The diminished harmonic system produces three eight-note

Transcription

1 Diminished System Diminished Scale Construction The diminished harmonic system produces three eight-note symmetric scales ased on the minor third interval (four equal divisions of the octave). Each scale is constructed y alternating hole and half steps, the sum of hich is a minor third. Each diminished scale may also e visualized as to minor tetrachords divided y a half step, to diminished seventh chords a hole step apart, or four major/minor triads a minor third appart. The diminished scale uilt on C: 1/2 1 1/2 1 1/2 1 1/2 1 ( ) C minor tetrachord F minor tetrachord D diminished 7th C diminished 7th Four major/minor triads (enharmonic spellings used for simplification): ( n) ( ) ( ) ( n) 78

2 The symmetry of the diminished system is ased on the minor third interval (the sum of the hole step half step repeating pattern). Each of the three semitones ithin the minor third interval is a possile starting tone for the scale. The scale uilt on the fourth semitone is identical to the first, confirming the three transpositions of the diminished system. Like all symmetric scales, the diminished scale is nonmodal. In addition to the major/minor triads, four diminished seventh chords and four dominant seventh chords, each separated y the interval of a minor third, are diatonic to each diminished scale. These chord qualities are unique to the diminished system and are presented in depth in the folloing section on diminished scale harmony. A chart shoing the three diminished scales and their respective diminished seventh and dominant seventh chords. C C D E E F scales F G G A B B C o 7 Eo7 F o7 A o7 C o7 E o7 G o 7 Bo7 D o 7 F o 7 G o7 B o7 chords A 7( 9) B7( 9) D7( 9) F7( 9) A7( 9) C7( 9) E 7( 9) F 7( 9) B 7( 9) D 7( 9) E7( 9) G7( 9) 79

3 Diminished Scale Harmony Each degree of the diminished scale produces a diminished seventh chord. The first, third, fifth, and seventh scale degrees of the scale produce a diminished seventh chord ith extensions of a major seventh, 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 seventh chord ith complete extensions is sometimes referred to as a doule diminished chord: B o 7 Co7 The second, fourth, sixth, and eight scale degrees produce a diminished seventh chord ith extensions of a flatted seventh, flatted ninth, flatted eleventh, and natural thirteenth. On these chords the extensions clash ith the diminished seventh chord elo. Hoever, if the flatted eleventh is repositioned as the major third, and the minor third raised an octave to the position of sharped nine, this chord can e vieed as a dominant thirteenth, flat/ sharped nine, sharped eleventh. The author likes to refer to this chord as the diminished dominant chord. It is a very common sound in jazz harmony: = root 80

4 The next figure shos all eight of the diatonic chords of the C diminished scale, four diminished seventh chords and four diminished dominant seventh chords: ) D7 ( 9 11 Co ( 9 9 ) 11 Eo ( N ) F7 ( 9 9 ) F o ( 11 N ) G 7 ( 9 9 ) 11 Ao ( ) B7 ( 9 9 ) As can e seen in the aove figure the root of the diminished dominant seventh chord aligns itself ith the half/hole step alignment of the diminished scale. A diminished scale starting ith the half step (as opposed to the hole step) is often referred to as the auxiliary diminished scale. The author prefers the term diminished dominant scale. A great example of this diminished dominant chord/scale can e found in the Horace Silver composition Barara. The four major and minor triads found in the diminished scale can e used as upper structures for the diminished dominant chords. This translates into the common slash chord and polychord voicings for the diminished dominant chord of III/I, V/I, and VI/I, the ottom note representing either a ass note or a dominant seventh chord. Major triad upper structures derived from C diminished dominant:? E C7 ( III ) G ( ) A ( ) I7 C7 V I7 C7 VI I7 Note that these diminished dominant chords are derived from the C diminished dominant scale, making them diatonic to the Cµ, E, G, and B diminished scales. 81

5 Augmented System The augmented harmonic system produces four six-note symmetric scales ased on the major third interval (three equal divisions of the octave). Each scale is constructed y alternating augmented seconds and half steps, the sum of hich is a major third. The scale may also e visualized as the juxtaposition of to augment triads an augmented second apart*: aug 2 m 2 aug 2 m 2 aug 2 m 2 ( ) D augmented triad C augmented triad ( ) The major third interval is composed of four semitones, each representing a starting tone for the scale. The augmented scale pattern uilt on the fifth semitone is identical to that of the first, therefore there is a total of four transpositions of the augmented scale system. The four augmented scales*: C D D E scales E F F G A A B B chords C + E + A + D + F + A + D + F + B + E + G + B + (* Enharmonic spellings are used for simplification) 84

6 Augmented Sustitutions Melodic minor mode The augmented scale does not contain the tritone interval; therefore, unlike the diminished and hole-tone symmetric scales, it is not a dominant scale. Hoever, use of the augmented scale need not e limited to the augmented major seventh chord; its use may e roadened to include any chord containing an augmented triad or augmented major seventh upper structure. Since the melodic minor harmonic system and the augmented scale oth share an augmented major seventh, augmented scales can e used as exotic sustitutes for the melodic minor chord/scales, including the dominant scales: Augmented scale Ionian 3 or Phrygian 6 Lydianµ5 Lydian 7 n Mixolydian 6 Locrian 2 Locrian 4 or* * Does not share augmented major seventh, ut sustitutes ell ecause of other common tones. 86

7 The definition of a pentatonic scale can e expanded to include any five-note scale. Pentatonics of this type are often referred to as altered pentatonics. Altered pentatonics contain half steps and tritones and are more dissonant than pure pentatonics. They have less of the uilt-in melodic flexiility, ut are very useful as shapes hen improvising. Altered pentatonics are created y altering one or more tones of a pure pentatonic scale. Any alteration is possile, ut the most common alterations are the 3 (Dorian or minor 7 5 pentatonic), the 6 (major 6 pentatonic), the dominant7 (dominant 9 or minor 6 pentatonic) and the 2 (major 2 pentatonic). These pentatonics are illustrated in the folloing figure. Altered Pentatonics 3 alteration Dorian pentatonic (minor 7 5 pentatonic) 6 alteration major 6 pentatonic 7 alteration dominant 9 pentatonic (minor 6 pentatonic) 2 alteration major 2 pentatonic (dominant µ9 pentatonic) 89

8 C harmonic minor scale Component pentatonic F Dorian ( D ø ) C harmonic major scale Component pentatonics C( 6) G( 2) (E7µ9) F Dorian (D ø ) C diminished scale Component pentatonics n n D( 2) B7( 9) F( 2) D7( 9) A ( 2) F7( 9) B( 2) A 7( 9) 91

9 Some typical lues phrases: q» º 4 E7( 9) J œ^ œ^ œ> œ œ œ œ œ œ œ œ^ œ^ œ^ œ œ œ œ œ^ œ q» º 4 E 7 œ œ œ œ - œ - œ - œ œœ œ œ œ œ œ œ Œ Œ 3 œ œ œ œ - œ - œ - œ œ. œ œ œ œ œ œ œ} Œ œ - œ - œ- œ œ œ œ œ œ œ œ œ - œ^ œ - œ^ œ^ œ^ œ- œ^ œ^ œ J - œ^ J Œ œ œ œ œ ( ) œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ^ œ œ œ œ œ 4 4 A7 Ó œ œ œ œ œ œ œ œ œ œ 3 E7 œ œ œ œ œ œ œ œ œ œ œ 93

10 APPENDIX A Primary Color Tones of the Modes Each mode has a minimal numer of intervals hich, along ith the root, provide the asic color of the mode. This comination of primary color tones is not shared y any other mode. The unaltered modes each contain to primary color tones. The altered modes contain the same primary color tones as their unaltered counter parts, along ith the altered tone or tones as the third or fourth color tone. Example: Primary color tones of Dorian are 3 and 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 95

11 APPENDIX D Summary of Upper Structures (Grips) The folloing is a list of the most useful four-note grips. This list is not meant to e exhaustive. The author has limited this list to those grips that make particularly strong chord voicings ithin their respective systems. Even so, the possiilities are many. The grips are named for the type of seventh chord each represents, and the chord quality of the grip should not e confused ith the chord quality created hen the grip is comined ith a ass note. Each grip is presented elo folloed y scales(s) from hich it can e derived. The roman numeral(s) represent the location of the grip ithin the parent scale. Any grip extracted from a parent scale provides a potential voicing for any of the modes of that scale. Grip Parent Scale and degree Spelling Lydianadd3 major (IV) melodic minor ( III) Lydian add3 Lydianadd5 major (IV) harmonic minor ( VI) harmonic major (IV) Lydian add5 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) ( 5) melodic minor (I) harmonic minor (I, VI) harmonic major (IV) augmented (I, III, µv) 98

12 Grip Parent scale and degree Spelling (µ5) harmonic minor (I) harmonic major ( VI) diminished (I, III, V, VII) augmented (I, III, µv) ( 5) (µ5)sus4 harmonic minor (I, III)) harmonic major (I) diminished (I, III, V, VII) ( 5)sus4 o harmonic minor ( VI) harmonic major ( VI) diminished (I, III, VI, 7) o 7 major (II, III, VI) harmonic minor (IV) 7 ø major (VII) melodic minor (II, VI, VII) harmonic minor (II, IV) harmonic major (II) diminished (II, IV, VI, VII) ø o 7 harmonic minor (II, IV, VI, VII) harmonic major (II, IV, VI, VII) diminished (I, III, V, VII) o7 99