User:AthiTrydhen/11-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 1/1:5/4:11/8:3/2:11/6 is a 15-limit [[anomalous saturated suspension]]. | ||
==Symmetry group== | ==Symmetry group== | ||
Revision as of 15:17, 5 December 2020
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]