Mint family

The mint family of rank-3 temperaments tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.

Mint

Period: 1\1

Optimal (POTE) generators: ~3/2 = 698.6351, ~5/4 = 404.2809

EDO generators: (2, 1)\4, (3, 2)\5, (7, 4)\12

Scales:

Technical data

Comma list: 36/35

Mapping: [⟨1 0 0 2], ⟨0 1 0 2], ⟨0 0 1 -1]]

Badness: 0.0637 × 10^-3

Nickel

Period: 1\1

Optimal (POTE) generators: ~3/2 = 688.8370, ~5/4 = 391.8801

EDO generators: (4, 2)\7, (5, 3)\9, (7, 4)\12

Scales:

Technical data

Comma list: 36/35, 45/44

Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 2 2], ⟨0 0 1 -1 1]]

Badness: 0.463 × 10^-3

13-limit

Period: 1\1

Optimal (POTE) generators: ~3/2 = 685.0048, ~5/4 = 390.2563

EDO generators: (4, 2)\7, (5, 3)\9, (7, 4)\12

Scales:

Technical data

Comma list: 27/26, 36/35, 45/44

Mapping: [⟨1 0 0 2 -2 -1], ⟨0 1 0 2 2 3], ⟨0 0 1 -1 1 0]]

Badness: 0.647 × 10^-3