Gann 8x8

The 8x8 scale, or Gann 8x8, is a 13-limit just intonation scale with 33 pitches per octave, developed by Kyle Gann and used in his cycle Hyperchromatica for three player pianos.

The scale is formed by taking the first eight odd harmonics (1, 3, 5, 7, 9, 11, 13, and 15), and then taking the first eight odd harmonics of each of those pitches.

! Gann_8x8.scl
!
! Harmonics 8-16, reproduced on harmonics 8-16 (or 15-odd-limit order-2 otonal heterodyne)
!
Kyle Gann, 8x8 Scale ("Nursery Tunes for Demented Children", "Hyperchromatica")
33
!
65/64
33/32
135/128
35/32
143/128
9/8
75/64
77/64
39/32
5/4
81/64
165/128
21/16
169/128
11/8
45/32
91/64
3/2
195/128
49/32
99/64
25/16
13/8
105/64
27/16
55/32
7/4
225/128
117/64
15/8
121/64
63/32
2/1