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Subgroup temperaments: Difference between revisions

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→Fractional subgroup temperaments: cleanup (5/); normalize subgroup and wart usage
→Fractional subgroup temperaments: cleanup (6/6): these are by no means optimal ET sequences
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: [[gencom]]: [2 3/2; 352/351 364/363]
: [[gencom]]: [2 3/2; 352/351 364/363]


[[Optimal tuning]] ([[POL2]]): ~3/2 = 703.856
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856


{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}
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[[Comma list]]: 121/120
[[Comma list]]: 121/120


[[Gencom]]: [3/2 12/11; 121/120]
{{Mapping|legend=2| 1 1 1 | 0 2 -1 }}]


[[POTE generator]]: ~[[12/11]] = 158.29
: [[gencom]]: [3/2 12/11; 121/120]


[[Mapping]]: [{{val|1 1 1}}, {{val|0 2 -1}}]
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2, [12/11 = 158.29


{{Optimal ET sequence|legend=1|9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49}}
{{Optimal ET sequence|legend=1|9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49}}
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[[Subgroup]]: 5/2.7.11
[[Subgroup]]: 5/2.7.11


[[Comma list]]: 341796875/329832448
[[Comma list]]: {{monzo| 11 1 -5 }}


[[Gencom]]: [5/2 125/88; 341796875/329832448]
{{Mapping|legend=2| 1 4 3 | 0 -5 -1 }}


[[POTE generator]]: ~125/88 = 595.602
: [[gencom]]: [5/2 125/88; 341796875/329832448]


[[Mapping]]: [{{val|1 4 3}}, {{val|0 -5 -1}}]
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/2 = 1586.3137, ~125/88 = 593.6668


{{Optimal ET sequence|legend=1|8, 5[-7], 11[+7], 13[-7], 19[+7], 21[-7], 27[+7], 29[-7], 35[+7], 43[+7], 37[-7], 51[+7, +11], 45[-7], 59[+7, +11]|equave=f}}
Supporting ETs: *5[-7], *8, *19[+7], *21[-7], *27[+7], *29[-7], *35[+7], *43[+7], *37[-7], *51[+7, +11], *45[-7], *59[+7, +11]
 
<nowiki>*</nowiki> wart for 5/2


=== Doubleton ===
=== Doubleton ===
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[[Comma list]]: 1352/1323
[[Comma list]]: 1352/1323


[[CTE tuning|CTE generator]]: ~26/21 = 1\[[2edf]], ~28/9 = 1971.772
{{Mapping|legend=2| 2 0 3 | 0 1 1 }}


[[Mapping]]: [{{val|2 4 7}}, {{val|0 1 1}}]
: sval mapping generators: ~26/21, ~7


{{Optimal ET sequence|legend=1|6, 10, 16, 14[-13], 8[+7], 22, 18[-13], 26, 24[-13], 28[+7], 20[+7], 36[-13], 12[+7, +13], 34[-13]|equave=f}}
[[Optimal tuning]] ([[CTE]]): ~26/21 = 350.9775, ~28/9 = 1971.772{{clarify}}
 
Supporting ETs: *6, *10, *16, *14[-13], *8[+7], *22, *18[-13], *26, *24[-13], *28[+7], *20[+7], *36[-13], *12[+7, +13], *34[-13]
 
<nowiki>*</nowiki> wart for 3/2


=== Auk ===
=== Auk ===
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[[Comma list]]: 87808/85293
[[Comma list]]: 87808/85293


[[CTE tuning|CTE generator]]: ~28/9 = 1950.859
{{Mapping|legend=2| 1 0 -8 | 0 1 3 }}


[[Mapping]]: [{{val|1 2 -2}}, {{val|0 1 3}}]
: sval mapping generators: ~3/2, ~7


{{Optimal ET sequence|legend=1|5, 9, 13, 14, 6[+13], 17[-7, -13], 7[-7, -13], 22[-7], 19[+13], 23[+13], 11[+13], 21[-7, -13], 31[-7], 25[-7, -13]|equave=f}}
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9550, ~28/9 = 1950.859{{clarify}}


Supporting ETs: *5, *6[+13], *7[-7, -13], *9, *11[+13], *13, *14, *17[-7, -13], *19[+13], *21[-7, -13], *22[-7], *23[+13], *25[-7, -13], *31[-7]
<nowiki>*</nowiki> wart for 3/2


=== Halftone ===
=== Halftone ===
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[[Comma list]]: 9604/9375
[[Comma list]]: 9604/9375


[[CTE tuning|CTE generator]]: ~[[7/5]] = 128.783
{{Mapping|legend=2| 1 3 -4 | 0 -4 -5 }}
 
: sval mapping generators: ~3/2, ~15/14


[[Mapping]]: [{{val|1 3 -4}}, {{val|0 -4 -5}}]
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9550, ~15/14 = 128.783{{clarify}}


{{Optimal ET sequence|legend=1|11, 5, 6, 16, 27, 17[+5/2], 38, 21[-7/2], 7[+5/2, +7/2], 28[+5/2], 49, 43[-7/2], 9[-5/2, --7/2], 23[+5/2, +7/2]|equave=f}}
Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49


<nowiki>*</nowiki> wart for 3/2


[[Category:Subgroup temperaments| ]] <!-- main article -->
[[Category:Subgroup temperaments| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
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