User:AthiTrydhen/11-Hendrix diamond: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>FREEZE No edit summary |
AthiTrydhen (talk | contribs) m AthiTrydhen moved page 11-Hendrix diamond to User:AthiTrydhen/11-Hendrix diamond |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
The '''11- | The '''11-Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 45: | Line 45: | ||
| | 1/1 | | | 1/1 | ||
|} | |} | ||
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== | ||
| Line 55: | Line 55: | ||
===Orbits and Invariant Subsets=== | ===Orbits and Invariant Subsets=== | ||
[to be included] | [to be included] | ||
[[Category:Diamond]] | |||
[[Category:Hendrix]] | |||
Latest revision as of 05:47, 14 December 2024
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]