# Wesley family

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The wesley family of rank-2 temperaments tempers out the wesley comma, 78125/73728. The wesley comma is unchanged in Wesley Woolhouse's 7/26-comma meantone – it is an eigenmonzo (i.e. unchanged-interval). Here is a talk by Gene Ward Smith.

## Wesley

Subgroup: 2.3.5

Comma list: 78125/73728

Mapping[1 4 3], 0 -7 -2]]

mapping generators: ~2, ~125/96

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 414.509

Optimal ET sequence3, …, 23, 26, 29, 55c

Badness: 0.247718

## Septimal wesley

Subgroup: 2.3.5.7

Comma list: 405/392, 875/864

Mapping[1 4 3 8], 0 -7 -2 -15]]

Wedgie⟨⟨7 2 15 -13 4 29]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.519

Badness: 0.095344

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 875/864

Mapping: [1 4 3 8 9], 0 -7 -2 -15 -16]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769

Badness: 0.049066

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 78/77, 99/98, 325/324

Mapping: [1 4 3 8 9 12], 0 -7 -2 -15 -16 -24]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645

Badness: 0.038402

## Snipes

Subgroup: 2.3.5.7

Comma list: 225/224, 6125/5832

Mapping[1 4 3 9], 0 -7 -2 -18]]

Wedgie⟨⟨7 2 18 -13 9 36]]

Optimal tuning (POTE): ~2 = 1\1, ~35/27 = 413.513

Badness: 0.117943

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 225/224, 245/242

Mapping: [1 4 3 9 10], 0 -7 -2 -18 -19]]

Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490

Badness: 0.054296

## Roman

See also: Avicennmic temperaments #Roman

### 7-limit a.k.a. crusher

Subgroup: 2.3.5.7

Comma list: 525/512, 3125/3024

Mapping[1 4 3 -1], 0 -7 -2 11]]

Wedgie⟨⟨7 2 -11 -13 -37 -31]]

Optimal tuning (POTE): ~2 = 1\1, ~63/50 = 414.552

Badness: 0.113386

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 525/512

Mapping: [1 4 3 -1 0], 0 -7 -2 11 10]]

Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.471

Badness: 0.052841

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/64, 100/99, 105/104, 245/242

Mapping: [1 4 3 -1 0 3], 0 -7 -2 11 10 2]]

Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.472

Badness: 0.030043

## Dubbla

Subgroup: 2.3.5.7

Comma list: 50/49, 78125/73728

Mapping[2 1 4 5], 0 7 2 2]]

Wedgie⟨⟨14 4 4 -26 -33 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~192/175 = 185.738

Badness: 0.181726

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 125/121, 1344/1331

Mapping: [2 1 4 5 6], 0 7 2 2 3]]

Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879

Badness: 0.075842

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 105/104, 125/121, 144/143

Mapping: [2 1 4 5 6 4], 0 7 2 2 3 11]]

Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.702

Badness: 0.049603