Varunismic temperaments: Difference between revisions
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This is a collection of rank-2 | {{Technical data page}} | ||
This is a collection of [[rank-2 temperament]]s tempering out the [[varunisma]], 321489/320000 = {{monzo| -9 8 -4 2 }}. For the [[rank-3 temperament]] tempering out 321489/320000 in the 7-limit, see [[Miscellaneous 7-limit temperaments #Varuna]]. | |||
Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]] | * ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]] | ||
* ''[[Diaschismic]]'' (+126/125) → [[Diaschismic family # | * ''[[Diaschismic]]'' (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]] | ||
* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]] | * ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]] | ||
* ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]] | * ''[[Bamity]]'' (+245/243) → [[Amity family #Bamity|Amity family]] | ||
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* ''[[Bischismic]]'' (+3136/3125) → [[Schismatic family #Bischismic|Schismatic family]] | * ''[[Bischismic]]'' (+3136/3125) → [[Schismatic family #Bischismic|Schismatic family]] | ||
* ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]] | * ''[[Bison]]'' (+6144/6125) → [[Sensipent family #Bison|Sensipent family]] | ||
* ''[[ | * ''[[Bicommatic]]'' (+10976/10935) → [[Hemimage temperaments #Bicommatic|Hemimage temperaments]] | ||
* ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]] | * ''[[Narayana]]'' (+65625/65536) → [[Vishnuzmic family #Narayana|Vishnuzmic family]] | ||
* ''[[Decal]]'' (+235298/234375) → [[Pental family #Decal|Pental family]] | * ''[[Decal]]'' (+235298/234375) → [[Pental family #Decal|Pental family]] | ||
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: mapping generators: ~567/400, ~243/196 | : mapping generators: ~567/400, ~243/196 | ||
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~243/196 = 372.597 (~343/300 = 227.403) | |||
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~243/196 = 372.597 | |||
{{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }} | {{Optimal ET sequence|legend=1| 58, 132d, 190, 248, 438d, 686d }} | ||
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Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }} | Mapping: {{mapping| 2 10 27 23 33 | 0 -11 -36 -28 -42 }} | ||
Optimal tuning (POTE): ~99/70 = 1\2, ~150/121 = 372.599 | Optimal tuning (POTE): ~99/70 = 1\2, ~150/121 = 372.599 (~154/135 = 227.401) | ||
{{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }} | {{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }} | ||
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Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }} | Mapping: {{mapping| 2 10 27 23 33 31 | 0 -11 -36 -28 -42 -38 }} | ||
Optimal tuning (POTE): ~99/70 = 1\2, ~26/21 = 372.602 | Optimal tuning (POTE): ~99/70 = 1\2, ~26/21 = 372.602 (~154/135 = 227.398) | ||
{{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }} | {{Optimal ET sequence|legend=1| 58, 132de, 190, 248, 438d }} | ||
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: mapping generators: ~160/147, ~350/243 | : mapping generators: ~160/147, ~350/243 | ||
[[Optimal tuning]] ([[POTE]]): ~160/147 = 1\8, ~350/243 = 633.738 | [[Optimal tuning]] ([[POTE]]): ~160/147 = 1\8, ~350/243 = 633.738 (~49/48 = 33.738) | ||
{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }} | {{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }} | ||
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Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }} | Mapping: {{mapping| 8 0 -11 14 15 | 0 3 7 2 3 }} | ||
Optimal tuning (POTE): ~12/11 = 1\8, ~121/84 = 633.755 | Optimal tuning (POTE): ~12/11 = 1\8, ~121/84 = 633.755 (~49/48 = 33.755) | ||
{{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }} | {{Optimal ET sequence|legend=1| 32c, 72, 176, 248, 320 }} | ||
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Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }} | Mapping: {{mapping| 8 0 -11 14 15 -38 | 0 3 7 2 3 16 }} | ||
Optimal tuning (POTE): ~12/11 = 1\8, ~75/52 = 633.742 | Optimal tuning (POTE): ~12/11 = 1\8, ~75/52 = 633.742 (~49/48 = 33.742) | ||
{{Optimal ET sequence|legend=1| 72, 176f, 248, 320 }} | {{Optimal ET sequence|legend=1| 72, 176f, 248, 320 }} | ||
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Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }} | Mapping: {{mapping| 8 0 -11 14 15 0 | 0 3 7 2 3 7 }} | ||
Optimal tuning (POTE): ~12/11 = 1\8, ~13/9 = 633.8370 | Optimal tuning (POTE): ~12/11 = 1\8, ~13/9 = 633.8370 (~49/48 = 33.8370) | ||
{{Optimal ET sequence|legend=1| 32cf, 72, 176, 248f }} | {{Optimal ET sequence|legend=1| 32cf, 72, 176, 248f }} | ||