Example 1. Jazz harmonies from Diatonic, Acoustic, Octatonic, and Hexatonic Collections

Example 1a. Harmonies from C Diatonic Collection
(D0 = C, D, E, F, G, A, B, C)

Cmaj7, Cmaj7/9, C6/9 etc.
Fmaj7(11)
Dmin7/9, Dmin7/9/11, Dmin7/9/11/13
Gdom7/9, Gdom7/9/13
G7sus
Fmaj7/A
 

Example 1b. Harmonies from F Acoustic Collection
(A5 = F, G, A, B, C, D, E, F)
(Some harmonies include pcset [0148]:
C, E, G, B or E, G, B, D)

F13(11)
CminM7, CminM7/9, CminM7/9/11, CminM7/9/11/13, Cmin6/9, etc.
Amin7/9(5), Amin7/9/11(5), Amin7/9/11/13(5)
B7 altered (= 9, 9, 11, 13)
Emaj7(5), Emaj7/9(5)
 

Example 1c. Harmonies from D/E Octatonic Collection
(Oct 2,3 = D, E, F, G, A, A, B, C, D)

D7(9), D13(9), D13(9/11)
F7(9), F13(9), F13(9/11)
A7(9), A13(9), A13(9/11)
B7(9), B13(9), B13(9/11)
Co maj7, Co9(maj7), Co11(maj7), Co 13(maj7)
Eo maj7, Eo9(maj7), Eo11(maj7), Eo 13(maj7)
Go maj7, Go9(maj7), Go11(maj7), Go 13(maj7)
Ao maj7, Ao9(maj7), Ao11(maj7), Ao 13(maj7)
 

Example 1d. [0148] Harmonies from B/C Hexatonic Collection
(H0 = B, C, E, E, G, A)

Bmaj7(5), Emaj7(5), Gmaj7(5)
CminM7, EminM7, AminM7
 

Example 1e. Specific Hexatonic Harmonies in Post-1960s Compositions

Amaj7(5/9): Wayne Shorter, “Vonetta”
Amaj7(5)/E: Chick Corea, “Song of the Wind”
EminM7/A: Corea, “Song of the Wind”
Amaj7(5/5): Shorter, “Iris”