# Mint temperaments

These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.

## Progression

For the 5-limit version of this temperament, see High badness temperaments #Lafayette.

Subgroup: 2.3.5.7

Comma list: 36/35, 392/375

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

Wedgie⟨⟨5 3 7 -7 -3 8]]

POTE generator: ~15/14 = 140.927

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 77/75

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

POTE generators: ~12/11 = 140.747

Optimal GPV sequence: 8d, 9, 17c

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 56/55, 66/65

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

POTE generators: ~13/12 = 140.751

Optimal GPV sequence: 8d, 9, 17c

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 26/25, 36/35, 51/50, 56/55, 66/65

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

POTE generators: ~13/12 = 141.404

Optimal GPV sequence: 8d, 9, 17cg

### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

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

POTE generators: ~13/12 = 140.479

Optimal GPV sequence: 8d, 9, 17cg

## Ripple

Subgroup: 2.3.5.7

Comma list: 36/35, 2560/2401

Mapping: [1 2 3 3], 0 -5 -8 -2]]

Wedgie⟨⟨5 8 2 1 -11 -18]]

POTE generator: ~21/20 = 99.483

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 80/77, 126/121

Mapping: [1 2 3 3 4], 0 -5 -8 -2 -6]]

POTE generator: ~21/20 = 99.385

Optimal GPV sequence: 12

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 66/65, 147/143

Mapping: [1 2 3 3 4 4], 0 -5 -8 -2 -6 -3]]

POTE generator: ~21/20 = 98.572

Optimal GPV sequence: 12f

## Smate

Subgroup: 2.3.5.7

Comma list: 36/35, 2048/1875

Mapping: [1 3 2 6], 0 -4 1 -9]]

Wedgie⟨⟨4 -1 9 -11 3 24]]

POTE generator: ~5/4 = 422.275

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 243/242

Mapping: [1 3 2 6 7], 0 -4 1 -9 -10]]

POTE generator: ~5/4 = 422.217

Optimal GPV sequence: 3de, 14, 17c, 37ccddee

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 56/55, 243/242

Mapping: [1 3 2 6 7 3], 0 -4 1 -9 -10 2]]

POTE generator: ~5/4 = 423.020

Optimal GPV sequence: 3de, 14, 17c

## Subklei

For the 5-limit version of this temperament, see High badness temperaments #Delorean.

Subgroup: 2.3.5.7

Comma list: 36/35, 1029/1000

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

Wedgie⟨⟨6 7 5 -3 -9 -8]]

POTE generator: ~6/5 = 284.219

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 77/75, 352/343

Mapping: [1 3 4 4 7], 0 -6 -7 -5 -15]]

POTE generator: ~6/5 = 283.253

Optimal GPV sequence: 17c, 55ccd

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 66/65, 352/343

POTE generator: ~6/5 = 282.856

Mapping: [1 3 4 4 7 7], 0 -6 -7 -5 -15 -14]]

POTE generator: ~6/5 = 282.856

Optimal GPV sequence: 17c

### Subkla

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1000

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

POTE generator: ~6/5 = 283.822

Optimal GPV sequence: 4, 17c, 21, 38ce, 55ccde

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 56/55, 66/65, 640/637

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

POTE generator: ~6/5 = 283.882

Optimal GPV sequence: 4, 17c, 21, 38ce, 55ccde

## Slurpee

For the 5-limit version of this temperament, see High badness temperaments #Slurpee.

Subgroup: 2.3.5.7

Comma list: 36/35, 51200/50421

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

Wedgie⟨⟨7 11 3 1 -15 -24]]

POTE generator: ~21/20 = 72.303

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 121/120, 352/343

Mapping: [1 2 3 3 4], 0 -7 -11 -3 -9]]

POTE generator: ~21/20 = 72.297

Optimal GPV sequence: 16, 17c, 33, 50cd, 83bccd

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 66/65, 143/140, 352/343

Mapping: [1 2 3 3 4 4], 0 -7 -11 -3 -9 -5]]

POTE generator: ~21/20 = 72.409

Optimal GPV sequence: 16, 17c, 33, 83bccd