# Rastmic clan

The **rastmic clan** of temperaments tempers out 243/242.

## Neutral

Neutral can be thought of as the 2.3.11 version of either mohajira or neutrominant, as well as suhajira and ringo. Among other things, it is the temperament optimizing the neutral tetrad.

Subgroup: 2.3.11

Comma list: 243/242

Sval mapping: [⟨1 1 2], ⟨0 2 5]]

- mapping generators: ~2, ~11/9

Gencom mapping: [⟨1 1 0 0 2], ⟨0 2 0 0 5]]

- gencom: [2 11/9; 243/242]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.525

Optimal ET sequence: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380

RMS error: 0.3021 cents

Scales: neutral7, neutral10, neutral17

### Namo

Subgroup: 2.3.11.13

Comma list: 144/143, 243/242

Sval mapping: [⟨1 1 2 4], ⟨0 2 5 -1]]

Gencom mapping: [⟨1 1 0 0 2 4], ⟨0 2 0 0 5 -1]]

- gencom: [2 11/9; 144/143 243/242]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.488

Optimal ET sequence: 7, 10, 17, 24, 41

RMS error: 0.7038 cents

## Suhajira

Subgroup: 2.3.7.11

Comma list: 64/63, 243/242

Sval mapping: [⟨1 1 4 2], ⟨0 2 -4 5]]

- sval mapping generators: ~2, ~11/9

Gencom mapping: [⟨1 1 0 4 2], ⟨0 1 0 -4 5]]

- gencom: [2 3/2; 64/63 99/98]

Optimal tuning (POTE): ~11/9 = 353.958

Optimal ET sequence: 7, 10, 17, 44e, 61de

Scales: suhajira7, suhajira10, suhajira17

### 2.3.7.11.13 subgroup

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 144/143

Sval mapping: [⟨1 1 4 2 4], ⟨0 2 -4 5 -1]]

Gencom mapping: [⟨1 1 0 4 2 4], ⟨0 1 0 -4 5 -1]]

- gencom: [2 3/2; 64/63 78/77 99/98]

Optimal tuning (POTE): ~11/9 = 353.775

Optimal ET sequence: 7, 10, 17, 44e, 61de

Scales: suhajira7, suhajira10, suhajira17

## Mohaha

*See also: No-sevens subgroup temperaments #Mohaha*

Mohaha is the 2.3.5.11 subgroup temperament with a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 11/9. Mohaha can be thought of, intuitively, as "meantone with quartertones"; as is the 3/2 generator subdivided in half, so is the ~25/24 chromatic semitone divided into two equal ~33/32 quarter tones (in the 2.3.5.11 subgroup). Within this paradigm, mohaha is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10~12/11's, and that maps four 3/2's to 5/1. It has a heptatonic mos with three larger steps and four smaller ones, going sLsLsLs. Taking septimal meantone mapping of 7 leads to #Migration, flattone mapping of 7 leads to #Ptolemy, and dominant mapping of 7 leads to #Neutrominant.

### 2.3.5.11 subgroup

The S-expression-based comma list of this temperament is {S6/S8 = S9, S11}.

Subgroup: 2.3.5.11

Comma list: 81/80, 121/120

Sval mapping: [⟨1 1 0 2], ⟨0 2 8 5]]

- sval mapping generators: ~2, ~11/9

Gencom mapping: [⟨1 1 0 0 2], ⟨0 2 8 0 5]]

- gencom: [2 11/9; 81/80 121/120]

Optimal ET sequence: 7, 17c, 24, 31, 69e, 100e, 131bee

#### Mohoho

Subgroup: 2.3.5.11.13

Comma list: 66/65, 81/80, 121/120

Sval mapping: [⟨1 1 0 2 4], ⟨0 2 8 5 -1]]

- sval mapping generators: ~2, ~11/9

Gencom mapping: [⟨1 1 0 0 2 4], ⟨0 2 8 0 5 -1]]

- gencom: [2 11/9; 66/65 81/80 121/120]

Optimal tunings:

- CTE: ~2 = 1\1, ~11/9 = 348.8794
- POTE: ~2 = 1\1, ~11/9 = 348.9155

Optimal ET sequence: 7, 17c, 24, 31, 55

### Migration

Subgroup: 2.3.5.7.11

Comma list: 81/80, 121/120, 126/125

Mapping: [⟨1 1 0 -3 2], ⟨0 2 8 20 5]]

- mapping generators: ~2, ~11/9

Optimal tunings:

- CTE: ~2 = 1\1, ~11/9 = 348.5324
- POTE: ~2 = 1\1, ~11/9 = 348.182

Optimal ET sequence: 7d, 24d, 31, 100de, 131bdee, 162bdee

Badness: 0.025516

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 81/80, 121/120, 126/125

Mapping: [⟨1 1 0 -3 2 4], ⟨0 2 8 20 5 -1]]

Optimal tunings:

- CTE: ~2 = 1\1, ~11/9 = 348.5444
- POTE: ~2 = 1\1, ~11/9 = 348.490

Optimal ET sequence: 7d, 24d, 31

Badness: 0.028071

### Ptolemy

Subgroup: 2.3.5.7.11

Comma list: 81/80, 121/120, 525/512

Mapping: [⟨1 1 0 8 2], ⟨0 2 8 -18 5]]

- mapping generators: ~2, ~11/9

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 346.922

Optimal ET sequence: 7, 31dd, 38d, 45e, 83bcddee

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/64, 81/80, 105/104, 121/120

Mapping: [⟨1 1 0 8 2 6], ⟨0 2 8 -18 5 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 346.910

Optimal ET sequence: 7, 31ddf, 38df, 45ef, 83bcddeeff

Badness: 0.034316

### Neutrominant

The neutrominant temperament (formerly *maqamic* temperament) has a hemififth generator (~11/9) and tempers out 36/35 and 121/120. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation.

Subgroup: 2.3.5.7.11

Comma list: 36/35, 64/63, 121/120

Mapping: [⟨1 1 0 4 2], ⟨0 2 8 -4 5]]

- mapping generators: ~2, ~11/9

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.934

Optimal ET sequence: 7, 17c, 24d, 41cd

Badness: 0.040240

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 64/63, 66/65, 121/120

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

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.816

Optimal ET sequence: 7, 17c, 24d, 41cd

Badness: 0.027214