Trisedodge family

The trisedodge family tempers out the trisedodge comma, 30958682112/30517578125 = [19 10 -15⟩.

Temperaments discussed elsewhere include quindecic and decistearn.

Trisedodge

Subgroup: 2.3.5

Comma list: 30958682112/30517578125

Mapping: [⟨5 1 7], ⟨0 3 2]]

Mapping generators: ~144/125, ~864/625

POTE generator: ~25/24 = 74.0077

Badness: 0.252724

Countdown

Subgroup: 2.3.5.11

Comma list: 4000/3993, 6912/6875

Sval mapping: [⟨5 1 7 15], ⟨0 3 2 1]]

POTE generator: ~25/24 = 74.1247

Optimal GPV sequence: Template:Val list

RMS error: 0.3198 cents

Septimal trisedodge

Subgroup: 2.3.5.7

Comma list: 4000/3969, 110592/109375

Mapping: [⟨5 1 7 21], ⟨0 3 2 -3]]

POTE generator: ~25/24 = 74.9480

Badness: 0.137695

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1331/1323, 2560/2541

Mapping: [⟨5 1 7 21 15], ⟨0 3 2 -3 1]]

POTE generator: ~25/24 = 74.9401

Optimal GPV sequence: Template:Val list

Badness: 0.043508

Coblack

See also: Cloudy clan § Coblack

In addition to 126/125, the coblack temperament tempers out the cloudy comma, 16807/16384, which is the amount by which five septimal supermajor seconds (8/7) fall short of an octave.

Subgroup: 2.3.5.7

Comma list: 126/125, 16807/16384

Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]

POTE generator: ~21/20 = 73.044

Badness: 0.107282

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 245/242, 385/384

Mapping: [⟨5 1 7 14 15], ⟨0 3 2 0 1]]

POTE generator: ~21/20 = 73.264

Optimal GPV sequence: Template:Val list

Badness: 0.045070