Mavila family: Difference between revisions

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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 '''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.
The '''pelogic family''' tempers out [[135/128]], the pelogic 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 [[7edo|7-equal]] and [[9edo|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]]).  
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]]).  
Another salient feature of pelogic temperament is the fact that 9-note [[mos scale]]s 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]]).  


'Pelogic' (from the Indonesian word ''[[Wikipedia: Pelog|pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''.
'Pelogic' (from the Indonesian word ''[[Wikipedia: Pelog|pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''.


== Mavila ==
== Mavila ==
{{Main| Mavila }}
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


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{{Mapping|legend=1| 1 0 7 | 0 1 -3 }}
{{Mapping|legend=1| 1 0 7 | 0 1 -3 }}


: Mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 679.806
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 677.145


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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* ''[[Superpelog]]'' → [[Slendro clan #Superpelog|Slendro clan]]
* ''[[Superpelog]]'' → [[Slendro clan #Superpelog|Slendro clan]]
* ''[[Clyndro]]'' → [[Gamelismic clan #Clyndro|Gamelismic clan]]
* ''[[Clyndro]]'' → [[Gamelismic clan #Clyndro|Gamelismic clan]]
* ''[[Jamesbond]]'' → [[Dicot family #Jamesbond|Dicot family]]
* ''[[Jamesbond]]'' → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]


== Septimal mavila ==
== Septimal mavila ==

Revision as of 12:46, 24 January 2024

The pelogic family tempers out 135/128, the pelogic 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 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).

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

Mavila

Main article: Mavila

Subgroup: 2.3.5

Comma list: 135/128

Mapping: [⟨1 0 7], ⟨0 1 -3]]

mapping generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 677.145

Tuning ranges:

  • 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.)
  • 5-odd-limit diamond monotone and tradeoff: ~3/2 = [671.229, 685.714]

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

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 ]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 677.913

Tuning ranges:

  • 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]
  • 7-odd-limit diamond monotone and tradeoff: ~3/2 = [675.000, 678.261]

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 677.924

Optimal ET sequence: 7d, 16, 23de

Badness: 0.042049

Pelogic

Subgroup: 2.3.5.7

Comma list: 21/20, 135/128

Mapping: [⟨1 0 7 9], ⟨0 1 -3 -4]]

Wedgie: ⟨⟨ 1 -3 -4 -7 -9 -1 ]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 672.853

Tuning ranges:

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

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]]

Optimal tuning (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]]

Wedgie: ⟨⟨ 1 -3 5 -7 5 20 ]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 673.997

Tuning ranges:

  • 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]
  • 7-odd-limit diamond monotone and tradeoff: ~3/2 = [666.718, 675.000]

Optimal ET sequence: 7, 9, 16, 41b, 57bb

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 673.807

Optimal ET sequence: 7, 9, 16, 25b, 41be, 57bbee

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 673.763

Optimal ET sequence: 7, 9, 16, 41bef, 57bbeef

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 673.282

Optimal ET sequence: 7, 9, 16, 25bf, 41bef

Hornbostel

Subgroup: 2.3.5.7

Comma list: 135/128, 729/700

Mapping: [⟨1 0 7 -16], ⟨0 1 -3 12]]

Wedgie: ⟨⟨ 1 -3 12 -7 16 36 ]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 678.947

Optimal ET sequence: 7, 16d, 23d, 53bbccd, 76bbccdd

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 678.909

Optimal ET sequence: 7, 16d, 23de

Badness: 0.055036

Bipelog

Subgroup: 2.3.5.7

Comma list: 50/49, 135/128

Mapping: [⟨2 0 14 15], ⟨0 1 -3 -3]]

Wedgie: ⟨⟨ 2 -6 -6 -14 -15 3 ]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 681.195

Optimal ET sequence: 14c, 16, 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]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 681.280

Optimal ET sequence: 14c, 16, 30bce, 44bccdee

Badness: 0.035694

Mohavila

Subgroup: 2.3.5.7

Comma list: 135/128, 1323/1250

Mapping: [⟨1 1 4 7], ⟨0 2 -6 -15]]

Wedgie: ⟨⟨ 2 -6 -15 -14 -29 -18 ]]

Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 337.658

Optimal ET sequence: 7d, 18b, 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]]

Optimal tuning]] (POTE): ~2 = 1\1, ~25/21 = 337.633

Optimal ET sequence: 7d, 18b, 25b, 32bde

Badness: 0.092074

Listening examples

Gene Ward Smith
Mike Battaglia
John Moriarty
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