# Mint temperaments

(Redirected from Quartonic 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

Comma: 3456/3125

POTE generator: ~25/24 = 140.995

Map: [<1 1 2|, <0 5 3|]

EDOs: 8, 9, 17c

## 7-limit

Commas: 36/35, 392/375

POTE generator: ~15/14 = 140.927

Map: [<1 1 2 2|, <0 5 3 7|]

Wedgie: <<5 3 7 -7 -3 8||

EDOs: 9, 17c

## 11-limit

Commas: 36/35, 56/55, 77/75

POTE generator: ~15/14 = 140.747

Map: [<1 1 2 2 3|, <0 5 3 7 4|]

EDOs: 8, 9, 17

## 13-limit

Commas: 26/25, 36/35, 56/55, 66/65

POTE generator: ~15/14 = 140.751

Map: Map: [<1 1 2 2 3 3|, <0 5 3 7 4 6|]

EDOs: 8, 9, 17

## 17-limit

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

POTE generator: ~15/14 = 141.404

Map: [<1 1 2 2 3 3 4|, <0 5 3 7 4 6 1|]

EDOs: 8, 9, 17

### 19-limit

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

POTE generator: ~15/14 = 140.479

Map: [<1 1 2 2 3 3 4 4|, <0 5 3 7 4 6 1 2|]

EDOs: 8, 9, 17, 94

# Ripple

Comma: 6561/6250

POTE generator: ~27/25 = 100.838

Map: [<1 2 3|, <0 -5 -8|]

EDOs: 12, 71b, 83b, 95b, 107bc, 119bc

## 7-limit

Commas: 36/35, 2560/2401

POTE generator: ~21/20 = 99.483

Map: [<1 2 3 3|, <0 -5 -8 -2|]

Wedgie: <<5 8 2 1 -11 -18||

EDOs: 12, 23

## 11-limit

Commas: 36/35, 80/77, 126/121

POTE generator: ~21/20 = ~12/11 = 99.385

Map: [<1 2 3 3 4|, <0 -5 -8 -2 -6|]

EDOs: 12

## 13-limit

Commas: 36/35, 40/39, 66/65, 147/143

POTE generator: ~21/20 = ~12/11 = ~14/13 = 98.572

Map: [<1 2 3 3 4 4|, <0 -5 -8 -2 -6 -3|]

EDOs: 12f

# Smate

Comma: 2048/1875

POTE generator: ~5/4 = 420.855

Map: [<1 3 2|, <0 -4 1|]

EDOs: 11, 14, 17c, 20c, 37c

## 7-limit

Commas: 36/35, 2048/1875

POTE generator: ~5/4 = 422.275

Map: [<1 3 2 6|, <0 -4 1 -9|]

Wedgie: <<4 -1 9 -11 3 24||

EDOs: 14, 17c, 37cd

## 11-limit

Commas: 36/35 56/55 243/242

POTE generator: ~5/4 = 422.217

Map: [<1 3 2 6 7|, <0 -4 1 -9 -10|]

EDOs: 14, 17c, 37cde

## 13-limit

Commas: 26/25, 36/35, 56/55, 243/242

POTE generator: ~5/4 = 423.020

Map: [<1 3 2 6 7 3|, <0 -4 1 -9 -10 2|]

EDOs: 14, 17c

# Hemismate

commas: 256/245, 392/375

POTE generator: ~8/7 = 210.452

Map: [<1 3 2 3|, <0 -8 2 -1|]

Wedgie: <<8 -2 1 -22 -21 8||

EDOs: 6, 11, 17c, 40bcd

## 11-limit

Commas: 56/55, 77/75, 256/245

POTE generator: ~8/7 = 210.481

Map: [<1 3 2 3 4|, <0 -8 2 -1 -3|]

EDOs: 6, 11, 17c, 40bcde

## 13-limit

Commas: 26/25, 56/55, 77/75, 256/245

POTE generator: ~8/7 = 210.974

Map: [<1 3 2 3 4 3|, <0 -8 2 -1 -3 4|]

EDOs: 6, 11, 17c

# Subklei

Comma: 17496/15625

POTE generator: ~6/5 = 284.293

Map: [<1 3 4|, <0 -6 -7|]

EDOs: 4, 17c, 21, 38c

## 7-limit

Commas: 36/35, 1029/1000

POTE generator: ~6/5 = 284.219

Map: [<1 3 4 4|, <0 -6 -7 -5|]

Wedgie: <<6 7 5 -3 -9 -8||

EDOs: 4, 17c, 21, 38c

## 11-limit

Commas: 36/35, 77/75, 352/343

POTE generator: ~6/5 = 283.253

Map: [<1 3 4 4 7|, <0 -6 -7 -5 -15|]

EDOs: 17c, 55cd

## Subkla

Commas: 36/35, 56/55, 1029/1000

POTE generator: ~6/5 = 283.822

Map: [<1 3 4 4 3|, <0 -6 -7 -5 2|]

EDOs: 4, 17c, 21, 38ce, 55cde

### 13-limit

Commas: 36/35, 56/55, 66/65, 640/637

POTE generator: ~6/5 = 283.882

Map: [<1 3 4 4 3 3|, <0 -6 -7 -5 2 3|]

EDOs: 4, 17c, 21, 38ce, 55cde

## 13-limit

Commas: 26/25, 36/35, 66/65, 352/343

POTE generator: ~6/5 = 282.856

Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|]

EDOs: 17c

# Slurpee

Comma: 177147/156250

POTE generator: ~27/25 = 72.742

Map: [<1 2 3|, <0 -7 -11|]

EDOs: 16, 17c, 33

## 7-limit

Commas: 36/35, 51200/50421

POTE generator: ~21/20 = 72.303

Map: [<1 2 3 3|, <0 -7 -11 -3|]

Wedgie: <<7 11 3 1 -15 -24||

EDOs: 16, 17c, 33, 50cd, 83bcd

## 11-limit

Commas: 36/35, 121/120, 352/343

POTE generator: ~21/20 = 72.297

Map: [<1 2 3 3 4|, <0 -7 -11 -3 -9|]

EDOs: 16, 17c, 33, 50cd, 83bcd