# Mavila family

The **mavila family** of temperaments tempers out 135/128, the mavila comma, also known as the major chroma or major limma. The 5-limit temperament is mavila, so named after the Chopi village where it was discovered, and is the base from which higher limit temperaments are derived. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.

One of the most salient and characteristic features of mavila temperaments is that when you stack 4 of the tempered fifths you get to a minor third instead of the usual major third that you would get if the fifths were pure. This also means that the arrangement of small and large steps in a 7-note mavila scale is the inverse of a diatonic scale of 2 small steps and 5 large steps; mavila has 2 large steps and 5 small steps (see 2L 5s).

Another salient feature of mavila temperaments is the fact that 9-note mos scales may be produced, thus giving us three different mos scales to choose from that are not decidedly chromatic in nature (5-, 7-, and 9-note scales). This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16-tone equal temperament (see 7L 2s).

## Mavila

Subgroup: 2.3.5

Comma list: 135/128

Mapping: [⟨1 0 7], ⟨0 1 -3]]

- mapping generators: ~2, ~3

- 5-odd-limit diamond monotone: ~3/2 = [600.000, 685.714] (1\2 to 4\7)
- 5-odd-limit diamond tradeoff: ~3/2 = [671.229, 701.955] (1/3-comma to Pyth.)

Optimal ET sequence: 7, 9, 16, 23, 30bc

Badness: 0.039556

### Overview to extensions

The second comma of the normal comma list defines which 7-limit family member we are looking at. That means 126/125 for septimal mavila, 21/20 for pelogic, 36/35 for armodue, 875/864 for hornbostel, 49/48 for superpelog, and 50/49 for bipelog.

Temperaments discussed elsewhere include

*Wallaby*(+28/27) → Trienstonic clan*Medusa*(+15/14) → Very low accuracy temperaments*Superpelog*(+49/48) → Slendro clan*Clyndro*(+360/343) → Gamelismic clan*Jamesbond*(+25/24) → 7th-octave temperaments

### 2.3.5.11 subgroup

Subgroup: 2.3.5.11

Comma list: 33/32, 45/44

Gencom: [2 4/3; 33/32, 45/44]

Gencom mapping: [⟨1 2 1 0 3], ⟨0 -1 3 0 1]]

Sval mapping: [⟨1 2 1 3], ⟨0 -1 3 1]]

POL2 generator: ~4/3 = 520.212

Optimal ET sequence: 7, 16, 23e, 30bce

RMS error: 4.705 cents

## Septimal mavila

Subgroup: 2.3.5.7

Comma list: 126/125, 135/128

Mapping: [⟨1 0 7 20], ⟨0 1 -3 -11]]

Wedgie: ⟨⟨ 1 -3 -11 -7 -20 -17 ]]

- mapping generators: ~2, ~3

- 7-odd-limit diamond monotone: ~3/2 = [675.000, 678.261] (9\16 to 13\23)
- 7-odd-limit diamond tradeoff: ~3/2 = [671.229, 701.955]

Optimal ET sequence: 7d, 16, 23d

Badness: 0.089013

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 126/125

Mapping: [⟨1 0 7 20 5], ⟨0 1 -3 -11 -1]]

- mapping generators: ~2, ~3

Optimal tunings:

- CTE: ~2 = 1\1, ~3/2 = 675.6200
- POTE: ~2 = 1\1, ~3/2 = 677.924

Optimal ET sequence: 7d, 16, 23de

Badness: 0.042049

## Pelogic

'Pelogic' (from the Indonesian word *pelog*) should probably be pronounced /pɛˈlɒgɪk/ *pell-LOG-ik*.

Subgroup: 2.3.5.7

Comma list: 21/20, 135/128

Mapping: [⟨1 0 7 9], ⟨0 1 -3 -4]]

- mapping generators: ~2, ~3

Wedgie: ⟨⟨ 1 -3 -4 -7 -9 -1 ]]

- 7-odd-limit diamond monotone: ~3/2 = 666.667 (5\9)
- 7-odd-limit diamond tradeoff: ~3/2 = [617.488, 701.955]

Optimal ET sequence: 7d, 9, 16d

Badness: 0.038661

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 21/20, 33/32, 45/44

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

- mapping generators: ~2, ~3

Optimal tunings:

- CTE: ~2 = 1\1, ~3/2 = 667.1801
- POTE: ~2 = 1\1, ~3/2 = 672.644

Optimal ET sequence: 7d, 9, 16d

Badness: 0.022753

## Armodue

This temperament is also known as **hexadecimal**.

Subgroup: 2.3.5.7

Comma list: 36/35, 135/128

Mapping: [⟨1 0 7 -5], ⟨0 1 -3 5]]

- mapping generators: ~2, ~3

Wedgie: ⟨⟨ 1 -3 5 -7 5 20 ]]

- 7-odd-limit diamond monotone: ~3/2 = [666.667, 675.000] (5\9 to 9\16)
- 7-odd-limit diamond tradeoff: ~3/2 = [666.718, 701.955]

Optimal ET sequence: 7, 9, 16

Badness: 0.049038

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 36/35, 45/44

Mapping: [⟨1 0 7 -5 5], ⟨0 1 -3 5 -1]]

- mapping generators: ~2, ~3

Optimal tunings:

- CTE: ~2 = 1\1, ~3/2 = 674.6841
- POTE: ~2 = 1\1, ~3/2 = 673.807

Badness: 0.027211

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 33/32, 36/35, 45/44

Mapping: [⟨1 0 7 -5 5 -1], ⟨0 1 -3 5 -1 3]]

- mapping generators: ~2, ~3

Optimal tunings:

- CTE: ~2 = 1\1, ~3/2 = 675.2877
- POTE: ~2 = 1\1, ~3/2 = 673.763

Badness: 0.019351

#### Armodog

Subgroup: 2.3.5.7.11.13.19

Comma list: 27/26, 33/32, 36/35, 39/38, 45/44

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

- mapping generators: ~2, ~3

Optimal tunings:

- CTE: ~2 = 1\1, ~3/2 = 675.1703

Optimal ET sequence: 7, 9, 16, 25bf

Badness: 0.0160

## Hornbostel

Subgroup: 2.3.5.7

Comma list: 135/128, 729/700

Mapping: [⟨1 0 7 -16], ⟨0 1 -3 12]]

- mapping generators: ~2, ~3

Wedgie: ⟨⟨ 1 -3 12 -7 16 36 ]]

Optimal ET sequence: 7, 16d, 23d, 53bbccd

Badness: 0.121294

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 729/700

Mapping: [⟨1 0 7 -16 5], ⟨0 1 -3 12 -1]]

- mapping generators: ~2, ~3

Optimal tunings:

- CTE: ~2 = 1\1, ~3/2 = 680.2409
- POTE: ~2 = 1\1, ~3/2 = 678.909

Optimal ET sequence: 7, 16d, 23de, 53bbccdee

Badness: 0.055036

## Bipelog

Subgroup: 2.3.5.7

Comma list: 50/49, 135/128

Mapping: [⟨2 0 14 15], ⟨0 1 -3 -3]]

- mapping generators: ~7/5, ~3

Wedgie: ⟨⟨ 2 -6 -6 -14 -15 3 ]]

Optimal ET sequence: 14c, 30bc, 44bccd

Badness: 0.074703

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 50/49

Mapping: [⟨2 0 14 15 10], ⟨0 1 -3 -3 -1]]

- mapping generators: ~7/5, ~3

Optimal tunings:

- CTE: ~7/5 = 1\2, ~3/2 = 676.3926
- POTE: ~7/5 = 1\2, ~3/2 = 681.280

Optimal ET sequence: 14c, 30bce, 44bccdee

Badness: 0.035694

## Mohavila

Named by Mike Battaglia in 2012^{[1]}, mohavila splits the mavila fifth in two. Unlike mohaha, this generator is not used as an ~11/9. In fact, the prime 11 is the same as in mavila, so the ~11/9 is the major third, tempered together with ~5/4. The fifth is only split to derive septimal intervals.

Subgroup: 2.3.5.7

Comma list: 135/128, 1323/1250

Mapping: [⟨1 1 4 7], ⟨0 2 -6 -15]]

- mapping generators: ~2, ~25/21

Wedgie: ⟨⟨ 2 -6 -15 -14 -29 -18 ]]

Optimal ET sequence: 7d, 25b, 32bd

Badness: 0.222377

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 1323/1250

Mapping: [⟨1 1 4 7 4], ⟨0 2 -6 -15 -2]]

- mapping generators: ~2, ~25/21

Optimal tunings:

- CTE: ~2 = 1\1, ~25/21 = 336.0156
- POTE: ~2 = 1\1, ~25/21 = 337.633

Optimal ET sequence: 7d, 25b, 32bde

Badness: 0.092074

## Listening examples

- Mysterious Mush (spectrally mapped)
- Mysterious Mush (unmapped)
*Hopper*by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila

- The Mavila Experiments - 9-EDO Version
- The Mavila Experiments - 16-EDO Version
- The Mavila Experiments - 23-EDO Version
- The Mavila Experiments - 25-EDO Version