Quintosec family
The qintosec family tempers out the qintosec comma, 140737488355328/140126044921875 = [47 -15 -10⟩.
Qintosec
Subgroup: 2.3.5
Comma: 140737488355328/140126044921875
Mapping: [⟨5 1 22], ⟨0 2 -3]]
Mapping generators: ~524288/455625, ~16384/10125
POTE generator: ~16/15 = 111.105
Badness: 0.139191
Septimal qintosec
The qintosec temperament can be described as 10&65d temperament, tempering out the marvel comma, 225/224 in the 7-limit.
Subgroup: 2.3.5.7
Comma list: 225/224, 2560000/2470629
Mapping: [⟨5 1 22 21], ⟨0 2 -3 -2]]
Wedgie: ⟨⟨ 10 -15 -10 -47 -44 19 ]]
POTE generator: ~15/14 = 111.553
Badness: 0.156764
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 3840/3773
Mapping: [⟨5 1 22 21 0], ⟨0 2 -3 -2 5]]
POTE generator: ~15/14 = 111.311
Vals: Template:Val list
Badness: 0.077907
Qinto
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 332750/321489
Mapping: [⟨5 1 22 21 -7], ⟨0 2 -3 -2 7]]
POTE generator: ~15/14 = 112.448
Vals: Template:Val list
Badness: 0.127732
Sengasec
The sengasec temperament (10&55) tempers out the cloudy comma, 16807/16384 and the sengic comma, 686/675 in the 7-limit.
Subgroup: 2.3.5.7
Comma list: 686/675, 16807/16384
Mapping: [⟨5 1 22 14], ⟨0 2 -3 0]]
POTE generator: ~16/15 = 111.113
Badness: 0.156259
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384, 686/675
Mapping: [⟨5 1 22 14 0], ⟨0 2 -3 0 5]]
POTE generator: ~16/15 = 110.659
Vals: Template:Val list
Badness: 0.081607
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 243/242, 686/675
Mapping: [⟨5 1 22 14 0 22], ⟨0 2 -3 0 5 -1]]
POTE generator: ~16/15 = 110.910
Vals: Template:Val list
Badness: 0.056390
Decoid
Subgroup: 2.3.5.7
Comma list: 2401/2400, 67108864/66976875
Mapping: [⟨10 0 47 36], ⟨0 2 -3 -1]]
Mapping generators: ~15/14, ~8192/4725
Wedgie: ⟨⟨ 20 -30 -10 -94 -72 61 ]]
POTE generator: ~16/15 = 111.099
Badness: 0.033902
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 5632/5625, 9801/9800
Mapping: [⟨10 0 47 36 98], ⟨0 2 -3 -1 -8]]
POTE generator: ~16/15 = 111.070
Vals: Template:Val list
Badness: 0.018735
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
Mapping: [⟨10 0 47 36 98 37], ⟨0 2 -3 -1 -8 0]]
POTE generator: ~16/15 = 111.083
Vals: Template:Val list
Badness: 0.013475