Fifive family

The fifive family tempers out the fifive comma, 9765625/9565938 = [-1 -14 10.

Considered below are crepuscular, fifives, and fourfives.

Fifive

Subgroup: 2.3.5

Comma list: 9765625/9565938

Mapping[2 2 3], 0 5 7]]

mapping generators: ~78125/50421, ~27/25
• CTE: ~78125/50421 = 1\2, ~27/25 = 140.6349
• POTE: ~78125/50421 = 1\2, ~27/25 = 140.624
• Smith: 0.205812
• Dirichlet: 4.828

2.3.5.13 subgroup

Subgroup: 2.3.5.13

Comma list: 325/324, 20000/19773

Mapping: [2 2 3 6], 0 5 7 6]]

mapping generators: ~351/250, ~13/12

Optimal tunings:

• CTE: ~351/250 = 1\2, ~13/12 = 140.5685
• CWE: ~351/250 = 1\2, ~13/12 = 140.6232

Optimal ET sequence: 8, 18bcf, 26, 34, 94, 128

• Smith: 0.0240
• Dirichlet: 0.800

2.3.5.13.17 subgroup

Subgroup: 2.3.5.13.17

Comma list: 170/169, 289/288, 325/324

Mapping: [2 2 3 6 7], 0 5 7 6 5]]

mapping generators: ~17/12, ~13/12

Optimal tunings:

• CTE: ~17/12 = 1\2, ~13/12 = 140.5958
• CWE: ~17/12 = 1\2, ~13/12 = 140.6057

Optimal ET sequence: 8, 18bcfg, 26, 34, 94, 128

• Smith: 0.0110
• Dirichlet: 0.488

Crepuscular

Subgroup: 2.3.5.7

Comma list: 50/49, 4375/4374

Mapping[2 2 3 4], 0 5 7 7]]

Wedgie⟨⟨10 14 14 -1 -6 -7]]

Optimal tuning (POTE): ~7/5 = 1\2, ~27/25 = 140.349

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 864/847

Mapping: [2 2 3 4 6], 0 5 7 7 4]]

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 78/77, 99/98, 144/143

Mapping: [2 2 3 4 6 6], 0 5 7 7 4 6]]

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 50/49, 78/77, 85/84, 99/98, 144/143

Mapping: [2 2 3 4 6 6 7], 0 5 7 7 4 6 5]]

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405

Fifives

Subgroup: 2.3.5.7

Comma list: 875/864, 83349/81920

Mapping[2 2 3 7], 0 5 7 -6]]

Optimal tuning (POTE): ~567/400 = 1\2, ~27/25 = 139.909

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 3969/3872

Mapping: [2 2 3 7 6], 0 5 7 -6 4]]

Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 144/143, 1352/1331

Mapping: [2 2 3 7 6 6], 0 5 7 -6 4 6]]

Optimal tuning (POTE): ~55/39 = 1\2, ~12/11 = 139.867

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 100/99, 105/104, 144/143, 170/169, 221/220

Mapping: [2 2 3 7 6 6 7], 0 5 7 -6 4 6 5]]

Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868

Fourfives

Subgroup: 2.3.5.7

Comma list: 245/243, 235298/234375

Mapping[4 4 6 7], 0 5 7 9]]

mapping generators: ~25/21, ~27/25

Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.754

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 235298/234375

Mapping: [4 4 6 7 19], 0 5 7 9 -11]]

Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 385/384, 20000/19773

Mapping: [4 4 6 7 19 12], 0 5 7 9 -11 6]]

Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.760

Subgroup: 2.3.5.7.11

Comma list: 121/120, 245/243, 1375/1372

Mapping: [4 4 6 7 11], 0 5 7 9 6]]

Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 196/195, 245/243, 275/273

Mapping: [4 4 6 7 11 12], 0 5 7 9 6 6]]

Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.728