13-Hendrix diamond

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The 13-'Hendrix diamond' is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.

1/1 13/12 5/4 3/2 13/8
24/13 1/1 15/13 18/13 3/2
8/5 26/15 1/1 6/5 13/10
4/3 13/9 5/3 1/1 13/12
16/13 4/3 20/13 24/13 1/1

All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:13/12:5/4:3/2:13/8 is a 15-limit anomalous saturated suspension.

Symmetry group

The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are:

  • 3:2, 5:4, 13:8 → 13:12, 5:3, 13:9
  • 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13
  • 3:2, 5:4, 13:8 → 4:3, 8:5, 16:13

Orbits and Invariant Subsets

[to be included]