11-Hendrix diamond

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The 11-'Hendrix diamond' is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.

1/1 5/4 11/8 3/2 11/6
8/5 1/1 11/10 6/5 22/15
16/11 20/11 1/1 12/11 4/3
4/3 5/3 11/6 1/1 11/9
12/11 15/11 3/2 18/11 1/1

All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:5/4:11/8:3/2:11/6 is a 15-limit anomalous saturated suspension.

Symmetry group

The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:

  • 3:2, 5:4, 11:8 → 11:6, 5:3, 11:9
  • 3:2, 5:4, 11:8 → 3:2, 15:11, 18:11
  • 3:2, 5:4, 11:8 → 4:3, 8:5, 16:11

Orbits and Invariant Subsets

[to be included]