Hendrix diamond

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The Hendrix diamond is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.

1/1 7/6 5/4 3/2 7/4
12/7 1/1 15/14 9/7 3/2
8/5 28/15 1/1 6/5 7/5
4/3 14/9 5/3 1/1 7/6
8/7 4/3 10/7 12/7 1/1

All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:7/6:5/4:3/2:7/4 is a 15-limit anomalous saturated suspension.

Symmetry group

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

  • 3:2, 5:4, 7:4 → 7:6, 5:3, 14:9
  • 3:2, 5:4, 7:4 → 3:2, 15:14, 9:7
  • 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7

Orbits and Invariant Subsets

[to be included]