User:AthiTrydhen/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 1/1:7/6:5/4:3/2:7/4 is a 15-limit [[anomalous saturated suspension]]. | ||
==Symmetry group== | ==Symmetry group== | ||
Revision as of 15:19, 5 December 2020
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]