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