Passion family

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The passion family tempers out 262144/253125 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

POTE generator: ~16/15 = 98.670

Vals12, 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]]

Mapping generators: 2, 16/15

Wedgie⟨⟨5 -4 -10 -18 -30 -12]]

POTE generator: ~16/15 = 98.153

Vals12, 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]]

POTE generator: ~16/15 = 98.019

Vals: 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]]

POTE generator: ~16/15 = 97.910

Vals: 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]]

POTE generator: ~16/15 = 98.817

Vals12, 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]]

POTE generator: ~16/15 = 98.721

Vals: 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]]

POTE generator: ~16/15 = 98.627

Vals: 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]]

POTE generator: ~16/15 = 98.791

Vals: 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]]

POTE generator: ~16/15 = 98.809

Vals1, 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

POTE generator: ~48/35 = 550.9374

Vals13d, 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]]

POTE generator: ~11/8 = 550.9007

Vals: 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]]

POTE generator: ~11/8 = 550.9062

Vals: 13d, 24, 37, 61

Badness: 0.045864