Mavila family

The pelogic family tempers out 135/128, the pelogic comma, also known as the major chroma or major limma. The 5-limit temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. 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 pelogic temperament 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 pelogic temperament 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).

One of the most common temperaments talked about in the pelogic family is mavila, the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.

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

Mavila

Subgroup: 2.3.5

Comma list: 135/128

POTE generator: ~3/2 = 679.806

Mapping: [⟨1 0 7], ⟨0 1 -3]]

Tuning ranges:

• diamond monotone range: [514.286, 600.000] (3\7 to 1\2)

EDOs: 7, 9, 16, 23, 30bc

Septimal mavila

Commas: 126/125, 135/128

POTE generator: ~3/2 = 677.912

Map: [<1 0 7 20|, <0 1 -3 -11|]

EDOs: 7d, 16, 23d

Badness: 0.0890

Pelogic

Commas: 21/20, 135/128

POTE generator: ~3/2 = 672.853

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

Wedgie: <<1 -3 -4 -7 -9 -1||

EDOs: 7d, 9, 16d

Badness: 0.0387

11-limit

Commas: 21/20, 33/32, 45/44

POTE generator: ~3/2 = 672.644

Map: [<1 0 7 9 5|, <0 1 -3 -4 -1|]

EDOs: 7d, 9, 16d

Badness: 0.0228

Armodue

This temperament is also known as hexadecimal.

Commas: 36/35, 135/128

POTE generator: ~3/2 = 673.997

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

Wedgie: <<1 -3 5 -7 5 20||

EDOs: 7, 9, 16, 41b, 57bb

Badness: 0.0490

11-limit

Commas: 33/32, 36/35, 45/44

POTE generator: ~3/2 = 673.807

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

EDOs: 7, 9, 16, 25b, 41be, 57bbee

Badness: 0.0272

13-limit

Commas: 27/26, 33/32, 36/35, 45/44

POTE generator: ~3/2 = 673.763

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

EDOs: 7, 9, 16, 41bef, 57bbeef

Badness: 0.0194

Hornbostel

Commas: 135/128, 875/864

POTE generator: ~3/2 = 678.947

Map: [<1 0 7 -16|, <0 1 -3 12|]

Wedgie: <<1 -3 12 -7 16 36||

EDOs: 7, 16d, 23d

Badness: 0.1213

Superpelog

Commas: 49/48, 135/128

POTE generator: ~8/7 = 259.952

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

Wedgie: <<2 -6 1 -14 -4 19||

EDOs: 9, 14c, 23d, 37bcd, 60bbccdd

Badness: 0.0582

11-limit

Commas: 33/32, 45/44, 49/48

POTE generator: ~8/7 = 259.959

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

EDOs: 9, 14c, 23de, 37bcde

Badness: 0.0285

Mindaugas Rex Lithuaniae by Chris Vaisvil (in 5\23 tuning)

Bipelog

Commas: 50/49, 135/128

POTE generator: ~3/2 = 681.195

Map: [<2 0 14 15|, <0 1 -3 -3|]

Wedgie: <<2 -6 -6 -14 -15 3||

EDOs: 14c, 16, 30bc, 44bccd

Badness: 0.0747

11-limit

Commas: 33/32, 45/44, 50/49

POTE generator: ~3/2 = 681.280

Map: [<2 0 14 15 10|, <0 1 -3 -3 -1|]

EDOs: 14c, 16, 30bce, 44bccdee

Badness: 0.0357

Mohavila

Commas: 135/128, 1323/1250

POTE generator: ~25/21 = 337.658

Map: [<1 1 4 7|, <0 2 -6 -15|]

Wedgie: <<2 -6 -15 -14 -29 -18||

EDOs: 32bd, 36

Badness: 0.2224

11-limit

Commas: 33/32, 45/44, 1323/1250

POTE generator: ~25/21 = 337.633

Map: [<1 1 4 7 4|, <0 2 -6 -15 -2|]

EDOs: 32bde

Badness: 0.0921

Mavila listening examples

Gene Ward Smith

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

Mike Battaglia

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

John Moriarty

• Mavila