# Dimipent family

(Redirected from Dimipent)

The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo.

## Dimipent

Subgroup: 2.3.5

Comma list: 648/625

Mapping[4 0 3], 0 1 1]]

Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 699.507

## Diminished

Deutsch

Subgroup: 2.3.5.7

Comma list: 36/35, 50/49

Mapping[4 0 3 5], 0 1 1 1]]

Wedgie⟨⟨4 4 4 -3 -5 -2]]

Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 699.523

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 56/55

Mapping: [4 0 3 5 14], 0 1 1 1 0]]

Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109

Scales: diminished12

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 50/49, 66/65

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

Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773

Scales: diminished12

### Demolished

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 50/49

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

Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881

### Cohedim

This temperament has been documented in Graham Breed's temperament finder as hemidim, the same name as 11-limit 4e & 24 and 13-limit 4ef & 24. For 11-limit 8bce & 12 temperament, cohedim arguably makes more sense.

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 125/121

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

Mapping generators: ~6/5, ~11/7

Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 50/49, 66/65, 125/121

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

Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299

## Hemidim

Subgroup: 2.3.5.7

Comma list: 49/48, 648/625

Mapping[4 0 3 8], 0 2 2 1]]

Wedgie⟨⟨8 8 4 -6 -16 -13]]

Optimal tuning (POTE): ~6/5 = 1\4, ~7/6 = 252.555

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 77/75, 243/242

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

Optimal tuning (POTE): ~6/5 = 1\4, ~7/6 = 251.658

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 77/75, 243/242

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

Optimal tuning (POTE): ~6/5 = 1\4, ~7/6 = 252.225

## Semidim

Subgroup: 2.3.5.7

Comma list: 245/243, 392/375

Mapping[8 0 6 -3], 0 1 1 2]]

Wedgie⟨⟨8 8 16 -6 3 15]]

Optimal tuning (POTE): ~15/14 = 1\8, ~3/2 = 707.014

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 77/75, 245/243

Mapping: [8 0 6 -3 15], 0 1 1 2 1]]

Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 706.645