Trisedodge family
The trisedodge family tempers out the trisedodge comma, 30958682112/30517578125 = [19 10 -15⟩.
Trisedodge
Subgroup: 2.3.5
Comma list: 30958682112/30517578125
Mapping: [⟨5 7 11], ⟨0 3 2]]
POTE generator: ~25/24 = 74.0077
7-limit
Subgroup: 2.3.5.7
Comma list: 4000/3969, 110592/109375
Mapping: [⟨5 7 11 15], ⟨0 3 2 -3]]
POTE generator: ~25/24 = 74.9480
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 2560/2541
Mapping: [⟨5 7 11 15 17], ⟨0 3 2 -3 1]]
POTE generator: ~25/24 = 74.9401
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
POTE generator: ~21/20 = 73.044
Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]
Badness: 0.1073
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
POTE generator: ~21/20 = 73.264
Mapping: [⟨5 1 7 14 15], ⟨0 3 2 0 1]]
Quindecic
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 49/48, 55/54, 77/75
Map: [⟨15 24 35 42 52 0], ⟨0 0 0 0 0 1]]
POTE generator: ~66/65 = 27.0764