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

Optimal tuning (POTE): ~144/125 = 1\5, ~25/24 = 74.0077

Optimal ET sequence: 15, 50, 65, 340c, 405c, 470c, 535c, 600c

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]]

Optimal tuning (POTE): ~55/48 = 1\5, ~25/24 = 74.1247

Optimal ET sequence: 15, 35, 50, 65, 210e, 275e, 340ce

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]]

Optimal tuning (POTE): ~144/125 = 1\5, ~25/24 = 74.9480

Optimal ET sequence: 15, 50d, 65d, 80

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]]

Optimal tuning (POTE): ~55/48 = 1\5, ~25/24 = 74.9401

Optimal ET sequence: 15, 50d, 65d, 80

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]]

Optimal tuning (POTE): ~8/7 = 1\5, ~21/20 = 73.044

Optimal ET sequence: 15, 35, 50, 65, 115d

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]]

Optimal tuning (POTE): ~8/7 = 1\5, ~21/20 = 73.264

Optimal ET sequence: 15, 35, 50, 65, 115d

Badness: 0.045070