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© 2017 Tom Healy A Few Harmonic Substitutions for Jazz Guitar of 55

An Outline of a Few Harmonic Substitutions for Jazz Guitar

A paper on using the Cycle of 4th/5ths as an informative guide

IMPORTANT NOTE: You can explore any one of the substitution techniques outlined in this

paper in great depth. The purpose of this paper is to provide a basic outline of some harmonic

substitution techniques for jazz guitar using the cycle of 4ths/5ths as a guide. Content in this paper

comes from many excellent jazz guitarists’ in-person masterclasses, lessons, and writings. I reference

those jazz guitarists in this paper.

This paper assumes an intermediate understanding of music theory; such as a general knowledge of

intervals, enharmonic equivalents, chord spelling, and other related harmonic concepts. There are

many books on the subject of jazz music theory; one excellent example is The Jazz Theory Book by

Mark Levine. In addition, see the Glossary in the Appendix of this paper for some brief definitions

of terms.

Table of Contents

“Quick Guide” ............................................................................................................................................... 2

“Quick Guide” (continued) ............................................................................................................................ 3

Introduction .................................................................................................................................................. 4

Extensions, Alterations, and Inversions – In Brief......................................................................................... 9

Cadences ..................................................................................................................................................... 12

Diatonic Substitution .................................................................................................................................. 14

Companion Minor and “Back-cycling” ........................................................................................................ 16

Tritone Subs ................................................................................................................................................ 18

“Transformation” of Diminished Chords .................................................................................................... 19

Dom7b9 Chords .......................................................................................................................................... 21

“Transformation” of Augmented Triads ..................................................................................................... 22

Whole Tone ................................................................................................................................................. 23

Minor Harmony ........................................................................................................................................... 24

Natural Minor.......................................................................................................................................... 24

Harmonic Minor ...................................................................................................................................... 24

Melodic Minor......................................................................................................................................... 25

Minor Harmony Compared ......................................................................................................................... 27

Some General Summary Thoughts on Chord Substitution ......................................................................... 29

Appendix ..................................................................................................................................................... 30

Appendix A: The cycle of Fourths / Fifths major key centers and minor key centers: ........................... 31

Appendix B: Constructing Chords on the Guitar Fretboard .................................................................... 32

Appendix C: Glossary .............................................................................................................................. 46


“Quick Guide”

The basic harmonic ideas in this paper are as follows. See the body of this paper for a discussion of the ideas.

Color Extensions and Alterations

Play the chord changes as written, but extend or alter the chords.

Inversions Use an Inversion of the written chord.

Cadences There are common chord “cadences” that appear in many jazz tunes. Apply variations and substitution principles to these cadences.

Diatonic Substitution

Substitute the written chord changes with chords from the same diatonic key center.

Cyclical Movement in 4ths

Use the cycle of fourths/fifths to find new chord changes to substitute for the written chord changes.

Tritone Substitution

Use tritone substitution to create new root movement and substitute for the written chord changes.

Transforming Diminished and Augmented

Understand the underlying theory of chord transformation of diminished chords and augmented triads to access a palette of harmonic substitution possibilities.

Whole Tone Use whole tone harmony to substitute the written chord with a chord from the same whole tone family.

Natural Minor, Harmonic Minor, Melodic Minor

Derive and “borrow” chords from minor scales – i.e., natural minor, harmonic minor, and melodic minor.

Combine any of the above techniques.

More “quick guide” ideas follow on the next page.


“Quick Guide” (continued)

Trust your ear. Create strong bass movement and internal voice leading. The late, great Howard

Morgen said, “Find a line within the harmony and keep it going for as long as you can.”

The following are some ideas for chordal enrichment and substitution:

1. Use the same chord as written, but with: a. Extensions b. Alterations c. Inversions d. Change the “quality” of the chord type (major <-> minor <-> dominant) e. CESH (Contrapuntal Elaboration of Static Harmony)

2. Use a Substitution Chord to create strong root movement. a. Cycle of 4ths/5ths (back-cycle) b. ½ steps (tritone substitution, chromatics) c. Minor 3rds (dominant altered, diminished for dominant, half diminished) d. Whole steps (diatonic movement, 7#5 in whole steps) e. Diatonic substitutions

i. From the Major Scale ii. From the Melodic Minor Scale iii. from the Harmonic Scale

3. Use Any Chord. a. Trust your ear b. Use the melody line as the chord color extension c. Use shared common tones d. Quartal harmony e. Modal interchange f. Parallel chord movement


Introduction Music is a rich and multifaceted art form. Musicians combine sound to produce interesting form,

melody, harmony, and expression of emotion. This paper focuses on some examples of using the

cycle of 4ths/5ths as a guide to the progression of the roots of chords and possibilities for chord

substitutions. There are three basic ways to use the cycle; for example:

The “starting point” of the chord sequence. o Consider a substitution for the staring chord for a sequence of chords.

The “direction and flow” of the chord sequence. o Use the cycle as a ‘steering mechanism’ guide for the flow of the chords from

one to the next.

The “arrival point” of the chord sequence. o Consider a substitution for the arrival point of the chord sequence (i.e. a

‘resolution.’) Note: There are many sources elsewhere to learn much more about the cycle of 4ths/5ths. A short

working definition is – “The circle, or cycle, of 4ths/5ths, is a relationship among the 12 tones of

the chromatic scale, their corresponding key signatures, and the associated major and minor keys.”

View the cycle as a geometrical representation of relationships amongst the 12 pitch classes of the

chromatic scale. (See the Appendix for a graphic representation of the cycle of 4ths/5ths from the perspective of key

signatures, and major and minor keys. The terms “circle” or “cycle” are used interchangeably in this paper. However,

since this paper focuses on chord progressions, the term “cycle” is used most often.)

By no means does this paper purport to be a comprehensive representation of all harmonic (chord)

progressions. The examples are primarily given in Major keys. There is also a section regarding

harmony of the natural minor, melodic minor, and harmonic minor scales.

There are a vast number of harmonic variations and permutations. Let your ear by your guide. The

goal is exploration, creativity, and “play” in all meanings of that word. In addition, music is not

comprised of just “notes” and “rules,” it is equally, or even more important to play with dynamics,

time, feel, tone, phrasing, space, articulation, rhythm, creativity, and all other tools of musical

expression.

(Note: the construction of chords on the guitar fretboard is a vast subject. You can take a lifetime to

explore all the possibilities. Ted Greene was a master. See his books. Other recommendations

include instruction from people such as George Van Eps, Eddie Lang, and Howard Morgen.

The Appendix, “Constructing Chords on the Guitar Fretboard,” presents introductory instructional

material.)


The importance and power of the cycle in 4ths and 5ths in jazz is tremendous! Ted Greene said -- “One of the most (if not the most) important patterns or progressions in the history of music is the Cycle (circle) of 4ths (also called the Cycle (circle) of 5ths). Chunks or portions of this cycle dominate the flow of most chord progressions.”

Regarding the statement, “…chunks or portions of this cycle dominate the flow of most chord progressions.” The following are only a couple of examples diagraming the root movement of chords on the cycle of 4ths/5ths. The examples come from a few bars of common tunes: All The Things You Are |Fm7 | Bbm7 | Eb7 | Ab maj7 |

| Db maj7 | G7 | C maj7 | |


Fly Me to the Moon | Am7 | Dm7 | G7 | C maj7 C7 | | F maj7 | Bm7b5 | E7 | Am A7 |

Autumn Leaves | Am7 | Dm7 | G maj7 | | | F#m7b5 | B7b9 | Em | |

The Beauty of the Number 12 12 hours on the face of a clock. 12 inches in a foot. 12 months of the year. Organizing things by 12 is very useful – the number 12 is evenly divided by 2, 3, 4, and 6. (The number 10 is only evenly divided by 2 and 5.) So, why does this matter in any way to a Jazz Guitarist? There are 12 “pitch classes” available, regardless of what they are labeled (i.e., enharmonic equivalents). The sound of each of these is what is important.

(only a count; not a designation)

The Note; and

enharmonic

Other Enharmonic Equivalents (x = double sharp) (bb = double flat)

1 C B#, Dbb

2 C#, Db Bx

3 D Cx, Ebb

4 D#, Eb Fbb

5 E Dx, Fb

6 F E#, Gbb

7 F#, Gb Ex

8 G Fx, Abb

9 G#, Ab

10 A Gx, Bbb

11 A#, Bb Cbb

12 B Ax, Cb


This paper explores the mathematical nature of the cycle of 4ths/5ths from the perspective of chord substitutions and transformations. The following diagrams show equal divisions of the cycle of 4ths/5ths. See the body of this paper for further discussion regarding the applications for chord substitution.

12 divided by 2 yields 6 Tritones: (A tritone is a musical interval that spans three whole tones. The tritone divides the octave into two equal parts.)

12 divided by 3 yields 4 augmented triads:


12 divided by 4 yields 3 diminished chords:

12 divided by 6 yields 2 Whole Tone families:

You can combine any of the harmonic substitutions techniques in this paper. Creating strong root movement is a worthwhile goal of substitution; examples include:

Perfect 4th cycles

Chromatics; half-step from above or below

Diatonic root movement from the key center (whole steps and half steps in the key center)

Tritone substitutions

Movement in minor thirds Explore and play all of the choices then decide what you like. You may think “there is a lot to explore and there are many variations” – you are correct. Even though this paper started with the topic sentence: “Music is a rich and multifaceted art form,” you are not obligated to use every crayon in the coloring box. Sometimes substituting a single chord completely transforms the tune and creates a new color. Use your ear; it is your best guide.


A “whole brain” approach to creating art. Use your whole brain – both logic and intuition. This paper considers the mathematical nature of the cycle of 4ths/5ths. But, in addition, the paper attempts to consider the subject as a means toward the end of creating music and “playing” in all sense of that word.

Left Brain Hemisphere

Right Brain Hemisphere

Logical, organized, analytical, rational, symbolic, mathematical

Holistic, non-rational, emotional, intuitive, spatial, creative

Cycle of 4th/5ths as an organizational paradigm. Mathematical relationship of harmonic movement. Symbolic use of chord qualities; nomenclature. Substitutional principles based on the underlying music theory.

Trust the ear when applying the tools. Music is more than just the notes; i.e. dynamics, articulation, feel, space, etc. Application of imagination and personal taste.

Extensions, Alterations, and Inversions – In Brief

A short definition:

Extended chords come from the key center; i.e., enharmonically are: o 2nd / 9th o 4th / 11th o 6th / 13th.

Alterations; add a sharp or flat to the 5th, 9th, 11th, or 13th.

Inversions; a chord's inversion describes the relationship of its bass to the other tones in the chord.

One core jazz guitar technique is to use different color tones (extensions and alterations) for the

written chord progressions. Joe Pass frequently talked about simplifying chords into three main

types – major, minor, dominant.


A simplified point of view is:

1. Minor (a ‘traveling’ chord used between a tension and a release. However, this is not a fixed rule, because in “diatonic substitution,” a minor chord can also function as a ‘release.’)

2. Dominant function (most often, a ‘tension’ moving to a ‘release;’ but dominant chords are

sometimes ‘static.’). a. Diminished and augmented (can be similar to a dominant tension function).

3. Major (a ‘landing point’ – in other words, the ‘release’).

The very common chord sequence, ii – V7 – I, is an example of the three types: minor, dominant,

major.

Apply the use of extensions and alterations to any of the chords in the progression, or in chords

found with substitution principles. Some common color tones follow (but, use your ear and use

your taste according to the melody, moving lines, and applications of the chord substitution

principles described in this paper).

The 9th (enharmonically, the 2nd) Used on major, minor, or dominant chords.

The 11th (enharmonically, the 4th) Commonly added to chords that have a b3. In major chords, the 3rd is often omitted if the 11th is used.

The #11 (enharmonically, the #4, or b5) The #11 is added to many 7th chords that have a major 3rd. When #11 is used in major, it is often thought of as a “Lydian” sound.

The 13th (enharmonically, the 6th) Most commonly added to major and dominant chords. Less commonly used on minor chords.

b9 and #9 Used in different ways on dominant 7th chords.

“Alt” – all of the alterations; b9, #9, b5 (#11); and #5 (b13).

Used on dominant chords.

This is one example; if the chord progression is written: Dm G7 C Substitute with: Dm9 G7#9 C Major 6 There are many other variations of this extension and alteration method. A table of possible extensions and alterations follows.


An extension and alteration summary:

R b9 9 b3

#9

3 4/11 b5

#4

#11

5 #5

b13

6

13

b7 7

Major

R 9 3 11 #11 5 b13 6 /13 7

Minor

R b9 9 b3 11 (b5) (half diminished)

5 13 b7 7 (min-maj7)

Dom 7 R b9 9 #9 3 (sus) b5/#11 5 #5 13 b7

(Note: the term “half diminished” is used interchangeably with “m7b5” in this paper.) Examples:

Major Minor Dominant

C C6 Cmaj7 Cmaj9

Cm Cm6 Cm7 Cm9 Cm7b5

C7, C9, C11 C7#9 C7b9 (B diminished) C alt (b5 or #5, and b9 or #9) C7 #11 (enharmonically, C7b5)

Quality alteration substitution: This is another substitution technique. When the quality of a chord is changed, for example, a minor chord is substituted with a dominant seventh chord on the same root, the new chord is of similar construction but with only one pitch different. There are seven “basic chord qualities,” for example: B7, Bmin7, Bmin7b5, B diminished 7, Bmin6, B6, and B major 7th. You can experiment with substituting the written chord with a chord on the same root but of a different quality. Let your ear, and the melody note of the tune, be your guide. Inversions In an inverted chord, the root is not in the bass. The inversions are numbered in the order their bass tones would appear in a closed root position chord (from bottom to top).

In the first inversion of a C major, the bass is E, the 3rd of the triad, with the 5th and the root stacked above it (the root is shifted an octave higher), i.e. E, G, C.

In the second inversion, the bass is G —the 5th of the triad —with the root and the 3rd above it (both shifted an octave higher), i.e., G, C, E

Third inversions exist only for chords of four or more tones, such as 7th chords. In a third-inversion chord, the 7th of the chord is in the bass position.

See the Appendix: “Constructing Chords on the Guitar Fretboard,” for further information regarding forming chord inversions on the fretboard.


Cadences

A short definition: In Western music, a harmonic cadence is a progression of at least two chords that concludes a phrase, a section, or a piece of music. The graphics below show examples of cadences. The subject of this paper is the use of the cycle of 4ths/5ths in jazz guitar harmonic substitution. As jazz guitar master Ted Greene stated “One of the most (if not the most) important patterns or progressions in the history of music is the Cycle (circle) of 4ths (also called the Cycle (circle) of 5ths). Chunks or portions of this cycle dominate the flow of most chord progressions.” It is very important to understand why V7 to I is a strong and frequently used cadence. The following example is given in the key of C; but, you can “spin the wheel” to put the target chord on any other point in the circle and the movement in fourths from the preceding dominant chord to the resolution will apply. There is both strong root movement and internal voice leading. In this example below, the note B in the G7 chord moves up a half step to resolve to the note C in the C chord. The note F in the G7 chord moves down a half step to resolve to the note E in the C chord. This creates strong root movement and internal voice-leading resolutions.

Other common cadences follow. Apply substitutions principles to these cadences. “Spin the wheel” to place the target chord on other points in the circle; the relative relationships apply.


IV can progress to I

As a variation, IV can progress to V to I

bVII7 can progress to I This is sometimes

called “the backdoor.”

bVII7 can be thought

of as a “borrowed” chord from the parallel key

of C minor.


iv can progress to I

As a variation, iv can progress to IV to I

There are many variations on these common cadences. The following table gives a few examples.

V7 to I ii – V7 – I vi – ii – V7 – I iii – vi – ii – V7 – I

IV to I IV – V7 – I vi – IV – V7 – I

Variations Diatonic substitutions for any of the above: discussed later in this paper. Tritone substitutions for any of the above: discussed later in this paper.

Diatonic Substitution

In major key harmony, there are three basic tonalities. It is important to hear the sound of each of these three “groups,” not the theoretical name for them. Let your ear be your guide.

Tonic sounds (I, iii, and vi),

Sub-Dominant sounds (IV, and ii) and

Dominant sounds (V, and vii).


You can use any of the chords in the bullet-point lines below as a substitution for one another in that same line. This works because the chords on the bullet point line share tones. The tones not shared can function as chord extensions. Trust your ear as a guide. For example, in the key of C:

C major7; Em7; Am7 (I major7; iii; vi)

F major7; Dm7 (IV major7; ii)

G7; B half diminished (V7; vii half diminished) Use the diatonic substitutions to enhance harmony, color, and create interesting root movement. Here is one example based on a few bars from “All the Things You Are.” Chord changes as written: Fm7 Bbm7 Eb7 Ab major 7 (I) Diatonic substitutions:

Fm7 Bbm7 Eb7 Cm7 (iii)

Fm7

Bbm7

Eb7

Fm7 (vi)

Moreover, there are many more variations when applying this substitution principle.

“Spin the wheel” on the cycle of fourths and fifths to place the target chord (root) on a different major key center. The relationship pattern of the lines will apply from that new point.


Companion Minor and “Back-cycling”

You can precede any major chord in a progression by its supertonic (ii7) and dominant (V7); or, just it’s dominant. (See the section on Minor harmony; iim7b5 and V7b9 is often used to precede a minor chord.) In addition, you can also substitute the minor chord with a dominant chord; for example, ii-V7 can become II7 – V7. Some common Companion Minor to Dominant 7th couplings are:

ii-V7 iii-VI7 iv-bVII7 v-I7 vi-II7 bii-bV7

#iv-VII7 biii-bVI7

The main point is that the relationship is moving in the cycle of 4ths/5ths; i.e. G7-->C major; or Dm7-->G7-->C major; or Em7-->A7; etc. Building on the example in the previous section that discussed Diatonic Substitutions, the following are a few bars from “All the Things You Are.” The chord changes as written: Fm7 Bbm7 Eb7 Ab major 7 (I) Diatonic substitutions; plus adding preceding ii-V7 chords

Fm7 Bbm7 Dm7 G7 (ii / V7 to Cm)

Cm7 (iii)

Fm7

Bbm7

Gm7 C7 (ii / V7 to Fm)

Fm7 (vi)


Use the cycle of 4ths/5ths as your guide. Use your ear, the melody, and your taste to string chords together in different and interesting substitutions. Example companion minors follow. “Spin the wheel” to place the target chord (root) on a different major key center. The relationship pattern of the companion minors will apply from that new point:

The term “back cycling” is the application of this same idea. As an example, if the target chord is C Major, you can use the cycle of fourths in the following manner: Em7 to A7 to Dm7 to G7 to C major 7 In other words, the cycle starts back at Em7 and progresses through the cycle of fourths chord

changes to reach the targeted chord of C△ (the triangle symbol refers to any extension for the C major chord; i.e. major 7th, major 6th, major 9th, 6/9, etc.). In addition, of course, you can combine any of the substitution tools to the process by extending and altering any of the chords in the cycle. As well as using chord inversions to create interesting root movement and color.


Tritone Subs

A short definition: A “tritone” is the interval of three whole steps from one note to its tritone. (“Tri” = three whole steps.) This same interval is sometimes called an augmented fourth (#11) or a diminished fifth (b5). The tritone divides an octave exactly in half. The tritone substitution is widely used for V7 chords in the jazz chord progression "ii-V7-I.” Replace the V7 chord with a dominant chord whose root is a tritone away from the root of the V chord. Use Tritone substitution in the companion minor applications previously discussed in this paper.

You can combine any of the harmonic substitution techniques. Explore and play all of the choices

then decide what you like.

Again, using a few bars from “All the Things You Are” as an example: Fm7 Bbm7 Eb7 Ab major 7 Tritone Substitution; Plus, adding the preceding ii chord to the tritone sub

Fm7 Bbm7 A7 (Tritone to Eb7)

Ab major 7

Fm7

Bbm7

Em7 A7 (ii chord preceding A7)

Ab major 7

Use the cycle of 4ths as the guide. Use your ear, the melody, and your taste to string chords together in different and interesting substitutions. Here is an example of Tritone Substitution in a few bars of a Blues progression: Bb7 Eb7 Bb7 Bb7 Eb7 (blues

progression continues) Bb7

Eb7

Bb7

Bm7 E7 (The E7 is a tritone sub for Bb7; Bm7 is the preceding ii chord to E7)

Eb7


The tritones are opposite one another on the cycle in the illustration below. There are six sets of Tritones:

“Transformation” of Diminished Chords

To “transform” a diminished 7th chord to a dominant 7th chord, lower one note in the diminished 7th chord. There are 3 diminished “families.” Members of the same “family” are the notes that form a square in the illustration below.


Think of the term “families” as a “set” or “group.” The term “family” in this paper refers to their relationship to substitute for one another. Moreover, the transformations and rules of substitutions that apply to any one note in the family are equally applicable to the other notes in the family.

Diminished chord family members:

G E Db/C# Bb


D Bb Ab F


A F# Eb C

Using the Edmin7 “family” as an example (the four points on the square of E, G, Bb, Db); the column in the table below shows the spelling of Edim7 (but, since we know that since the tones are equidistant from each other, we could have just as correctly called this a G dim7, Bb dim7, or Db dmin7.) Each successive column in the table that follows lowers one tone to produce its ‘transformation’ into a Dominant 7th chord; i.e. • E is lowered to Eb to transform the diminished chord into an Eb7 • G is lowered to Gb to transform the diminished chord into Gb7 • Bb is lowered to A to transform the diminished chord into A7 • Db is lowered to C to transform the diminished chord into C7

You can use your ear to treat Eb7, Gb7, A7, and C7 as related substitutes since the underlying theory shows they came as a transformation from the same diminished chord family. And, taking this transformation process one step further, applying the ‘companion minor’ substitution rule of “you can preceded any chord in a progression by its supertonic (ii7),” each of the preceding “ii” chords to the dominant 7th chords can also be considered related since they came from the same transformational process. (This is something that Pat Martino does frequently. See his extensive and interesting writing on the subject.)


As an example: Bb min 7 – Eb7 Db min 7 – Gb7 E min 7 – A7 G min 7 – C7 Bb min7, Db min7, E min7, and G min7 are related since they came from the same diminished to dominant chord transformation process.

Dom7b9 Chords

Diminished chords relate closely to Dom7b9 chords (which can also move in Minor 3rds and substitute for one another). For example, F/B/D/Ab over a G root is a G7b9 chord. G7b9 shares four notes in common with the diminished chord. The illustration below displays the diminished tones F/B/D/Ab. Add the G as the root tone to create G7b9.

“Spin the wheel” to place the root of the chord on a different pitch to apply this process to each of the three diminished “families;” i.e., the three squares in the cycle of 4ths/5ths below:


“Transformation” of Augmented Triads

Since the cycle of 4ths/5ths can be evenly divided into 4 augmented triads, and since the notes in each of those 4 sets are equidistant from one another, then any one of them can be considered the “root.” Therefore, each note within one of the sets is part of the same “family.” In other words, C augmented is the same thing as E augmented which is also the same as G#/Ab augmented. Those three roots are part of the same augmented family. The four families (sets) of augmented triads are as follows (the 4 triangles) in the illustration below.

C, E, G#/Ab (can named be C aug, or E aug, or Ab aug)

G, B, D#/Eb

D, F#/Gb, A#/Bb

A, C#/Db, F(E#) It is visually easy to see in the diagram below that each pitch in a family is equidistant from the other pitches in the same family.


Transformation Example: To transform C augmented (C, E, G#) raise or lower one note in the triad by a half step; i.e. for Fm (raise the E to create F, Ab/G#, C); for Ab Major (lower the E to create Ab, C, Eb). Notice the major/relative minor relationship of the transformations (Ab major / F minor; see Appendix A). The chords contain the common tones of C and Ab.

C Augmented F Minor (the E is raised a ½ step F)

Ab Major (the E is lowered a ½ step to Eb)

“Spin the Wheel” to a different augment triad to apply this same transformation process to each of the augmented “families.”

Whole Tone

Dividing the cycle of 4ths/5ths by six yields two whole tone families.

• In either of the two, any note in the family is the root since they are all equidistant from one another.

• V7#5 (enharmonically V7b13) and V7b5 (enharmonically V7#11) chords can be derived from a whole tone family. V7#5 chords from a whole family can move in whole step substitutions for one another, an example follows:

So, for example, a whole tone scale starting on any of the pitches in the family can be used on V7#5 chords from that family, (i.e. C7#5 contains C, E, G#, Bb)

C7#5 (the family contains the b7 and the #5)

D7#5

E7#5

F#7#5

Ab7#5

Bb7#5 Of course, all the enharmonic equivalents apply.


One example:

D minor 7 G7 C△

Could become:

D minor 7 G7#5 A7#5 B7#5 C#7#5 C△

Minor Harmony

Natural Minor The “Natural Minor” scale has a b3, b6, and b7. Natural Minor is also known as “Relative Minor”

since the scale contains the same notes of a major scale starting from the 6th degree of the “parent”

major scale. The “relative minor” is based on the “parent major.” (And, yes, the sequence of notes

is also known as the “Aeolian mode.” A rose by any other name.)

What is important for the focus of this paper is that the chords built from the Natural Minor scale

align to the same chords of its relative major. (Note: jazz guitar master and teacher extraordinaire,

Don Mock, has written excellent books regarding the various uses of minor scales and harmony.

Consult his books for detailed information.)

The table below shows an example Major scale chord harmony and its Relative Minor scale

harmony. The top row is a C major harmonized scale. The second row displays the chord symbols

for Major. The third row displays the chord symbols for Natural Minor – i.e. the same notes of a

major scale starting from the 6th degree of the “parent” major scale. Note that the quality of the

chords (major, minor, and dominant) are the same, but the staring degrees are different.

C Major 7 Dm7 Em7 F Major 7 G7 Am7 Bm7b5 C Major7 Dm7 Em7 F Major 7 G7 Am7

I Major 7 ii minor 7 iii minor 7 IV Major 7 V Dom7 vi minor 7 vii half dim I Major 7

i minor ii half dim bIII Maj7 iv minor7 v minor7 bVI Maj7

bVII Dom7

i minor

Harmonic Minor Notice that in Natural Minor the “Two Chord” is a half diminished chord (ii m7b5) and the “Five

Chord” is a minor chord (v minor 7). Because the Natural Minor harmony contains a “v minor 7” it

does not have a strong dominant motion back to the “One Chord” (the root). In order to address

this, Harmonic Minor raises the Third in the minor v chord to create a Dominant 7th chord, which

does have a strong resolution back to the tonic root chord.

Notice in the example below that the note G has been raised to a G#. G# is the third of the E

chord, thus creating a V7 dominant chord rather than a v minor chord. Since the G# must now be

used to construct the other chords in the scale, the resultant chords are displayed in the table below

and on the illustration of the cycle of fourths. (Also, notice that the “Five Chord” in Harmonic


Minor has the characteristic 7b9 sound. As discussed in a previous section in this paper, 7b9 chords

can move in minor thirds.)

Am7/maj7 Bm7b5 C Major7#5

Dm7 E7b9 F Major7#9

G# diminished 7

Am7

i minor/ major 7th

ii half dim bIII Maj7#5

iv minor7 V7b9 bVI Maj7 vii dim 7

In the cycle of 4ths/5ths notice the ii half diminished chord to the V7b9 chord. This movement in

4ths creates a strong motion toward a minor chord resolution; but, it is not limited to minor

resolution, sometimes iim7b5 to V7b9 progresses to a major chord resolution to create an

interesting color. Scan the changes of a tune to find any iim7b5 to V7b9 chord changes. This

usually signals movement in a minor key. Playing the appropriate harmonic minor scale on the

V7b9 chord creates a strong color and motion toward a minor resolution.

Melodic Minor Notice that the interval from the 6th degree to the 7th degree in the Harmonic Scale is a step-and-a-

half. In order to address this sometimes-awkward melodic interval, Melodic Minor raises the 6th

scale degree a half step. (Note: In classical music theory, the Melodic Minor scale is different going

down than going up. It is simply a natural minor scale when descending. However, in Jazz usage,

Melodic Minor is the same going up and going down.)

The chart of chords and the cycle of 4ths below displays the result of chord construction based on

raising the 6th a half step. The Melodic Minor scale example below has a flatted third (i.e. A to C


natural is an interval of a minor third), a natural 6th (in this example, F#), and a natural 7th (in this

example, G#).

Am7/maj7 Bm7 C

Major7#5#11

D7#11 E7 (natural 9)

F# m7b5 G# alt Am7/maj7

i minor/ major 7th

ii minor7 bIII Maj7#5#11

IV7#11 V7 vi half dim

VII7 (b5, #5, b9, #9)

Notice that the Melodic Minor harmony has two sets of Tritone pairs (bIII Major 7#5 / vi m7b5)

and (IV7#11 and VII7 alt.) From the previous discussion regarding Tritone substitution, you can

use the pairs as substitutes for one another to create strong root movement in a progression. They

can resolve to the same chord.

The 7#11 chord is an interesting color – often called “Lydian Dominant.” The chord can be

thought of as a “static” dominant chord. In other words, it is not necessarily pushing toward a

resolution. The following example is a few bars from “Stella by Starlight.” Note the 5th bar:

G7 aug Cm7

Ab7#11 (enharmonically Ab7b5)

Bb major 9


The Major7 #5 chord is also an interesting color – often called “Lydian Augmented.” The chord can

substitute for a Major 7 chord. The following example is a few bars from “All the Things You Are.”

The example combines tritone substitution, companion minors, a 7b9 chord, (which could also

move in minor 3rds), and a Major 7 #5 chord as the resolution point. The first line is the written

chord changes, the second line contains substitutes for those changes.

Fm7 Bbm7 Eb7 Ab major 7 Fm7

Bm7 E7

Em7 A7b9

Ab major 7 #5

Regarding the VII “alt” chord – typically in Jazz terminology an alt chord (i.e. G#7 alt) refers to a

dominant chord in which both the fifth and the ninth is raised or lowered by a half step; i.e b5, #5,

b9, #9. In addition, sometimes the b5 is written as its enharmonic equivalent, #11. An alt chord

creates strong tension toward a resolution point.

Minor Harmony Compared The following three tables discussed above appear again below as a summary to compare and

contrast Natural Minor, Harmonic Minor, and Melodic Minor chord harmony:

Natural Minor

Am7 Bm7b5 C Major7 Dm7 Em7 F Major7 G7 Am7

i minor ii half dim bIII Maj7 iv minor7 v minor7 bVI Maj7 bVII Dom7

Raise the third in the “Five Chord” to create a dominant chord:

Harmonic Minor

Am7/maj7 Bm7b5 C Major7#5

Dm7 E7b9 F Major7#9

G# diminished 7

Am7

i minor/ major 7th

ii half dim bIII Maj7#5

iv minor7 V7b9 bVI Maj7 vii dim 7

Raise the 6th to create whole step between the sixth and seventh scale degrees, rather than the step-

and-half that occurs in harmonic minor:

Melodic Minor

Am7/maj7 Bm7 C Major7#5#11

D7#11 E7 (natural 9)

F# m7b5 G# alt Am7/maj7

i minor/ major 7th

ii minor7 bIII Maj7#5#11

IV7#11 V7 vi half dim

VII7 (b5, #5, b9, #9)


It is useful to notice the differences in the “Two Chord” and the “Five Chord” in each of the above

harmonies. The “Two” – “Five” extensions are a signal for the underlying version of the minor

scale and can be used to create strong harmonic motion -- for example, the V7b9 chord from

harmonic minor; and, the VII alt chord derived from melodic minor.

Minor Harmony Summary Chart:

"Scale

degrees"

Natural Minor Harmonic Minor Melodic Minor

1 i minor seventh i minor/major seventh i minor/major seventh

b2

2 ii half diminished ii half diminished ii minor seventh (nat. 5)

b3 bIII major seventh bIII major seventh #5 bIII major seventh #5

3

4 iv minor seventh iv minor seventh IV dominant 7th (#11)

b5

5 v minor seventh V dominant seventh (b9) V dominant seventh (nat. 9)

b6 bVI major seventh bVI major seventh

6 vi half diminished

b7 bVII dominant seventh

7 vii diminished 7th vii half diminished

1 i minor seventh i minor/major seventh i minor/major seventh

{paper continues with a summary and an appendix}


Some General Summary Thoughts on Chord Substitution

Music is a rich and multifaceted art form.

Musicians combine sound to produce interesting form, melody, harmony, and expression of emotion.

This paper focused on examples using the cycle of 4ths/5ths as a guide for root movement in progressions of chords. (There is a great deal written elsewhere regarding the use of the cycle of 4ths/5ths for identifying key centers and scalar material. That was not the subject of this paper.)

The importance and power of the cycle in 4ths and 5ths in jazz is tremendous.

There are a vast number of harmonic variations and permutations. Let your ear by your guide.

Music isn’t comprised of just “notes” and “harmonic rules,” it is equally important to play with dynamics, time, feel, tone, phrasing, space, articulation, rhythm, creativity, and all other tools of musical expression.

You can combine any of the harmonic techniques in this paper. Mix and match. Trust your ear

Explore and play all of the choices then decide what you like. Use what you like, when you like.

You are creating art. You can use your whole brain. Left: logical, organized, analytical, symbolic, and mathematical. Right: holistic, emotional, intuitive, creative, non-verbal. Like two sides of the same coin, right-brain creativity and left-brain logic secure and balance each other.

This paper attempted to explore the mathematical characteristics of the cycle of 4ths/5ths as a guide for chord progressions and chord substitutions. The goal is to discover and utilize interesting harmonic colors in the service of making music.

Appendix Follows


Appendix

A. The cycle of Fourths / Fifths major key centers and minor key centers

B. Constructing Chords on the Guitar Fretboard

C. Glossary


Appendix A: The cycle of Fourths / Fifths major key centers and minor key centers:

Major Keys and their corresponding signatures are on the outside of the circle.

Minor keys are on the inside of the circle.

The minor key signature is the same as its relative major immediately adjacent on the outer ring of the circle. For example: Ab Major / F minor; the key signature is 4 flats

As a memory-aid visualization on the guitar fretboard:


Appendix B: Constructing Chords on the Guitar Fretboard The following is a step-by-step process for considering the layout of the guitar fretboard and constructing chords. First, consider the pattern of Octaves on the fretboard. This particular pattern starts on the note “F” on the first fret, but you can start the pattern on any fret and the relative positions will apply. Image that the fretboard extends for infinity in both directions, i.e., toward the nut and toward the sound hole, the relative pattern will continue in both directions.


Next, if we consider that starting point in this example as the Root of the chord (the 1 – the note “F” in this example), locate the major 3rd of the chord in relationship to that root:


At this point, it is worth noting that the open strings of the guitar are organized into four pairs of Perfect 4ths and one Major 3rd.

The pairs of open strings:

The interval between those strings:

The 6th string to the 5th string Perfect 4th

The 5th string to the 4th string Perfect 4th

The 4th string to the 3rd string Perfect 4th

The 3rd string to the 2nd string Major 3rd

The 2nd string to the 1st string Perfect 4th

Therefore, when constructing chords on the guitar fretboard, you must visualize and compensate for the Major 3rd that occurs between the 3rd and 2nd strings. In the following example, move the pattern of fretted notes directly across to adjacent higher strings. Raise the note that falls on the 2nd string one fret (i.e., the note represented on the fretboard as an open circle is raised up to the solid circle to compensate for the major 3rd that occurs between the 3rd and 2nd strings).

→

In addition, conversely, if transposing from high strings to low strings, move the pattern of fretted notes directly across the adjacent lower string, lower the note that falls on the third string by one fret.

←

This “string transposing” process becomes very important as you build other chords on the guitar fretboard. Notice in the preceding example regarding locating the 3rds in relationships to the root, that the 3rd on the 2nd string is directly adjacent to the root, whereas the 3rds one the other strings are one fret below the adjacent root.


Next, if we consider that starting point in this example as the Root of the chord (the 1), locate the Perfect 5th of the chord in relationship to that root:


Continuing the process, now combine the locations of the Major 3rds and the Perfect 5ths in relationship to the root:

A useful pattern emerges. There are two harmonic sets: 1, 3, 5, 1; and, 1, 5, 1, 3.

The set 1, 5, 1, 3 always has the root on a fret lower than the other fretted notes; in other words, those fretted notes are toward the sound hole.

The set 1, 3, 5, 1 always has the root on a fret above the other fretted notes; in other words, those fretted notes are toward the nut.


If you consider the patterns a bit further, and use the principle of string transference previously discussed, you find that there are six sets on adjacent strings. You can place the root of the chord on either the 6th string, 5th string, or 4th string. There is a 1, 3, 5, 1 set from that root; and, a 1, 5, 1, 3 set from that root:

Here is an example using the six sets in the key of A:


At this point, you may be asking yourself about Inversions. The inversion are located within the six sets; i.e.: 3, 5, 1 and 5, 1, 3 So far, we have only consider chords with the pitches 1, 3, and 5 on adjacent strings. In addition, chords are formed skipping strings on the guitar. However, the same ‘construction’ process applies to chords formed on non-adjacent strings. Moving forward in this chord construction process; consider that starting point in this example as the Root of the chord (the 1), locate the Major 7th of the chord in relationship to that root. The Major 7th is a half-step (one fret) below the root.


Combine the process with the 3rd, 5th, and 7th


This is a visualization of the Major 7th chord inversions. The lines connect chord shapes starting on

the 3rd of the Major 7th chord, the 5th of the chord, and the 7th of the chord. This is only one

example of inversion fingerings for F Major 7th.


Continuing the chord construction process, add the Major 6th (which is enharmonically the 13th). The chart becomes more complex, but it is still based on simple underlying construction principles.


You don’t have to limit yourself to selecting notes from within the brackets. You can consider the available pitches as the colors on a palette and select from any combinations. You can see that this process of adding extensions and alterations can continue. The following adds the Major 2nd, which is enharmonically the Major 9th.


And, the following adds the Perfect 4th, which is enharmonically the 11th. All the major scale diatonic pitches are now in this example diagram; Root (1), 2 (9), 3, 4 (11), 5, 6 (13), 7.


As the chord construction process adds extensions and alterations, it is still very useful to consider “visualizing” and “anchoring” to the simple sets of 1, 3, 5, 1; and, 1, 5, 1, 3 that was the starting point in this discussion. The guitar master Howard Roberts wrote a great deal regarding visualizing the fretboard and “controlling the voices.” For example, lower the 7th to create dominant sounds; or, lower the 3rd to create minor sounds. “Control the voices” to construct all of the chord qualities and their variations, alterations, and inversions. For example: dominant 7th, minor 7th, 7b5, Diminished 7, minor 6, 6th, major 7th, etc. Rather than memorize an encyclopedia of guitar chord “grips,” use a basic understanding of music theory, and an understanding of the organization of the guitar fretboard to control the voices and construct the chord colors you want to use.

1. On a single string

2. Adjacent strings

3. Skipping one string

4. Skipping two strings

5. Skipping three strings

6. Skipping four strings

7. Skipping five strings

Whole steps (W) and half steps (1/2) “formula”

m2

M2 m3 M3 P4 TT P5 m6 M6 m7 M7

½ step

W W + ½ 2 W 2 W + ½ 3 W 3 W + ½ 4 W 4 W + ½ 5 W 5 W + ½

Example follows on the next page.


Dominant (7th is lowered to b7)

Minor (3rd is lowered to b3)


Appendix C: Glossary

Term Definition

"Two Chord" "Five Chord" "One Chord", etc.

The chord built from the scale degree (1, 2, 3, 4, 5, 6, 7) of the underlying scale. For example, "The One Chord" is a major chord when based on a Major Scale; the "One Chord" is minor when based on a Natural Minor scale. For example, "The Five Chord" is minor when based on a Natural Minor scale; the "Five Chord" is a dominant 7thb5 when based on a Harmonic Minor scale.

△ Represents any variation of a Major Chord; i.e. C△ could be played as C Major 7, C Major 6, C Major 9, C 6/9, etc.

♭; ♯ Lower or raise the root of the chord while retaining the quality of the chord (major, minor, dominant, diminished, augmented); For example, in the key of C: bii = Db minor #ii = D# minor bII7 = Db dominant 7th #II7 = D# dominant 7th etc.

Alteration Alteration is a chord with one or more diatonic notes replaced by a neighboring pitch in the chromatic scale; for example, in Jazz it is somewhat common, contingent on the context of the tune, to add a sharp or flat to the 5th, 9th, 11th, or 13th. Use your ear and the rules of harmony.

Arrows in the cycle diagrams

Indicates the direction of the harmonic progression.


Augmented Triads An augmented triad is constructed of two major. The term "augmented" comes from the top note, the fifth of the triad, raised a half step compared to a major triad. The fifth is "augmented," in other words, raised a half step. Example: major triad = C, E, G; augmented = C, E, G#. Since the circle of 5th/4ths can be evenly divided into 4 augmented triads, and since the notes in each of those 4 sets are equal-distant from one another, any one of them can be considered the “root.” So, each note within one of the sets can be considered part of the same “family,” C augmented is the same thing as E augmented which is also the same as G#/Ab augmented. Those three pitches are part of the same augmented family. The four sets (families) of augmented triads are as follows. Any one of the tones in a family can substitute for one another for either chords or improvisational material: C, E, G#/Ab (can be C aug, E aug, or Ab aug) G, B, D#/Eb D, F#/Gb, A#/Bb A, C#/Db, F(E#)

Augmented for Dominant

The augmented triad on the fifth scale degree may be used as a substitute

dominant, and may also be considered as ♭III+, for example in C: V+ =

G-B-D♯, ♭III+ = (enharmonically) E♭-G-B♮.

The chord a minor third above, ♭VII7, may be substituted for the dominant, and may be preceded by its ii: iv7. Due to common use the

two chords of the backdoor progression (IV7-♭VII7) may be substituted for the dominant chord. In C major the dominant would be G7: GBDF, sharing two common

tones with B♭7: B♭DFA♭. A♭ and F serve as upper leading-tones back

to G and E, respectively, rather than B♮ and F serving as the lower and upper leading-tones to C and E.

Back Cycling For example, insert the related dominant prior to its major chord resolution. Insert the dominant's related ii chord. Insert the dominant for that related ii chord, etc. When written simply as I major; it can yield iii - VI7 -- ii -- V7 - I.

Cadence In Western music, a harmonic cadence is a progression of at least two chords that concludes a phrase, a section, or a piece of music.


Chord Construction Major: Major 3rd - minor 3rd - Major 3rd Dom 7: Major 3rd - minor 3rd - minor 3rd Min 7: minor 3rd - Major 3rd - minor 3rd M7b5: minor 3rd - minor 3rd - Major 3rd Aug: Major 3rd - Major 3rd - Major 3rd Dim7: minor 3rd - minor 3rd - minor 3rd (any one can be considered root)

Chord Quality; 7ths, 6ths

Major 7 Dominant 7 Minor 7 Minor/Major 7 Half Diminished Full Diminished Major 6th Minor 6th

Chords A chord is any harmonic set of pitches consisting of usually three notes (also called "pitches") played simultaneously. This paper discusses chords for application in jazz harmonic enhancements and substitutions.

Color Alteration Any chord can be played using another color. It works particularly well on chords than have already been substituted. For instance, if you play Db7 instead of a G7… Try Db major 7th, or… Db diminished 7th, or… Db major 6th, or… any ideas

Companion Minor (ii-V subs)

When a chord or each chord in a progression is preceded by its supertonic (ii7) and dominant (V7), or simply its dominant. This chord enhancement is often simply called a "two-five," sometimes this is true but often it's not. Some common Companion Minor - Dom7 couplings

are ii V7, iii VI7, iv bVII7, v I7, vi II7, bii bV7, iv# VII7, biii bVI7.


Consonance / Dissonance

Tension and release. From the overtone series we can derive a concept regarding pitches which we will term as either being active or resting. The first three overtones present in the overtones series are the P1/P8, P5 and M3. Tones a half step above or below those pitches have a "gravitational" pull toward the 'resting tone.' Intervals in order of Most Consonant to Most Dissonant: Octave Perfect 5th Perfect 4th Major 3rd Major 6th minor 6th minor 3rd Tritone minor 7th Major 2 Major 7th minor 2nd

Cycle of 4ths/5ths The circle, or cycle of 4ths/5ths, is a relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys.

Diatonic Diatonic chords are generally understood as those that are built using only notes from the same diatonic scale -- i.e. "stacking" the notes from the underlying scale. Therefore, the diatonic chords derived from scales such as major, natural minor, harmonic minor, and melodic minor will have different extensions and alterations.

Diatonic Substitutions I, iii, vi (Tonic sounds) ii, IV (Sub-Dominant sounds) vii, V (Dominant sounds)

Diminished A diminished triad, also known as the minor flatted fifth (m♭5), is a triad consisting of two minor thirds above the root. For example, if built on

C, a diminished triad would have a C, an E♭ and a G♭. Therefore, it resembles a minor triad with a lowered (flattened) fifth. In Jazz harmony, the m7b5 chord is common. For example, in Cm7b5 would be C, Eb, Gb, and Bb. m7b5 is also interchangeably known as 'half diminished' because a fully diminished chord would be C, Eb, G, and Bbb (double flat).


Diminished for Dominant

Play a diminished on the 3rd, 5th, b7th or b9th of any dom7(b9) chord.

• Regarding G7 as V7 in the key of C -- G7 is related to Bb7, Db7 and E7 via

the diminished cycle.

o All four chords relate to Bdim7 which is one of the 3 dim7 chords related to

the key of C.

o The three are vii dim; i dim; and, bii dim

o Each Dom7 can have a "Companion Minor7,” and depending on voice

leading, each pair can resolve to C major.

Dominant -- Altered sounds

b5, #5, b9, #9

Dominant 7th A dominant seventh chord is composed of a root, major third, perfect fifth, and minor seventh. It can be also viewed as a major triad with an additional minor seventh.

Enharmonic An enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. Thus, the enharmonic spelling of a written note, interval, or chord is an alternative way to write that note, interval, or

chord. For example, the notes C♯ and D♭ are enharmonic (or enharmonically equivalent) notes. They are the same fretted note on the guitar fretboard, and therefore they are identical in pitch, although they have different names and different roles in harmony and chord progressions.

Extension (Extended chords)

Extended chords come from the key center; i.e. 2nd/9th, 4th/11th, 6th/13th.

Half diminished A diminished triad, also known as the minor flatted fifth (m♭5), is a triad consisting of two minor thirds above the root. For example, if built on

C, a diminished triad would have a C, an E♭ and a G♭. Therefore, it resembles a minor triad with a lowered (flattened) fifth. In Jazz harmony, the m7b5 chord is common. For example, in Cm7b5 would be C, Eb, Gb, and Bb. m7b5 is also interchangeably known as 'half diminished' because a fully diminished chord would be C, Eb, G, and Bbb (double flat).

Harmonic Minor The notes of the harmonic minor scale are the same as the natural minor except that the seventh degree is raised by a half step, making a step-and-a-half (i.e. augmented second) between the sixth and seventh degrees of the harmonic minor scale. This paper discusses the differences between Natural Minor harmony, which has a minor "Five Chord," and Harmonic Minor, which has a Dominant "Five Chord."


Harmony; Harmonic Progressions

Harmony involves chords, their construction, and the principles of chord progressions (movement from chord to chord). Harmony is often said to refer to the "vertical" aspect of music; contrasted to melodic line, or the "horizontal" aspect of music. The paper attempts to discuss harmony from a jazz guitar perspective.

Hemisphere -- Left Brain

The brain is formed by two cerebral hemispheres that are separated by a groove, the longitudinal fissure. The brain can be described as being divided into left and right cerebral hemispheres. Although it is an overgeneralization and brain functions across both hemispheres, the Left Brain is sometimes described as logical, organized, analytical, rational, symbolic, and mathematical. For the purposes of this paper, the study of jazz guitar harmony can benefit from both logical and intuitive approaches.

Hemisphere -- Right Brain

The brain is formed by two cerebral hemispheres that are separated by a groove, the longitudinal fissure. The brain can be described as being divided into left and right cerebral hemispheres. Although it is an overgeneralization and brain functions across both hemispheres, the Right Brain is sometimes described as Holistic, non-rational, emotional, intuitive, spatial, and creative. For the purposes of this paper, the study of jazz guitar harmony can benefit from both logical and intuitive approaches.

Interval An interval is the difference between two pitches. An interval may be described as horizontal or linear (i.e. melodic). When the pitches are vertical (i.e. harmonic) the interval is describing the pitches sounding at the same time, as in a triad, or chord. In jazz usage, intervals are most commonly differences between notes of a diatonic scale. The smallest interval is a half-step.

Inversion A chord's inversion describes the relationship of its bass to the other tones in the chord. For example a C major triad contains the tones C, E and G; its inversion is determined by which of these tones is the bottom note in the chord; E, G, C; or G, E, C. This same process is used for any extended chord. For example, C major seventh, C, E, G, B; can be inverted as E, G, B, C; or, G, B, C, E; or, B, C, E, G.


Key Center The key of a musical piece is a group of pitches, or scale, upon which the music is composed. The group of pitches features a tonic note and its corresponding chords, also called a tonic or tonic chord, providing a 'sense of arrival.' Notes and chords other than the tonic in a musical composition (or chord substitution) can create varying degrees of tension, resolved when the tonic chord returns. The key may be derived from major or minor scales. In jazz, the key center can change from a set of measures to a set of measures.

Lines or dashes in the cycle diagrams

Indicates a harmonic connection between the chords.

Melodic Minor The harmonic minor scale has an interval of a step-and-a-half between the sixth and seventh degrees of the scale. In the history of music, some composers felt it to be an awkward leap, particularly in vocal music, and considered a whole step between these two scale degrees more conducive to smooth melody writing. The sixth scale degree was raised to create Melodic Minor, which has only whole steps and half steps in the scale.

Melodic Minor Chord Forms

For instance, for a G7 altered, you might play Ab Melodic Minor, if you harmonize Ab Melodic Minor into 7th chords you can use any of the resultant chords as a sub for G7 alt. If you use chords built on any two adjacent scale degrees, say, Abmin/maj7 and Bbmin7, you'll get all of the altered tones along with the 3 b7. Don't forget to try this idea for Tonic minor, min7b5 and 7#11 and any other situation that you might like melodic minor derived sounds.

Modal Interchange A borrowed chord (also called mode mixture and modal interchange) is a chord borrowed from the parallel key (minor or major scale with the same tonic). Borrowed chords are typically used as "color chords", providing variety through contrasting scale forms, major and the three forms of minor. Similarly, chords may be borrowed from the parallel modes, the various modes beginning on the same tonic as a scale, for example Dorian with D major. bVII7 can be substituted for V7. This is borrowed from the Aeolian mode of C (based on major scale of Eb – Cm7, Dø7, Ebma7, Fm7, Gm7, Abma7, Bb7, Cm7), but used in a major key. IVm7 (or IVm6) can also be substituted for V7. Also borrowed from the Aeolian mode (Cm7, Dø7, Ebma7, Fm7, Gm7, Abma7, Bb7, Cm7).

Modulations Common-chord modulation (also known as diatonic-pivot-chord modulation) moves from the original key to the destination key (usually a closely related key) by way of a chord both keys share.


Natural Minor Every major key has a Relative Minor (i.e. Natural Minor), which starts on the sixth scale degree. For example, the sixth degree of F major is D, and therefore its relative minor is D minor. The relative natural minor of a major key always shares the same notes: for example, F major consists

of F, G, A, B♭, C, D, and E, while D natural minor consists of D, E, F,

G, A, B♭, and C -- the same set of notes. Natural Minor, Relative Minor, and the Aeolian mode, are terms to describe the same set of notes.

Ostinato Pattern; in bass or in other voices

Pedal points Chords move across the pedal. Produces tension to lead to release. Tonic pedals V in the bass as pedal "Inverted pedals" -- i.e. in high voice Or internal pedals -- middle voice Double pedal tones

Pentatonic chords Chords built from pentatonic scales

Perfect 4th A fourth is a musical interval encompassing four staff positions. A Perfect Fourth specifically spans five half steps. The abbreviation P4 is occasionally used to indicate a Perfect Fourth.

Perfect 5th A fifth is a musical interval encompassing five staff positions. A Perfect Fifth specifically spans seven half steps. The abbreviation P5 is occasionally used to indicate a Perfect Fourth.

Pitch Pitch is the acoustical quality that makes it possible for humans to judge sounds as "higher" and "lower" associated with musical melodies. Musical notes are often referred to as "pitches." In Western music, standard frequencies have been accepted to describe pitches, for example The A above middle C is usually set at 440 Hz (often written as "A = 440 Hz" or sometimes "A440").

Polychords Two or more chords, one on top of the other. In shorthand, they are written with the top chord above a line and the bottom chord below.

Progression A chord progression or harmonic progression is a succession of musical chords, which are three or more notes, sounded simultaneously. Chord progressions are the foundation of harmony in Western music. For example: By whole steps: IV-V; V-vi; ii-iii. By cycle: V-I; ii-V; vi-ii; iii-vi; vii-iii


Quality alteration When the quality of a chord is changed, and the new chord of similar root and construction, but with one pitch different, is substituted for the original chord, for example the minor sixth for the major seventh, or the major seventh for the minor.

Quartel voicing Any harmonization based on the interval of a fourth or its inversion, a fifth.

Relative major/minor substitution

Shares two common tones and is so called because it involves the relation between major and minor keys with the same key signatures, such as C major and A minor.

Resolution (Resolve) Resolution in western tonal music theory is the movement of a note or chord from dissonance (an unstable sound) to a consonance (a more final or stable sounding one). Dissonance, resolution, and suspense can be used to create musical interest.

Roman numerals for chords

Upper Case is used for major chords; usually Major 7th or any of the extension or alteration chord colors for major. I is the root of the key center. Lower case numeral is for a Minor chord; usually Minor 7 or any of the extension or alteration chord colors for minor; i.e. ii, iii, vi. Upper Case (numeric) 7 is used for Dominant chords, or any of the extension or alteration chord colors for Dominant; i.e. V7.

Secondary Dominants V of V. Pitches are "borrowed" from the scale of the secondary key ("tonicization").

Tone A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre (or quality). The term Tone is sometimes used interchangeably with "Note" or "Pitch" (although not accurately from the point of view of classical theory terminology).

Triadic Functions Major; Minor; Augmented; Diminished

Tritone A “tritone” is the interval of three whole steps from one note to its tritone. (“Tri” – think three whole steps.) This same interval is sometimes called an augmented fourth (#11) or a diminished fifth (b5). The tritone divides an octave exactly in half. The tritone substitution is widely used for V7 chords in the popular jazz chord progression "ii-V-I" (This type of substitution is also called a Neapolitan Sixth.) Two dominant chords that are a tritone apart (three whole-steps) share the same 3rd and b7th but “inverted.” Tritone subs transform the “up a fourth” motion into the “descending by semi-tones” motion.


Voice-leading Voice leading is the term used to describe the linear progression of melodic lines (voices) and their interaction with one another to create harmonies, according to the principles of common-practice harmony. This paper discusses the use of the cycle of 4ths/5ths to find interesting chord substitutions, which use strong root movement and voice leading from chord to chord.

Whole tone A major second interval (sometimes called a Whole Tone) spans two half steps. For example the notes C to D is a whole tone; the notes D to E is a whole tone; the notes E to F# is a whole tone, etc. Dividing the cycle of 4ths/5ths by six yields two whole tone families. In either of the two, any note in the family is the root since they are all equidistant from one another.

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an outline of a few harmonic substitutions for jazz guitar · pdf fileuse a substitution chord...

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