# Keemic temperaments

These temper out the keema, [-5 -3 3 1 = 875/864. Keemic temperaments include doublewide, flattone, porcupine, superkleismic, magic, keemun, and sycamore. Discussed below are quasitemp and barbad.

## Quasitemp

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

Subgroup: 2.3.5.7

Comma list: 875/864, 2401/2400

Mapping[1 5 5 5], 0 -14 -11 -9]]

mapping generators: ~2, ~25/21

Wedgie⟨⟨14 11 9 -15 -25 -10]]

Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.710

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 1375/1372

Mapping: [1 5 5 5 2], 0 -14 -11 -9 6]]

Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.547

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 196/195, 275/273, 385/384

Mapping: [1 5 5 5 2 2], 0 -14 -11 -9 6 7]]

Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 292.457

### Quato

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 625/616

Mapping: [1 5 5 5 12], 0 -14 -11 -9 -35]]

Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.851

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 243/242, 275/273, 325/324

Mapping: [1 5 5 5 12 12], 0 -14 -11 -9 -35 -34]]

Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 292.928

## Chromo

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

Subgroup: 2.3.5.7

Comma list: 875/864, 2430/2401

Mapping[1 1 2 2], 0 13 7 18]]

mapping generators: ~2, ~25/24

Optimal tuning (POTE): ~2 = 1\1, ~25/24 = 53.816

## Undeka

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

Subgroup: 2.3.5.7

Comma list: 875/864, 3200/3087

Mapping[11 0 8 31], 0 1 1 0]]

mapping generators: ~21/20, ~3

Wedgie⟨⟨11 11 0 -8 -31 -31]]

Optimal tuning (POTE): ~21/20 = 1\11, ~3/2 = 708.792

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 352/343, 385/384

Mapping: [11 0 8 31 38], 0 1 1 0 0]]

Optimal tuning (POTE): ~21/20 = 1\11, ~3/2 = 706.768

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/63, 100/99, 169/165, 352/343

Mapping: [11 0 8 31 38 23], 0 1 1 0 0 1]]

Optimal tuning (POTE): ~13/12 = 1\11, ~3/2 = 707.764

Subgroup: 2.3.5.7

Comma list: 875/864, 16875/16807

Mapping[1 9 7 11], 0 -19 -12 -21]]

mapping generators: ~2, ~98/75

Wedgie⟨⟨19 12 21 -25 -20 15]]

Optimal tuning (POTE): ~2 = 1\1, ~98/75 = 468.331

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/242, 540/539, 625/616

Mapping: [1 9 7 11 14], 0 -19 -12 -21 -27]]

Optimal tuning (POTE): ~2 = 1\1, ~98/75 = 468.367

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 245/242, 275/273

Mapping: [1 9 7 11 14 8], 0 -19 -12 -21 -27 -11]]

Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 468.270

## Hyperkleismic

Subgroup: 2.3.5.7

Comma list: 875/864, 51200/50421

Mapping[1 -3 -2 2], 0 17 16 3]]

mapping generators: ~2, ~6/5

Wedgie⟨⟨17 16 3 -14 -43 -38]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.780

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 2420/2401

Mapping: [1 -3 -2 2 4], 0 17 16 3 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.796

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 169/168, 275/273, 385/384

Mapping: [1 -3 -2 2 4 1], 0 17 16 3 -2 10]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.790

## Sevond

10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.

Subgroup: 2.3.5.7

Comma list: 875/864, 327680/321489

Mapping[7 0 -6 53], 0 1 2 -3]]

mapping generators: ~10/9, ~3

Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.613

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 6655/6561

Mapping: [7 0 -6 53 2], 0 1 2 -3 2]]

Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.518