Dimcomp family

The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, 390625/388962.

Dimcomp

Subgroup: 2.3.5.7

Comma list: 390625/388962

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

mapping generators: ~25/21, ~3, ~5

Optimal ET sequence: 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952

Badness: 0.783 × 10^-3

Undecimal dimcomp

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 6250/6237

Mapping: [⟨4 0 0 -1 5], ⟨0 1 0 -1 -3], ⟨0 0 1 2 3]]

Optimal ET sequence: 68, 72, 140, 152, 224, 364, 436, 588

Badness: 0.624 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1375/1372, 2080/2079

Mapping: [⟨4 0 0 -1 5 -16], ⟨0 1 0 -1 -3 -1], ⟨0 0 1 2 3 4]]

Optimal ET sequence: 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c

Badness: 0.820 × 10^-3

Octopod

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 1375/1372, 4000/3993

Mapping: [⟨8 1 3 3 16 0], ⟨0 3 4 5 3 0], ⟨0 0 0 0 0 1]]

Optimal ET sequence: 72, 144, 152f, 224, 824d

Badness: 1.244 × 10^-3