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Mavila family: Difference between revisions

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The '''mavila family''' of [[regular temperament|temperaments]] [[tempering out|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 [[7edo|7-equal]] and [[9edo|9-equal]].
The '''mavila family''' of [[regular temperament|temperaments]] [[tempering out|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 [[7edo]] and [[9edo]].


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]]).  
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]]).  
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 677.145
* [[CTE]]: ~2 = 1200.000, ~3/2 = 677.145
* [[POTE]]: ~2 = 1\1, ~3/2 = 679.806
* [[POTE]]: ~2 = 1200.000, ~3/2 = 679.806


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


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=== 2.3.5.11 subgroup ===
=== 2.3.5.11 subgroup ===
Subgroup: 2.3.5.11
[[Subgroup]]: 2.3.5.11


[[Comma list]]: 33/32, 45/44
[[Comma list]]: 33/32, 45/44


[[Gencom]]: [2 4/3; 33/32, 45/44]
{{Mapping|legend=2| 1 0 7 5 | 0 1 -3 -1 }}


[[Gencom|Gencom mapping]]: [{{val|1 2 1 0 3}}, {{val|0 -1 3 0 1}}]
{{Mapping|legend=3| 1 0 7 0 5 | 0 1 -3 0 -1 }}


[[Mapping|Sval mapping]]: [{{val|1 2 1 3}}, {{val|0 -1 3 1}}]
: [[Gencom]]: [2 3; 33/32, 45/44]


[[Tp tuning|POL2 generator]]: ~4/3 = 520.212
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000, ~3/2 = 679.788


{{Optimal ET sequence|legend=1| 7, 16, 23e, 30bce }}
{{Optimal ET sequence|legend=1| 7, 16, 23e, 30bce }}
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[[Optimal tuning]]s
[[Optimal tuning]]s
* [[CTE]]: ~2 = 1\1, ~3/2 = 675.7492
* [[CTE]]: ~2 = 1200.000, ~3/2 = 675.7492
* [[POTE]]: ~2 = 1\1, ~3/2 = 677.913
* [[POTE]]: ~2 = 1200.000, ~3/2 = 677.913


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


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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 675.6200
* CTE: ~2 = 1200.000, ~3/2 = 675.620
* POTE: ~2 = 1\1, ~3/2 = 677.924
* POTE: ~2 = 1200.000, ~3/2 = 677.924


Optimal ET sequence: {{Optimal ET sequence| 7d, 16, 23de }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 16, 23de }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 667.5573
* [[CTE]]: ~2 = 1200.000, ~3/2 = 667.557
* [[POTE]]: ~2 = 1\1, ~3/2 = 672.853
* [[POTE]]: ~2 = 1200.000, ~3/2 = 672.853


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


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Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 667.1801
* CTE: ~2 = 1200.000, ~3/2 = 667.180
* POTE: ~2 = 1\1, ~3/2 = 672.644
* POTE: ~2 = 1200.000, ~3/2 = 672.644


Optimal ET sequence: {{Optimal ET sequence| 7d, 9, 16d }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 9, 16d }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 675.0988
* [[CTE]]: ~2 = 1200.000, ~3/2 = 675.099
* [[POTE]]: ~2 = 1\1, ~3/2 = 673.997
* [[POTE]]: ~2 = 1200.000, ~3/2 = 673.997


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


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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 674.6841
* CTE: ~2 = 1200.000, ~3/2 = 674.684
* POTE: ~2 = 1\1, ~3/2 = 673.807
* POTE: ~2 = 1200.000, ~3/2 = 673.807


Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 675.2877
* CTE: ~2 = 1200.000, ~3/2 = 675.288
* POTE: ~2 = 1\1, ~3/2 = 673.763
* POTE: ~2 = 1200.000, ~3/2 = 673.763


Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 675.1703
* CTE: ~2 = 1200.000, ~3/2 = 675.170


Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16, 25bf }}
Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16, 25bf }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 680.3705
* [[CTE]]: ~2 = 1200.000, ~3/2 = 680.371
* [[POTE]]: ~2 = 1\1, ~3/2 = 678.947
* [[POTE]]: ~2 = 1200.000, ~3/2 = 678.947


{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}
{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 680.2409
* CTE: ~2 = 1200.000, ~3/2 = 680.241
* POTE: ~2 = 1\1, ~3/2 = 678.909
* POTE: ~2 = 1200.000, ~3/2 = 678.909


Optimal ET sequence: {{Optimal ET sequence| 7, 16d, 23de, 53bbccdee }}
Optimal ET sequence: {{Optimal ET sequence| 7, 16d, 23de, 53bbccdee }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~3/2 = 677.114
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 677.114
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 681.195
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 681.195


{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}
{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}
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Optimal tunings:
Optimal tunings:
* CTE: ~7/5 = 1\2, ~3/2 = 676.3926
* CTE: ~7/5 = 600.000, ~3/2 = 676.393
* POTE: ~7/5 = 1\2, ~3/2 = 681.280
* POTE: ~7/5 = 600.000, ~3/2 = 681.280


Optimal ET sequence: {{Optimal ET sequence| 14c, 30bce, 44bccdee }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 30bce, 44bccdee }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~25/21 = 336.1216
* [[CTE]]: ~2 = 1200.000, ~25/21 = 336.122
* [[POTE]]: ~2 = 1\1, ~25/21 = 337.658
* [[POTE]]: ~2 = 1200.000, ~25/21 = 337.658


{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}
{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}
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Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1\1, ~25/21 = 336.0156
* CTE: ~2 = 1200.000, ~25/21 = 336.016
* POTE: ~2 = 1\1, ~25/21 = 337.633
* POTE: ~2 = 1200.000, ~25/21 = 337.633


Optimal ET sequence: {{Optimal ET sequence| 7d, 25b, 32bde }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 25b, 32bde }}
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