chords are essentially the same and function in the same key:

&

?

wwœœ

œwwœ

wwww#

b

wwww

bb

# I°7 V°7

C#°7 G°7

Enharmonic equivalents

harmony 3

Diminished 7th Chord Scales



As illustrated in the previous section, diminished seventh chords which have diatonic function imply this diatonic orientation with the use of diatonic non-chord tones. The resulting chord scales contain chord tones, diatonic tensions, and diatonic avoid notes (examples are in C major):

&

&

&

&

&

&

&

&

w w wb œnwb œn w w w

w# œ w œ w w wb wn w#

wb œnwb œn w w w w wb

w# œ w# œ w w w wn w#

w# œ w w w w wb wn w#

w w wb w wb œn w œ w

w# œ w œ w w w wn w#

wb œn w œ w w w w wb

T9 Tmaj7

T b13 Tmaj7

T b13 Tmaj7

T b13 Tmaj7

T11 T b13 Tmaj7

T9 T11

T b13 Tmaj7

T b13 Tmaj7

I°7

#I°7

bIII°7

#II°7

#IV°7

V°7

#V°7

bVI°7


Chord Scale Names Unlike previous chord scales, the above diminished scales appear to have no names. However, a comparison with secondary dominant chords re-veals identical chord scales for diminished and altered secondary domi-nant chords.

# I°7 # I°7 is expected to resolve to II–7.

&

w# œ w œ w w wb wn w#

# I°7

b13 maj7

V7( b9)/II has the same function:

& w wb w w

w#

# œ

œ

w

w

w

œ

w

w

w

w wb wn w#

A7( b9)

C #°7

The chord scale for # I°7 can be identified as the same scale as V7( b9)/II starting on the 3rd of the dominant chord. This is the leading-tone of the root of the target chord. (The conditional avoid note occurring for the dominant chord does not occur for the diminished chord since the third of the diminished chord must be used.)

V°7 Since V°7 contains the same chord tones as # I°7, it uses the same scale as V7( b9)/II starting on the root of the V°7:

& w w wb w wb œn w œ w

V°7

9 11

There is an alternate version of the scales for # I°7 and V°7. Between the Bb and C # (or B b and D b) there are actually two diatonic choices: B and C (in the key of C). Using C (as illustrated above) instead of B results in a chord scale that contains one less avoid note:

# II°7 # II°7 is expected to resolve to III–7:

&

w# œ w# œ w w w wn w#

# II°7

T b13 Tmaj7

harmony 3



V7( b9)/III has the same function:

&w w w w

w#

# œ

œ

w

w#

# w

œ

w

w

w

w w wn w#

B7( b9)

D #°7

The chord scale for # II°7 can be identified as the same scale V7(b9)/III starting on the 3rd of the dominant chord. (This is the tone leading to the root of the target chord.) There are two avoid notes.

I°7, bIII°7, # IV°7 Since bIII°7, # IV°7, and I°7 contain the same chord tones as # II°7, their chord scales can be identified as the same scale as V7(b9)/III. Each starts on the respective diminished chord’s root and contains two avoid notes:

&

&

&

w w wb œnwb œn w w w

wb œnwb œn w w w wn wb

w# œ w w w w wb œn w#

I°7

9 maj7

bIII°7

# IV°7

b13 maj7

11 b13

There is also an alternate version of the scale for each of these chords. Be-tween the D # and F # (E b and G b ) there are actually two diatonic choices: E and F (in the key of C). Replacing E with F results in a chord scale that is still diatonic, but contains one less avoid note. Either choice is accept-able.

#V°7 #V°7 is expected to resolve to VI–7. The chord scale for #V°7 can be iden-tified as the same scale as V7( b9)/VI starting on the 3rd of the dominant chord. (This is the tone leading to the root of the target chord.) As in the previous diminished scales, there are two avoid notes.

& w# œ w œ w w w wn w#

#V°7

b13 maj7


V7( b9)/VI has the same function:

&w w w w

w#

# œ

œ

w

w

w

œ

w

w

w

w w wn w#

E7( b9)

G #°7

bVI°7 Since bVI°7 is enharmonically identical to #V°7, its chord scale is also the same scale as V7( b9)/VI, starting on the root of the diminished chord and containing two avoid notes:

& wb œn w œ w w w w wbbVI°7

b13 maj7

Symmetric Diminished

Tensions for diminished seventh chords can be characterized as either diatonic for a diatonic situation or non-diatonic for a non-diatonic situa-tion.

Using tensions that are a whole-step above each chord tone results in T9, T11, T b13 and Tmaj7. If an extended structure is created with all these tensions available, the result will not be diatonic to any key:

&

wwwwwwww#

#

n

#

b

# I°7

C #°7maj7b13119

If the above chord’s tensions are displaced an octave lower between each chord tone, a symmetric diminished scale is created. It is not a mode of any major or minor scale. This scale is composed of alternating whole steps and half-steps:

&

?

wwww#

n

#

wwww#

b

w# w# w w# w w w wn w#

C #°7

Whole- and half-steps: 1 ½ 1 ½ 1 ½ 1 ½

harmony 3

Symmetric Diminished

part 4 Modulation Considerations 1

In the “whole-half” symmetric diminished scale all non-chord tones are available tensions (a whole-step above each chord tone):

&

w# w# w w# w w wb w wb

1 T9 b3 T11 b5 T b13 °7 Tmaj7 1

Even though the symmetric diminished scale has no diatonic function (since its tensions are not all diatonic), it can still be used creatively, espe-cially on I°7 and bIII°7.

Summary of Diminished Chord Scales

n The chord scales for all the ascending diminished 7th chords are de-rived from the secondary dominant chord scales of the target chords for the ascending diminished 7ths:

V7( b9)/II = # I°7 to II–7V7( b9)/III = # II°7 to III–7V7( b9)/V = # IV°7 to V7V7( b9)/VI = #V°7 to VI–7

n The descending and auxiliary diminished chords use the same chord scales as their enharmonic equivalents.

bIII°7 = # II°7bVI°7 = #V°7I°7 = # II°7V°7 = # I°7

n There are optional scales for all diminished chords except #V°7 and bVI°7. The optional scales use other diatonic tensions.

n Diminished chords which are NOT functioning in a diatonic situation use a symmetric diminished scale (alternating whole-step – half-step).

n The symmetric dominant scale (alternating half-step – whole-step, also known as a combination dominant scale) is used for dominant functioning chords, not for diminished 7th chords (see page 8).


part 4 Modulation Considerations

Modulation is the movement of melodies and/or harmonies from one key into another. Modulations may be implied or actual. When a modula-tion actually takes place, the listener’s focus will switch from the original tonic reference to the new tonic reference.

&b4

4 œ œ œ ˙ œ œ œ œ œœœ œ œ œ ˙ .œ

j

œ œ œœœ

&b.˙ œ .˙ œ .œ

j

œ œœ ˙ ˙#

&bœœ œ ˙ œ œ œ œb œ

œœ œ œ œ ˙ .œ

J

œ œ œœbœ

&b

.˙

œ

.˙ œ w w

Fmaj7 A b7 G–7 C7 D– D–7⁄ C B–7(b5) B b–6

V7⁄IV Imaj7

V7⁄III A–7 D7(b9) G–7 C7 Fmaj7 F+7

Imaj7

B bmaj7 D b7 C–7 F7 G– G–7⁄ F E–7(b5) Eb–6

subV7⁄II

Imaj7 bVII7 II–7 V7 Imaj7

B bmaj7 A b7 G–7 C7 Fmaj7

( )

( )

The above 16 measure tune contains a modulation from F major into B b major and returns to F major. B b major is the secondary key and F major is the primary key. Notice that the phrase in B b may stand alone:

&b4

4 ˙# œœ œ ˙ œ œ œ œb œ œ œ

&bœ œ œ ˙ .œ

J

œ œ œœbœ

.˙

F+7 B bmaj7 D b7 C–7 F7

G– G–7⁄ F E–7(b5) Eb–6 B bmaj7

2 harmony 3

Modulation Considerations


Parenthetical Analysis Modulation indicators (a small arrow and interval number) are not nec-essary, but are sometimes added to the analysis to clearly show the rela-tionship between the two keys. Dominant chords that resolve deceptively into a new key are placed in parentheses. Dual Roman numeral analysis shows their dual function. The old function (secondary dominant) is parenthesized; the new function (primary dominant of the new key) is placed below it.

Accidental Usage When modulations occur within tunes, it is common practice to use accidentals as opposed to changing key signatures. The fewer accidentals necessary in a modulation, the more closely the keys are related and the more subtle the modulation. In the previous example, the modulation from F to Bb only requires one additional accidental. Modulations to distantly related keys are more obvious.

Retrospective Hearing Most listeners are conditioned to expect the primary key’s return after a modulation. The experienced musician has a musical memory which allows for hearing in retrospect. For example, everyone can remember the previous chord while hearing the chord being played; some musicians can remember back to the original key and have the expectation for its return.

& 4

4 œœœ ≈ œ

œb œ œ œœœ œ œ .˙b

œœœ ≈ œ

œb œ œœ

œ w

&

œbœbœ≈ œ

œb œ œb œœœ œb œb

.˙b

œbœbœ≈ œ

œb œ œœ

œb w

C7 F7 C7 F7

D b7 G b7 D b7 G b7

The modulation in the example above is up a half-step from C major into D b major. This particular modulation, although sometimes used in the actual structure of a song, is a device more commonly used by arrang-ers, since these keys are harmonically quite distant. The use of chromatic modulations upward tends to keep the music moving forward and builds excitement.

In a song structure (from verse to chorus for example), it is much more common to modulate to a closely related key, or the relative major or minor. Movement between relative major and minor is particularly com-mon in contemporary rock tunes, but has long been a feature in popular songs; Irving Berlin’s “Blue Skies” and Hoagy Carmichael’s “Georgia” are two prominent examples.


Most modulations in songs are perceived as occurring in an upward di-rection, although downward modulation (for example to the key of bVI) allows for strong upward movement on the return to the original key. There is no formula for using modulation effectively in a composition or arrangement. What follows is an examination of some of the mechanisms by which songs modulate.

Implied Modulations Implied modulations trick the listener into believing that a new key is about to be established. The following example contains an implied modulation up a half-step into G b :

&b4

4 .. Œ

œ ˙ œ œ œ.œ

J

œ w œœ œ

.œ

j

œ

&b

œ .˙ œ œ œ.œ

j

œw .˙ œ

&b .

..œJ

œ œ œb œb œ .œ

j

œb˙

.œ

j

œ.œb

J

œw

Imaj7

Fmaj7 A b7 G–7 C7 A–7 A b°7 G–7 C7

Imaj7

A–7 D7 G7 C7(sus4) F°7 Fmaj7

bIImaj7 IV–7 bVII7 III–7 V7⁄II V7

G bmaj7 B b–7 Eb7 A–7 D7(alt) G7 C7( )

Brief passages like measure 9–10 above don’t constitute a true modula-tion, but instead a short series of modal interchange chords that resemble diatonic activity in G b major. The analysis shows their audible relation-ship to the primary key.

Several factors go into establishing a modulation, but an important one is often a confirming cadence : the re-occurrence of the new tonic, reinforced by a V7 or II–7 V7. Duration of the new tonality also helps to reinforce its importance to the listener. The following example is a modification of the previous one, now containing a confirming cadence in measure 11–12, and longer duration in the new key.

4 harmony 3

Modulation Considerations


&b4

4Œ œ ˙ œ œ œ

.œ

J

œ w œœ œ

.œ

j

œ

&b

œ .˙ œ œ œ.œ

j

œw .˙ œ

&b

.œJ

œ œ œb œb œ .œ

j

œb˙

.œb

j

œb

.œ

j

œw

&b .

..œbJ

œb œbœ œb œ .˙b œb œ œb œb

œb ˙œ œ

œ œœ

A–7 D7 G7 C7(sus4) F°7 Fmaj7

G bmaj7 B b–7 Eb7 A b–7 D b7 G b°7 G bmaj7

C bmaj7 B b–7 A b–7 D b7sus4 D b7 C7sus4 C7

Latin, q=120

Fmaj7 A b7 G–7 C7 A–7 A b°7 G–7 C7

Establishing a Modulation Establishment of a modulation is not solely dependent on the use of the tonic chord of the new key after a modulation has occurred. The modu-lation can clearly occur despite the lack of a I chord, especially in music where the modulation is sequential or melody-driven.

&

#

4

4Œ

œ œœ œœ

3

w œb œn œ .œ

J

œ œ.˙

&

#œb œb œ

.œ

J

œb w œ œ# œ.œ#

j

œ# œ#

D7 Gmaj7 G7 C–7 F7 C–7 F7

B b–7 Eb7 G b7 F7 C # –7 F#7 Bmaj7

G major B b major

Ab major Bmajor

Open Key Signatures When tunes or arrangements have multiple secondary keys, the writer may choose to use an open key signature, where there is no stated key signature and all the accidentals are written into the music.

Melody Forced Modulation Shifting melodies into a new tonality will force a modulation. This is a very common way of creating variety while repeating melodic fragments.


Direct Modulation

Direct From I Modulations may occur directly from any diatonic chord. The most common form of direct modulation is from the I chord, since the I chord establishes a point of tonal finality.

&b4

4 œ œ œ˙ œ œ œ œ œ

œ

œ œœ

˙ w

&b œb œb œ

˙ œ œb œb œ œœ

œb œb œ˙b .˙ œb œ

Imaj7 V7 Imaj7

Fmaj7 G–7 A–7 D7 G–7 C7 Fmaj7

Imaj7 V7 Imaj7 D bmaj7 Eb–7 F–7 B b7 Eb–7 A b7 D bmaj7

When the harmony modulates, the melody may or may not modulate. As seen above, however, when the melody modulates the harmonies must modulate. This modulation is strengthened by transposing both the melody and the harmony to the new key.

In addition to melody, it is important to consider harmonic rhythm, phrasing, and form when understanding modulation. In the following example there are two four-bar phrases and the melody is a sequence with slight variation.

&b

b

4

4 ..

œ œ œ ˙ œ œ œ œ œœ w .˙ œ

&b

b..

œb œ œ ˙ œ œb œb œ œ œwb .˙

Œ

Imaj7 III–7 II–7 Imaj7 II–7

B bmaj7 D b7 C–7 F7 D–7 C–7 B bmaj7 C–7

Imaj7 (bIIImaj7) III–7 II–7 Imaj7 D bmaj7 Fb7 Eb–7 A b7 F–7 Eb–7 D bmaj7

Direct from Other The passage above is usually heard as a direct modulation from the II–7 chord, although the new Imaj7 (D bmaj7) in bar 5 relates to the old key as bIIImaj7.

Direct modulations from diatonic chords other than I usually involve stepwise root motion.

Diatonic Chords

harmony 3

Direct Modulation


Melodically Forced Modulation The melody may force a modulation. In the following example, the melody is transposed to the new key a tritone higher; the chords are transposed by the same interval. (In this case, the dominant chord is not functional in the new key, the sequential melody drives the modulation):

&b

b

4

4#

#

#

#˙ ˙ ˙ ˙

&

#

#

#

#˙ ˙ ˙ ˙

II–7 V7

C–7 G7(b9) C–7 F7

II–7 V7

F#–7 C #7(b9) F# –7 B7

1.

Direct From V7 Direct modulations from the V7 chord, as in the examples above and below, are frequently used as a device to extend phrases and/or heighten the forward motion of the music. Direct modulations utilizing the II–V’s of first the original key, then of the new key are relatively common:

&

?

b

b

4

4

4

4

b

b

b

b

b

b

b

b

˙.œ

J

œ

˙˙

˙

.

.

.

œœ

œ

j

œœ

œ

œ œœ œ œ

œ

w

.

.

.

œœ

œ

j

œœ

œ

œœ

œ

œ

œ

œ

œ

œ

œ

b

b

œ

œb œ œ

œ œœ

w

.

.œ

œ

j

œ

œ

˙

˙

œ œ

œ ˙

bII–7 V7 II–7 V7 II–7 V7

G–7 C7 G–7 C7 B b–7 Eb72.

Both modulations above represent non-functional use of the V7 chord. The controlling factor is the modulation itself, driven by either the melody or the key relationship. The progression follows the direction of the modulation: up a tritone in the former situation when melody moves up a half-step from the F to the F # (ex.1); up a minor third in the latter situation, where the melody does not move but the chords move with the modulation (ex.2).


Pivot Chord Modulation

Pivot Chords Chords which function in both the original/primary key and in the new/secondary key are pivot chords. Their dual functions are indicated by two analysis symbols; one showing initial function, and one indicating the function in the new key:

&b C ..

œœœ œ œ œ w œ œ œ œ œ œ œ

œ œ ˙

&b œ œ œ œ œb œ w œ œb œ œ œ œb œ œ ˙

&b

œ# œ# œ œœ# œ# w œ# œ# œ

‰ œn

j

œ w

&b .

.œ# œ# œ‰ œ

J

œn œœ#œn ‰ œ#

J

œ ˙

.œ#

j

œ# w

(II–7 I–7) Imaj7 II–7 Imaj7 III–7 II–7 Fmaj7 G–7 Fmaj7 G–7 F–7

Imaj7 II–7 VI–7 subV7⁄V

Ebmaj7 F–7 C–7 B7

( bIImaj7) Imaj7 VI–7 Imaj7 VI–7

Emaj7 C # –7 Emaj7 C # –7

II–7 III–7 IVmaj7 Imaj7

F# –7 G # –7 Amaj7 Emaj7

Samba, h =90

( )

Pivot Function Possibilities The pivot chord in the 4th measure is analyzed first in the original key then in the new key as a dual function. In the case of G–7, in F major it is II–7. (Other dual possibilities for G–7 are: in E b major it is III–7; VI–7 in B b major; IV–7 in D major; V–7 in C major.)

The B7 in measure 8 also represents a pivot function. It initially sounds like subV7/V in E b major, but actually resolves to the new tonic of E major.

After the repeat, the Fmaj7 in measure 1 will initially sound like bIImaj7 in E; then as the tune progresses, the original key is re-established.

harmony 3

Pivot Chord Modulation


Chord Scales for Pivot Chords The most basic choice of chord scale for a pivot chord is based on the chord’s function in the original key. The chord scales for the analysis of the previous example are:

&b C ..

&b

&b

&b .

.

2nd X: (bIImaj7) (II–7 I–7) Imaj7 II–7 Imaj7 III–7 II–7 Fmaj7 G–7 Fmaj7 G–7 F–7

( bIImaj7) Imaj7 VI–7 Imaj7 VI–7 Emaj7 C # –7 Emaj7 C # –7

II–7 III–7 IVmaj7 Imaj7 F# –7 G # –7 Amaj7 Emaj7

Ionian IonianDorian Dorian Dorian

Ionian Dorian Aeolian Lydian b7

Ionian Aeolian Ionian Aeolian

Dorian Phrygian Lydian Ionian

Imaj7 II–7 VI–7 subV7⁄V

Ebmaj7 F–7 C–7 B7( )

Alternate Chord Scales Alternate chord scale possibilities are generated from the dual analysis symbols. The parentheses around pivot chords indicate that their per-ceived function changes as the music progresses. Initially, a chord has a clear function in one key, but it’s alternate function is exploited to create the modulation.

A player or writer can manipulate the listener’s expectation through the choice of chord scale. Using the chord scale of the original function cre-ates more surprise by withholding notes from the new key until the last moment. Using a scale that reflects the chord’s function in the new key will prepare the listener for it’s arrival, lessening the surprise.

In the example above, a perfectly acceptable alternate chord scale for the Emaj7 in measure 9 would be E Lydian, reflecting it’s momentary sound as bIImaj7 in the old key of E b (measures 5–8). There is nothing in the melody that specifically requires an Ionian scale; using Lydian would prolong the sense that the piece is still in E b .

Conversely, if the intent were to prepare the listener more clearly for the arrival of E major, a B Mixolydian scale in measure 8 would help to do so. This would require an adjustment in the melody, a creative choice that would have to be balanced with all the composer’s intentions.


Chromatic Approach Chords Another mechanism to create a modulation is the use of chromatic ap-proach chords. The approach chord(s) and the target chord must have the same quality, e.g. minor 7; any other diatonic function that the approach chord has (such as a substitute dominant function) is most often stronger than the chromatic function.

Chromatic approach chords are analyzed using a scale degree indicator to show their relationship to the key. In the example below, Emaj7, Fmaj7 and G bmaj7 are approach chords to the new tonic chord of Gmaj7. The chord scale for chromatic approach chords is generally the same as the scale for the target chord.

&b

b

b 4

4

.œ

j

œ

j

œ œ

j

œ w

.œ

j

œ

j

œ œ

j

œ w

&b

b

b

.œ

j

œœœœ œ

j

œ œœ œn

J

œ .œ

j

œA .œ

j

œ .œ

j

œ ˙

&b

b

b.œ#

j

œœn

œœ .˙

œ .œ

j

œn ˙

Œ . j

œn œ

œn

Imaj7 VI–7 Ebmaj7 C–7

II–7 V7 (I) F–7 B b7 Ebmaj7 Emaj7 Fmaj7 G bmaj7

Imaj7 VI–7 II–7 bVIImaj7 Gmaj7 E–7 A–7 Fmaj7

chromatic

Medium bossa

harmony 3

Dominant Chord Modulation



Modulations from dominant chords, like other pivot chord modulations, may exhibit dual function (deceptive resolution and actual resolution). A dominant chord functioning in a key may resolve deceptively to any new key. The root motion from a dominant 7th will usually be either down a perfect fifth, down a half-step or up a step, although root motion from any of the standard deceptive resolutions is possible.

The following examples show modulations based on root motion of standard deceptive resolutions of the primary dominant in the key of C major.

Deceptive Resolution From V7 Down a half-step: (V7) has a subV7 relationship to new key:

&

?

4

4

4

4

b

b

b

b

b

b

b

b

b

b

b

b

w

ww

b

w

wb

b

˙

˙˙

˙

˙˙

˙

˙

˙

˙

w

ww

w

w

(V7)

subV7⁄V V7sus4 subV7 Imaj7 A b7( #11) G7sus4 G7(9) G bmaj7

Down a tritone: (V7/I) to bIImaj7 as a new Imaj7:

&

?

4

4

4

4

b

b

b

b

b

b

b

b

b

b

wwb

w

w

wb

b

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

w

w

w

w

w

(bIImaj7)

subV7⁄V V7sus4 (V7) Imaj7 A b7( #11) G7sus4 G7(9) D bmaj7

Down a major third: (V7/I) to bIIImaj7 as a new Imaj7:

&

?

4

4

4

4

b

b

b

b

b

b

wwb

w

w

wb

b

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

w

w

ww

w

(bIIImaj7)

subV7⁄V V7sus4 (V7) Imaj7 A b7( #11) G7sus4 G7(9) E bmaj7


Up a half-step: (V7) to bVImaj7 as a new Imaj7:

&

?

4

4

4

4

b

b

b

b

b

b

b

b

wwb

w

w

wb

b

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

ww

w

w

w

(bVImaj7)

subV7⁄V V7sus4 (V7) Imaj7 A b7( #11) G7sus4 G7(9) A bmaj7

Direct modulation (not a standard deceptive resolution) up a whole-step: V7/I has a bVII7 relationship to the new key:

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(V7)

subV7⁄V V7sus4 bVII7 Imaj7 A b7( #11) G7sus4 G7(9) Amaj7

Deceptive Resolution From In the following five examples, the secondary dominants in the key of D resolve deceptively. As pivot chords they have an actual resolution to a new key. In each case the dominant chord resolves down a perfect fifth to the expected root but unexpected quality.

(V7/II) has a V7 relationship to new key:

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V7⁄II

Imaj7 IVmaj7 bVIImaj7 V7 Dmaj7 Gmaj7 Cmaj7 B7

( )

Imaj7 VI–7 IVmaj7 V7 Imaj7

Emaj7 C# –7 Amaj7 B7 Emaj7

Secondary Dominants

2 harmony 3



(V7/III) has a V7 relationship to new key:

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V7⁄III

Imaj7 II–7 III–7 VII–7 b5 V7( )

Imaj7 VI–7 IVmaj7 V7 Imaj7

(V7/IV) has a V7 relationship to the new key. (Since this is very closely related to the original key, it may not initially sound like a modulation. Duration, melody activity and a confirming cadence would help to more clearly establish the new key.)

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Imaj7 III–7 IVmaj7 V7⁄V V7 II–7 V7

( )

Imaj7 III–7 V7sus4 V7 Imaj7


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VI–7

V7⁄V

I IV I V7

Imaj7 IVmaj7 V7sus4 V7 Imaj7

( )

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Imaj7 IVmaj7 bIIImaj7 bIImaj7 Imaj7 F #maj7 Bmaj7 Amaj7 Gmaj7 F #maj7

V7sus4 V7⁄VI

I IVmaj7 VI–7

V7

A Dmaj7 B–7 C#7sus4 C#7

( )

4 harmony 3

Transitional Modulation


Transitional Modulation

Passages containing several consecutive extended dominants, extended substitute dominants (with or without related II–7 chords), or many modal interchange chords may eventually result in a modulation. This technique of using familiar functional relationships to momentarily ob-scure the tonality is called transitional modulation .

With the many non-diatonic chords involved, transitional modulations result in the listener temporarily losing a clear sense of tonality. The composer or arranger controls the transition to the new key, usually over a span of several measures. The new key only becomes clear at the end of the transitional area.

There is no single rule for creating a transitional modulation; it typically relies on deceptive resolutions of dominant chords, extended dominants and/or familiar diatonic patterns. Factors that make a transitional modu-lation coherent and effective include:

n melodic sequence or repetitionn common tones in the chordsn common tones in the melodyn pattern-driven bass linesn familiar diatonic chord patterns

Transitional modulations are unusual as part of a composition; they are much more commonly used as an arranging device. Stevie Wonder em-ploys this idea very effectively in his tune “Lately.”

The example below uses deceptive subV7 motion in the original key (measure 5), substantial modal interchange in the transitional key of B b (measure 6–8), then finally G bmaj7 functions as a pivot chord ( bIImaj7) to the final key of F major:

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Gmaj7 Cmaj7 B–7 E–7 A–7 D7sus4 D7

Cmaj7 B7 B bmaj7 C–7 D–7 Eb–7 F–7 G bmaj7

Fmaj7 B bmaj7 C7sus4 C7 Fmaj7


The same example could easily modulate to a different key with very little change. The final modulation is now to E b major, prepared by the F–7 B b7 in measure 8:

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Cmaj7 B7 B bmaj7 C–7 D–7 Eb–7 F–7 B b7

Ebmaj7 A bmaj7 B b7sus4 B b7 Ebmaj7

Since dominant chords have many potential resolutions, transitional modulations may result in movement to almost any key. Here is the same example again, with the B b7 in measure 8 resolving up a whole-step, as bVII7 often does:

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Cmaj7 B7 B bmaj7 C–7 D–7 Eb–7 F–7 B b7

Cmaj7 Fmaj7 G7sus4 G7 Cmaj7

76 harmony 3

Conclusion

This is the end of Harmony 3. Harmony 4 will extend the application of the important concepts presented in this volume. In addition, modal har-mony and specialized topics will be explored. All these concepts can and should be used to expand your musical horizons, regardless of the style in which you work. Listen, write, and play; the joy is in discovering your voice through application of new ideas.

by barrie nettles - harmonyandimprov.com · transitional period in berklee’s history. ... a...

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