User:AthiTrydhen/13-Hendrix diamond: Difference between revisions
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All notes in the Hendrix diamond are also found in the [[ | 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== | ==Symmetry group== | ||
Revision as of 15:18, 5 December 2020
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]