User:Francium/Miscellaneous rank-3 temperaments: Difference between revisions
Created page with "On this page, I explore some unnamed rank-3 temperaments that catched my interest. == 31 & 53 & 227 == Subgroup: 2.3.5.7 Comma list: 65625/65536 Mapping: <br> {| class="ri..." |
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Badness: 0.761 | Badness: 0.761 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 385/384, 3388/3375 | |||
Mapping: <br> | |||
{| class="right-all" | |||
| [⟨ || 1 || 0 || 1 || 11 || -5 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 1 || -6 || 6 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 2 || -10 || 8 || ], | |||
|} | |||
CTE generators: ~2 = 1200.2769, ~3 = 1902.4434, ~175/192 = -157.9651 | |||
{{Optimal ET sequence|legend=1|9, 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee}} | |||
Badness: 0.771 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 385/384, 352/351, 1001/1000 | |||
Mapping: <br> | |||
{| class="right-all" | |||
| [⟨ || 1 || 0 || 1 || 11 || -5 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 1 || -6 || 6 || 3 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 2 || -10 || 8 || 8 || ], | |||
|} | |||
CTE generators: ~2 = 1200.1146, ~3 = 1902.7798, ~175/192 = -158.3562 | |||
{{Optimal ET sequence|legend=1|9f, 22, 31, 53, 84e, 87, 118, 140, 258e}} | |||
Badness: 0.986 | |||
Revision as of 17:36, 22 August 2024
On this page, I explore some unnamed rank-3 temperaments that catched my interest.
31 & 53 & 227
Subgroup: 2.3.5.7
Comma list: 65625/65536
Mapping:
| [⟨ | 1 | 0 | 1 | 11 | ], |
| ⟨ | 0 | 1 | 1 | -6 | ], |
| ⟨ | 0 | 0 | 2 | -10 | ], |
CTE generators: ~2 = 1200.0937, ~3 = 1901.9403, ~175/192 = -157.9391
Optimal ET sequence: 9, 19d, 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd
Badness: 0.761
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375
Mapping:
| [⟨ | 1 | 0 | 1 | 11 | -5 | ], |
| ⟨ | 0 | 1 | 1 | -6 | 6 | ], |
| ⟨ | 0 | 0 | 2 | -10 | 8 | ], |
CTE generators: ~2 = 1200.2769, ~3 = 1902.4434, ~175/192 = -157.9651
Optimal ET sequence: 9, 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee
Badness: 0.771
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 352/351, 1001/1000
Mapping:
| [⟨ | 1 | 0 | 1 | 11 | -5 | 0 | ], |
| ⟨ | 0 | 1 | 1 | -6 | 6 | 3 | ], |
| ⟨ | 0 | 0 | 2 | -10 | 8 | 8 | ], |
CTE generators: ~2 = 1200.1146, ~3 = 1902.7798, ~175/192 = -158.3562
Optimal ET sequence: 9f, 22, 31, 53, 84e, 87, 118, 140, 258e
Badness: 0.986