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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.

5-limit Parent Temperament

Mavila

Other languages: Deutsch

Commas: 135/128
POTE generator: 679.806
Map: [<1 0 7|, <0 1 -3|]
EDOs: 7, 9, 16, 23, 25b, 30bc, 34b, 41b



7-limit children

Septimal Mavila

Commas: 135/128, 126/125
POTE generator: 677.912
Map: [<1 0 7 20|, <0 1 -3 -11|]
EDOs: 7, 16, 23d
Badness: 0.0890


Pelogic

Commas: 135/128, 21/20
POTE generator: 672.853
Map: [<1 0 7 9|, <0 1 -3 -4|]
Wedgie: <<1 -3 -4 -7 -9 -1||
EDOs: 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: 9, 16d
Badness: 0.0228

Armodue

Commas: 135/128, 36/35
POTE generator: 673.997
Map: [<1 0 7 -5|, <0 1 -3 5|]
Wedgie: <<1 -3 5 -7 5 20||
EDOs: 9, 16, 23p, 25b
Badness: 0.0490

11-limit Armodue

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: 9, 16, 23e, 25b
Badness: 0.0272

13-limit Armodue

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, 57bef
Badness: 0.0194

Hornbostel

Commas: 135/128, 875/864
POTE generator: 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: 135/128, 49/48
POTE generator: 259.952
Map: [<1 0 7 2|, <0 2 -6 1|]
Wedgie: <<2 -6 1 -14 -4 19||
EDOs: 9, 14c, 23d, 37bcd, 60bcd
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: 135/128, 50/49
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, 23d, 37bcd
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, 44bcde
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