Mavila family: Difference between revisions
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Map: [<1 0 7|, <0 1 -3|] | Map: [<1 0 7|, <0 1 -3|] | ||
EDOs: {{EDOs|7, 9, 16, 23, 30bc}} | EDOs: {{EDOs| 7, 9, 16, 23, 30bc }} | ||
= Septimal mavila = | = Septimal mavila = | ||
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Map: [<1 0 7 20|, <0 1 -3 -11|] | Map: [<1 0 7 20|, <0 1 -3 -11|] | ||
EDOs: {{EDOs|7d, 16, 23d}} | EDOs: {{EDOs| 7d, 16, 23d }} | ||
Badness: 0.0890 | Badness: 0.0890 | ||
| Line 41: | Line 41: | ||
[[Wedgie]]: <<1 -3 -4 -7 -9 -1|| | [[Wedgie]]: <<1 -3 -4 -7 -9 -1|| | ||
EDOs: {{EDOs|7d, 9, 16d}} | EDOs: {{EDOs| 7d, 9, 16d }} | ||
Badness: 0.0387 | Badness: 0.0387 | ||
| Line 52: | Line 52: | ||
Map: [<1 0 7 9 5|, <0 1 -3 -4 -1|] | Map: [<1 0 7 9 5|, <0 1 -3 -4 -1|] | ||
EDOs: {{EDOs|7d, 9, 16d}} | EDOs: {{EDOs| 7d, 9, 16d }} | ||
Badness: 0.0228 | Badness: 0.0228 | ||
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[[Wedgie]]: <<1 -3 5 -7 5 20|| | [[Wedgie]]: <<1 -3 5 -7 5 20|| | ||
EDOs: {{EDOs|7, 9, 16, 41b, 57bb}} | EDOs: {{EDOs| 7, 9, 16, 41b, 57bb }} | ||
Badness: 0.0490 | Badness: 0.0490 | ||
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Map: [<1 0 7 -5 5|, <0 1 -3 5 -1|] | Map: [<1 0 7 -5 5|, <0 1 -3 5 -1|] | ||
EDOs: {{EDOs|7, 9, 16, 25b, 41be, 57bbee}} | EDOs: {{EDOs| 7, 9, 16, 25b, 41be, 57bbee }} | ||
Badness: 0.0272 | Badness: 0.0272 | ||
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Map: [<1 0 7 -5 5 -1|, <0 1 -3 5 -1 3|] | Map: [<1 0 7 -5 5 -1|, <0 1 -3 5 -1 3|] | ||
EDOs: {{EDOs|7, 9, 16, 41bef, 57bbeef}} | EDOs: {{EDOs| 7, 9, 16, 41bef, 57bbeef }} | ||
Badness: 0.0194 | Badness: 0.0194 | ||
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[[wedgie|Wedgie]]: <<1 -3 12 -7 16 36|| | [[wedgie|Wedgie]]: <<1 -3 12 -7 16 36|| | ||
EDOs: {{EDOs|7, 16d, 23d}} | EDOs: {{EDOs| 7, 16d, 23d }} | ||
Badness: 0.1213 | Badness: 0.1213 | ||
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[[wedgie|Wedgie]]: <<2 -6 1 -14 -4 19|| | [[wedgie|Wedgie]]: <<2 -6 1 -14 -4 19|| | ||
EDOs: {{EDOs|9, 14c, 23d, 37bcd, 60bbccdd}} | EDOs: {{EDOs| 9, 14c, 23d, 37bcd, 60bbccdd }} | ||
Badness: 0.0582 | Badness: 0.0582 | ||
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Map: [<1 0 7 2 5|, <0 2 -6 1 -2|] | Map: [<1 0 7 2 5|, <0 2 -6 1 -2|] | ||
EDOs: {{EDOs|9, 14c, 23de, 37bcde}} | EDOs: {{EDOs| 9, 14c, 23de, 37bcde }} | ||
Badness: 0.0285 | Badness: 0.0285 | ||
| Line 141: | Line 141: | ||
[[wedgie|Wedgie]]: <<2 -6 -6 -14 -15 3|| | [[wedgie|Wedgie]]: <<2 -6 -6 -14 -15 3|| | ||
EDOs: {{EDOs|14c, 16, 30bc, 44bccd}} | EDOs: {{EDOs| 14c, 16, 30bc, 44bccd }} | ||
Badness: 0.0747 | Badness: 0.0747 | ||
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Map: [<2 0 14 15 10|, <0 1 -3 -3 -1|] | Map: [<2 0 14 15 10|, <0 1 -3 -3 -1|] | ||
EDOs: {{EDOs|14c, 16, 30bce, 44bccdee}} | EDOs: {{EDOs| 14c, 16, 30bce, 44bccdee }} | ||
Badness: 0.0357 | Badness: 0.0357 | ||
| Line 165: | Line 165: | ||
Wedgie: <<2 -6 -15 -14 -29 -18|| | Wedgie: <<2 -6 -15 -14 -29 -18|| | ||
EDOs: {{EDOs|32bd, 36}} | EDOs: {{EDOs| 32bd, 36 }} | ||
Badness: 0.2224 | Badness: 0.2224 | ||
| Line 176: | Line 176: | ||
Map: [<1 1 4 7 4|, <0 2 -6 -15 -2|] | Map: [<1 1 4 7 4|, <0 2 -6 -15 -2|] | ||
EDOs: {{EDOs|32bde}} | EDOs: {{EDOs| 32bde }} | ||
Badness: 0.0921 | Badness: 0.0921 | ||
Revision as of 12:24, 11 November 2020
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
Other languages: Deutsch
Comma: 135/128
POTE generator: ~3/2 = 679.806
Map: [<1 0 7|, <0 1 -3|]
Septimal mavila
Commas: 126/125, 135/128
POTE generator: ~3/2 = 677.912
Map: [<1 0 7 20|, <0 1 -3 -11|]
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||
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|]
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||
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||
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|]
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||
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||
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
- Mysterious Mush (spectrally mapped)
- Mysterious Mush (unmapped)
- Hopper by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila