Passion family
The passion family tempers out the passion comma, 262144/253125 = [18 -4 -5⟩ in the 5-limit, which equates five instances of 16/15 with 4/3.
Passion
Subgroup: 2.3.5
Comma list: 262144/253125
Mapping: [⟨1 2 2], ⟨0 -5 4]]
- mapping generators: ~2, ~16/15
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.670
Optimal ET sequence: 12, 49, 61, 73
Badness: 0.168550
Septimal passion
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/3087
Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]
Wedgie: ⟨⟨5 -4 -10 -18 -30 -12]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.153
Optimal ET sequence: 12, 37, 49, 110bcd
Badness: 0.062327
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1375/1372
Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.019
Optimal ET sequence: 12, 37, 49
Badness: 0.040809
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 196/195, 275/273
Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 97.910
Optimal ET sequence: 12f, 25f, 37, 49f
Badness: 0.030886
Passionate
Subgroup: 2.3.5.7
Comma list: 126/125, 131072/127575
Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]
Wedgie: ⟨⟨5 -4 -22 -18 -49 -40]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.817
Optimal ET sequence: 12, 61, 73, 85c
Badness: 0.121293
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 8192/8019
Mapping: [⟨1 2 2 1 1], ⟨0 -5 4 22 30]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.721
Optimal ET sequence: 12, 61, 73, 158bccee
Badness: 0.068322
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 343/338, 364/363
Mapping: [⟨1 2 2 1 1 1], ⟨0 -5 4 22 30 33]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.627
Optimal ET sequence: 12f, 61, 73f
Badness: 0.052302
Pash
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 1352/1331
Mapping: [⟨1 2 2 1 1 0], ⟨0 -5 4 22 30 45]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.791
Optimal ET sequence: 12f, 61f, 73, 85ce
Badness: 0.056386
Passive
Subgroup: 2.3.5.7
Comma list: 225/224, 256/245
Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.809
Optimal ET sequence: 1, 11, 12, 49dd
Badness: 0.075055
Freivald
Subgroup: 2.3.5.7
Comma list: 6144/6125, 6272/6075
Mapping: [⟨1 7 -2 12], ⟨0 -10 8 -17]]
- mapping generator: ~2, ~35/24
Optimal tuning (POTE): ~2 = 1\1, ~48/35 = 550.9374
Optimal ET sequence: 13d, 24, 37, 61, 98b
Badness: 0.209095
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2744/2673
Mapping: [⟨1 7 -2 12 4], ⟨0 -10 8 -17 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9007
Optimal ET sequence: 13d, 24, 37, 61
Badness: 0.077504
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 176/175, 512/507
Mapping: [⟨1 7 -2 12 4 1], ⟨0 -10 8 -17 -1 5]]
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9062
Optimal ET sequence: 13d, 24, 37, 61
Badness: 0.045864