The diminished harmonic system produces three eight-notesymmetric scales based on the minor third interval (four equal

divisions of the octave). Each scale is constructed by alternatingwhole and half steps, the sum of which is a minor third. Eachdiminished scale may also be visualized as two minor tetrachordsdivided by a half step, two diminished seventh chords a whole stepapart, or four major/minor triads a minor third appart. The dimin-ished scale built on C:

Four major/minor triads (enharmonic spellings used for simpli-fication):

78

Diminished System

Diminished ScaleConstruction

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1 1/2 1 1/2 1 1/2 1 1/2

C minor tetrachord F# minor tetrachord

D diminished 7th

C diminished 7th

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The symmetry of the diminished system is based on the minor thirdinterval (the sum of the whole step – half step repeating pattern). Eachof the three semitones within the minor third interval is a possiblestarting tone for the scale. The scale built on the fourth semitone isidentical to the first, confirming the three transpositions of the dimin-ished system. Like all symmetric scales, the diminished scale is non-modal.

In addition to the major/minor triads, four diminished seventhchords and four dominant seventh chords, each separated by the inter-val of a minor third, are diatonic to each diminished scale. These chordqualities are unique to the diminished system and are presented indepth in the following section on diminished scale harmony. A chartshowing the three diminished scales and their respective diminishedseventh and dominant seventh chords.

79

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C

wb w w# w# w w w w

Eb

w# w# w w w w wb wF#

w w w w wb w w# w#A

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Ab7(b9) B7(b9) D7(b9) F7(b9)

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D

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F

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w w# w w w w w# w#B

Do7 Fo7 G#o7 Bo7

Bb7(b9) Db7(b9) E7(b9) G7(b9)

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Each degree of the diminished scale produces a diminished seventhchord. The first, third, fifth, and seventh scale degrees of the scaleproduce a diminished seventh chord with extensions of a majorseventh, natural ninth, natural eleventh, and flatted thirteenth.Note that these extensions form the other diatonic diminished seventh chord of the scale. For this reason this diminished seventhchord with complete extensions is sometimes referred to as a “double” diminished chord:

The second, fourth, sixth, and eight scale degrees produce adiminished seventh chord with extensions of a flatted seventh, flat-ted ninth, flatted eleventh, and natural thirteenth. On these chordsthe extensions clash with the diminished seventh chord below.However, if the flatted eleventh is repositioned as the major third,and the minor third raised an octave to the position of sharpednine, this chord can be viewed as a dominant thirteenth, flat/sharped nine, sharped eleventh. The author likes to refer to thischord as the diminished dominant chord. It is a very commonsound in jazz harmony:

80

Diminished Scale Harmony

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The next figure shows all eight of the diatonic chords of the C diminished scale, four diminished seventh chords and fourdiminished dominant seventh chords:

As can be seen in the above figure the root of the diminisheddominant seventh chord aligns itself with the half/whole stepalignment of the diminished scale. A diminished scale starting withthe half step (as opposed to the whole step) is often referred to asthe “auxiliary” diminished scale. The author prefers the term“diminished dominant scale.” A great example of this diminisheddominant chord/scale can be found in the Horace Silver composi-tion Barbara.

The four major and minor triads found in the diminished scalecan be used as upper structures for the diminished dominantchords. This translates into the common slash chord and poly-chord voicings for the diminished dominant chord of ¥III/I, ¥V/I,and VI/I, the bottom note representing either a bass note or a dominant seventh chord.

Major triad upper structures derived from C diminished dominant:

Note that these diminished dominant chords are derived fromthe C diminished dominant scale, making them diatonic to the Cµ,E, G, and B¥ diminished scales.

81

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The augmented harmonic system produces four six-note sym-metric scales based on the major third interval (three equal

divisions of the octave). Each scale is constructed by alternatingaugmented seconds and half steps, the sum of which is a majorthird. The scale may also be visualized as the juxtaposition of twoaugment triads an augmented second apart*:

The major third interval is composed of four semitones, each representing a starting tone for the scale. The augmented scale pattern built on the fifth semitone is identical to that of the first,therefore there is a total of four transpositions of the augmentedscale system.

The four augmented scales*:

84

AugmentedSystem

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C augmented triad

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(* Enharmonic spellings are used for simplification)

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The augmented scale does not contain the tritone interval; there-fore, unlike the diminished and whole-tone symmetric scales, it isnot a dominant scale. However, use of the augmented scale neednot be limited to the augmented major seventh chord; its use maybe broadened to include any chord containing an augmented triador augmented major seventh upper structure. Since the melodicminor harmonic system and the augmented scale both share anaugmented major seventh, augmented scales can be used as exoticsubstitutes for the melodic minor chord/scales, including thedominant scales:

86

Augmented Substitutions

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Melodic minor mode Augmented scale

* Does not share augmented major seventh, butsubstitutes well because of other common tones.

Ionian¥3

Phrygian∂6

Lydianµ5

Lydian¥7

Mixolydian¥6

Locrian ∂2

Locrian ¥4 or*

The definition of a pentatonic scale can be expanded to include anyfive-note scale. Pentatonics of this type are often referred to asaltered pentatonics. Altered pentatonics contain half steps and tri-tones and are more dissonant than pure pentatonics. They haveless of the “built-in” melodic flexibility, but are very useful as“shapes” when improvising.

Altered pentatonics are created by altering one or more tones of apure pentatonic scale. Any alteration is possible, but the most com-mon alterations are the ¥3 (Dorian or minor 7¥5 pentatonic), the¥6 (major ¥6 pentatonic), the dominant7 (dominant 9 or minor 6pentatonic) and the ¥2 (major ¥2 pentatonic). These pentatonicsare illustrated in the following figure.

89

Altered Pentatonics

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¥6 alteration

¥7 alteration

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Component pentatonics

93

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Each mode has a minimal number of intervals which, along withthe root, provide the basic color of the mode. This combination

of primary color tones is not shared by any other mode. The un-altered modes each contain two primary color tones. The alteredmodes contain the same primary color tones as their unalteredcounter parts, along with the altered tone or tones as the third orfourth color tone. Example: Primary color tones of Dorian are ¥3and ∂6. Primary color tones of Dorian∂7 are ¥3, 6, and ∂7.

Primary color tones of the unaltered modes:

Ionian: 4, 7

Dorian: ¥3, 6

Phrygian: ¥2, 5

Lydian µ4, 7

Mixolydian 3, ¥7

Aeolian: ¥6, 2

Locrian ¥5, ¥2

APPENDIX APrimary Color Tones of the Modes

The following is a list of the most useful four-note grips. Thislist is not meant to be exhaustive. The author has limited this

list to those grips that make particularly strong chord voicings within their respective systems. Even so, the possibilities are many.

The grips are named for the type of seventh chord each repre-sents, and the chord quality of the grip should not be confusedwith the chord quality created when the grip is combined with abass note. Each grip is presented below followed by scales(s) fromwhich it can be derived. The roman numeral(s) represent the loca-tion of the grip within the parent scale. Any grip extracted from aparent scale provides a potential voicing for any of the modes ofthat scale.

98

APPENDIX DSummary of Upper Structures (Grips)

Grip Parent Scale and degree Spelling

Lydianadd3 major (IV)melodic minor (¥III)

Lydianadd5 major (IV)harmonic minor (¥VI)harmonic major (IV)

∆ major (I, IV)harmonic minor (¥VI)harmonic major (I)augmented (I, III, µV)

∆(µ5) melodic minor (¥III)harmonic minor (¥III)harmonic major (I, ¥VI)augmented (I, III, µV)

–∆ melodic minor (I)harmonic minor (I, ¥VI)harmonic major (IV)augmented (I, III, µV)

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99

Grip Parent scale and degree Spelling

–∆(µ5) harmonic minor (I)harmonic major (¥VI)diminished (I, ¥III, ¥V, ¥¥VII) augmented (I, III, µV)

∆(µ5)sus4 harmonic minor (I, ¥III))harmonic major (I)diminished (I, ¥III, ¥V, ¥¥VII)

o∆ harmonic minor (¥VI)harmonic major (¥VI)diminished (I, ¥III, ¥VI, ¥¥7)

–7 major (II, III, VI)harmonic minor (IV)

ø major (VII)melodic minor (II, VI, VII)harmonic minor (II, IV)harmonic major (II)diminished (II, IV, ¥VI, VII)

o7 harmonic minor (II, IV, ¥VI, VII)harmonic major (II, IV, ¥VI, VII)diminished (I, ¥III, ¥V, ¥¥VII)

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