# Passion family

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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

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

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

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

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

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