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Mavila family: Difference between revisions

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== Mavila ==
== Mavila ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 135/128
[[Comma list]]: 135/128


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


[[POTE generator]]: ~3/2 = 679.806
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~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]
* 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]
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [671.229, 685.714]


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[[Badness]]: 0.039556
[[Badness]]: 0.039556


=== Extensions ===
=== Overview to extensions ===
The second comma of the [[Normal lists|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.
The second comma of the [[Normal lists|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.


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== Septimal mavila ==
== Septimal mavila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 135/128
[[Comma list]]: 126/125, 135/128


[[Mapping]]: [{{val|1 0 7 20}}, {{val|0 1 -3 -11}}]
{{Mapping|legend=1| 1 0 7 20 | 0 1 -3 -11 }}


{{Multival|legend=1|1 -3 -11 -7 -20 -17}}
{{Multival|legend=1|1 -3 -11 -7 -20 -17}}


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


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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Comma list: 33/32, 45/44, 126/125
Comma list: 33/32, 45/44, 126/125


Mapping: [{{val|1 0 7 20 5}}, {{val|0 1 -3 -11 -1}}]
Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}


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


{{Optimal ET sequence|legend=1| 7d, 16, 23de }}
{{Optimal ET sequence|legend=1| 7d, 16, 23de }}
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== Pelogic ==
== Pelogic ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 21/20, 135/128
[[Comma list]]: 21/20, 135/128


[[Mapping]]: [{{val|1 0 7 9}}, {{val|0 1 -3 -4}}]
{{Mapping|legend=1| 1 0 7 9 | 0 1 -3 -4}}


{{Multival|legend=1|1 -3 -4 -7 -9 -1}}
{{Multival|legend=1| 1 -3 -4 -7 -9 -1 }}


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


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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Comma list: 21/20, 33/32, 45/44
Comma list: 21/20, 33/32, 45/44


Mapping: [{{val|1 0 7 9 5}}, {{val|0 1 -3 -4 -1}}]
Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}


POTE generator: ~3/2 = 672.644
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 672.644


{{Optimal ET sequence|legend=1| 7d, 9, 16d }}
{{Optimal ET sequence|legend=1| 7d, 9, 16d }}
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This temperament is also known as '''hexadecimal'''.  
This temperament is also known as '''hexadecimal'''.  


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 135/128
[[Comma list]]: 36/35, 135/128


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


{{Multival|legend=1|1 -3 5 -7 5 20}}
{{Multival|legend=1|1 -3 5 -7 5 20}}


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


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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Comma list: 33/32, 36/35, 45/44
Comma list: 33/32, 36/35, 45/44


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


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


{{Optimal ET sequence|legend=1| 7, 9, 16, 25b, 41be, 57bbee }}
{{Optimal ET sequence|legend=1| 7, 9, 16, 25b, 41be, 57bbee }}
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Comma list: 27/26, 33/32, 36/35, 45/44
Comma list: 27/26, 33/32, 36/35, 45/44


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


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


{{Optimal ET sequence|legend=1| 7, 9, 16, 41bef, 57bbeef }}
{{Optimal ET sequence|legend=1| 7, 9, 16, 41bef, 57bbeef }}
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== Hornbostel ==
== Hornbostel ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 135/128, 729/700
[[Comma list]]: 135/128, 729/700


[[Mapping]]: [{{val|1 0 7 -16}}, {{val|0 1 -3 12}}]
{{Mapping|legend=1| 1 0 7 -16 | 0 1 -3 12 }}


{{Multival|legend=1|1 -3 12 -7 16 36}}
{{Multival|legend=1| 1 -3 12 -7 16 36 }}


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


{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd, 76bbccdd }}
{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd, 76bbccdd }}
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Comma list: 33/32, 45/44, 729/700
Comma list: 33/32, 45/44, 729/700


Mapping: [{{val|1 0 7 -16 5}}, {{val|0 1 -3 12 -1}}]
Mapping: {{mapping| 1 0 7 -16 5 | 0 1 -3 12 -1 }}


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


{{Optimal ET sequence|legend=1| 7, 16d, 23de }}
{{Optimal ET sequence|legend=1| 7, 16d, 23de }}
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== Superpelog ==
== Superpelog ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 135/128
[[Comma list]]: 49/48, 135/128


[[Mapping]]: [{{val|1 0 7 2}}, {{val|0 2 -6 1}}]
{{Mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}


{{Multival|legend=1|2 -6 1 -14 -4 19}}
{{Multival|legend=1| 2 -6 1 -14 -4 19 }}


[[POTE generator]]: ~8/7 = 259.952
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 259.952


{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}
{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}
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Comma list: 33/32, 45/44, 49/48
Comma list: 33/32, 45/44, 49/48


Mapping: [{{val|1 0 7 2 5}}, {{val|0 2 -6 1 -2}}]
Mapping: {{mapping| 1 0 7 2 5 | 0 2 -6 1 -2 }}


POTE generator: ~8/7 = 259.959
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 259.959


{{Optimal ET sequence|legend=1| 9, 14c, 23de, 37bcde }}
{{Optimal ET sequence|legend=1| 9, 14c, 23de, 37bcde }}
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== Bipelog ==
== Bipelog ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 135/128
[[Comma list]]: 50/49, 135/128


[[Mapping]]: [{{val|2 0 14 15}}, {{val|0 1 -3 -3}}]
{{Mapping|legend=1| 2 0 14 15 | 0 1 -3 -3 }}


{{Multival|legend=1|2 -6 -6 -14 -15 3}}
{{Multival|legend=1|2 -6 -6 -14 -15 3}}


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


{{Optimal ET sequence|legend=1| 14c, 16, 30bc, 44bccd }}
{{Optimal ET sequence|legend=1| 14c, 16, 30bc, 44bccd }}
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Comma list: 33/32, 45/44, 50/49
Comma list: 33/32, 45/44, 50/49


Mapping: [{{val|2 0 14 15 10}}, {{val|0 1 -3 -3 -1}}]
Mapping: {{mapping| 2 0 14 15 10 | 0 1 -3 -3 -1}}


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


{{Optimal ET sequence|legend=1| 14c, 16, 30bce, 44bccdee }}
{{Optimal ET sequence|legend=1| 14c, 16, 30bce, 44bccdee }}
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== Mohavila ==
== Mohavila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 135/128, 1323/1250
[[Comma list]]: 135/128, 1323/1250


[[Mapping]]: [{{val|1 1 4 7}}, {{val|0 2 -6 -15}}]
{{Mapping|legend=1| 1 1 4 7 | 0 2 -6 -15 }}


{{Multival|legend=1|2 -6 -15 -14 -29 -18}}
{{Multival|legend=1| 2 -6 -15 -14 -29 -18 }}


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


{{Optimal ET sequence|legend=1| 7d, 18b, 25b, 32bd }}
{{Optimal ET sequence|legend=1| 7d, 18b, 25b, 32bd }}
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Comma list: 33/32, 45/44, 1323/1250
Comma list: 33/32, 45/44, 1323/1250


Mapping: [{{val|1 1 4 7 4}}, {{val|0 2 -6 -15 -2}}]
Mapping: {{mapping| 1 1 4 7 4 | 0 2 -6 -15 -2 }}


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


{{Optimal ET sequence|legend=1| 7d, 18b, 25b, 32bde }}
{{Optimal ET sequence|legend=1| 7d, 18b, 25b, 32bde }}
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