User:Francium/Miscellaneous rank-3 temperaments
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
31 & 311 & 431
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 2401/2400, 190512/190333
Mapping:
| [⟨ | 1 | 1 | 5 | 4 | 4 | 1 | ], |
| ⟨ | 0 | 2 | 5 | 3 | 7 | -12 | ], |
| ⟨ | 0 | 0 | 8 | 4 | 5 | -12 | ], |
CTE generators: ~2 = 1199.9603, ~49/40 = 350.9859, ~63/44 = 621.0427
Optimal ET sequence: 31, 58f, 89, 120, 191, 222f, 280, 311, 400, 711, 742, 1053, 1453
Badness: 2.258
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 4096/4095, 2401/2400, 14400/14399, 11016/11011
Mapping:
| [⟨ | 1 | 1 | 5 | 4 | 4 | 1 | 6 | ], |
| ⟨ | 0 | 2 | 5 | 3 | 7 | -12 | -3 | ], |
| ⟨ | 0 | 0 | 8 | 4 | 5 | -12 | 2 | ], |
CTE generators: ~2 = 1199.9677, ~49/40 = 350.9737, ~63/44 = 621.0347
Optimal ET sequence: 31, 58f, 89, 120g, 191g, 222f, 280, 311, 400, 711, 742, 1453, 2195ef
Badness: 1.410
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2926/2925, 4096/4095, 3136/3135, 5985/5984, 11016/11011
Mapping:
| [⟨ | 1 | 1 | 5 | 4 | 4 | 1 | 6 | 4 | ], |
| ⟨ | 0 | 2 | 5 | 3 | 7 | -12 | -3 | -8 | ], |
| ⟨ | 0 | 0 | 8 | 4 | 5 | -12 | 2 | -5 | ], |
CTE generators: ~2 = 1199.9748, ~49/40 = 350.9675, ~63/44 = 621.0343
Optimal ET sequence: 31, 58f, 89, 120g, 191g, 222f, 280, 311, 400, 653f, 711, 742, 1453, 1795f, 2195ef
Badness: 1.069
37 & 109 & 577
Subgroup: 2.5.7.11
Comma list: 102487/102400
Mapping:
| [⟨ | 1 | 0 | 4 | 2 | ], |
| ⟨ | 0 | 1 | 6 | -1 | ], |
| ⟨ | 0 | 0 | 8 | -2 | ], |
CTE generators: ~2 = 1200.048, ~5/4 = 386.260, ~11/8 = 550.980
Optimal ET sequence: 7, 11cd, 13, 15, 22, 35, 37, 72, 109, 233, 270, 342, 379, 612, 1333, 1603, 1945e, 2557e, 2936e, 3548ee
Badness: 0.189
13-limit
Subgroup: 2.5.7.11.13
Comma list: 1001/1000, 6656/6655
Mapping:
| [⟨ | 1 | 0 | 4 | 2 | -3 | ], |
| ⟨ | 0 | 1 | 6 | -1 | -2 | ], |
| ⟨ | 0 | 0 | 8 | -2 | -6 | ], |
CTE generators: ~2 = 1200.021, ~5/4 = 386.630, ~11/8 = 551.170
Optimal ET sequence: 11cdf, 13, 15, 22, 35f, 37, 87, 109, 124, 161, 196, 233, 270, 503, 627, 664, 897, 1167
Badness: 0.177