User:Eliora/Leaves

Leaves

Defined as the 323 & 2023 temperament. 2 generators reach 17/13, 7 generators reach 5/4, 10 generators produce 13/11.

Subgroup: 2.3.5.7

Comma list: 1729951171875/1727094849536, [10 39 -14 -14⟩

Mapping: [⟨17 10 31 9], ⟨0 14 7 32]]

mapping generators: ~25/24, ~6125/5832

Optimal tunings:

• CTE: ~25/24 = 70.588 ¢, ~6125/5832 = 85.427 ¢
• CWE: ~25/24 = 70.588 ¢, ~6125/5832 = 85.426 ¢

Optimal ET sequence: 323, 1700d, 2023, 2346

Badness (Sintel): 32.032

11-limit

Subgroup: 2.3.5.7.11

Comma list: 160083/160000, 198359290368/198165034375, 1729951171875/1727094849536

Mapping: [⟨17 10 31 9 106], ⟨0 14 7 32 -39]]

Optimal tunings:

• CTE: ~25/24 = 70.588 ¢, ~6125/5832 = 85.421 ¢
• CWE: ~25/24 = 70.588 ¢, ~6125/5832 = 85.420 ¢

Optimal ET sequence: 323, 1700d, 2023, 2346e

Badness (Sintel): 20.456

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 160083/160000, 928125/927472, 1990656/1990625, 4831530/4826809

Mapping: [⟨17 10 31 9 106 98], ⟨0 14 7 32 -39 -29]]

Optimal tunings:

• CTE: ~25/24 = 70.588 ¢, ~1024/975 = 85.421 ¢
• CWE: ~25/24 = 70.588 ¢, ~1024/975 = 85.420 ¢

Optimal ET sequence: 323, 1700d, 2023, 2346e

Badness (Sintel): 10.096

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 39325/39304, 57375/57344, 71874/71825, 111537/111475, 140800/140777

Mapping: [⟨17 10 31 9 106 98 107], ⟨0 14 7 32 -39 -29 -31]]

Optimal tunings:

• CTE: ~25/24 = 70.588 ¢, ~765/728 = 85.421 ¢
• CWE: ~25/24 = 70.588 ¢, ~765/728 = 85.421 ¢

Optimal ET sequence: 323, 1700d, 2023, 2346e

Badness (Sintel): 6.678