Nuwell family

The nuwell family of rank-3 temperaments temper out the nuwell comma, 2430/2401.

Nuwell

Subgroup: 2.3.5.7

Comma list: 2430/2401

Mapping: [⟨1 0 3 1], ⟨0 1 3 2], ⟨0 0 -4 -1]]

mapping generators: ~2, ~3, ~18/7

Optimal ET sequence: 9, 22, 31, 53, 84, 137

Badness: 0.519 × 10^-3

Projection pair: 5 2401/486 to 2.3.7

Big brother

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120

Mapping: [⟨1 0 3 1 3], ⟨0 1 3 2 2], ⟨0 0 -4 -1 -2]]

Optimal ET sequence: 8d, 9, 22, 31, 53

Badness: 0.507 × 10^-3

Projection pairs: 5 2401/486 11 98/9 to 2.3.7

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 99/98, 121/120

Mapping: [⟨1 0 3 1 3 1], ⟨0 1 3 2 2 0], ⟨0 0 -4 -1 -2 2]]

Optimal ET sequence: 8d, 9, 22f, 31