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Subgroup temperaments: Difference between revisions

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[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69


<nowiki>*</nowiki> wart for 4
<nowiki />* Wart for 4


==== 4.6.5.7 subgroup (tetrominant) ====
==== 4.6.5.7 subgroup (tetrominant) ====
Line 566: Line 566:
[[Support]]ing [[ET]]s: *7, *10, *17, *24, *27[+5], *31, *38[+7], *41, *44[+5], *55[+7], *58[+5, +7], *65[+5, +7], *75[+5, +7]
[[Support]]ing [[ET]]s: *7, *10, *17, *24, *27[+5], *31, *38[+7], *41, *44[+5], *55[+7], *58[+5, +7], *65[+5, +7], *75[+5, +7]


<nowiki>*</nowiki> wart for 4
<nowiki />* Wart for 4


=== Fourwar ===
=== Fourwar ===
Line 892: Line 892:
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}


<nowiki>*</nowiki> wart for 5/3
<nowiki />* Wart for 5/3


[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
Line 942: Line 942:
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}


<nowiki>*</nowiki> wart for 11/3
<nowiki />* Wart for 11/3


[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
Line 992: Line 992:
{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}


<nowiki>*</nowiki> wart for 13/11
<nowiki />* Wart for 13/11


[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
Line 1,015: Line 1,015:
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010


{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*† }}
{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}


<nowiki>*</nowiki> wart for 7/3
<nowiki />* Wart for 7/3


† wart for 11/3
<sup>†</sup> Wart for 11/3


[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
Line 1,064: Line 1,064:
* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1\1, ~9/7 = 440.902
* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1\1, ~9/7 = 440.902


{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166†, 197*†, 215†, 264*† }}
{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166<sup>†</sup>, 197*<sup>†</sup>, 215<sup>†</sup>, 264*<sup>†</sup> }}


<nowiki>*</nowiki> wart for 5/3
<nowiki />* Wart for 5/3


† wart for 9/7
<sup>†</sup> Wart for 9/7


[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
Line 1,222: Line 1,222:
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}


<nowiki>*</nowiki> wart for 9/7
<nowiki />* Wart for 9/7


[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
Line 1,457: Line 1,457:
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~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*<sup>†</sup> }}


<nowiki>*</nowiki> wart for 11/7
<nowiki />* Wart for 11/7


<nowiki>†</nowiki> wart for 13/7
<sup>†</sup> Wart for 13/7


[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
Line 1,519: Line 1,519:
{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}


<nowiki>*</nowiki> wart for 13/5
<nowiki />* Wart for 13/5


=== Oceanfront ===
=== Oceanfront ===
Line 1,584: Line 1,584:
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
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
<nowiki />* Wart for 3/2


==== 3/2.5/2.7/2.11/2 ====
==== 3/2.5/2.7/2.11/2 ====
Line 1,599: Line 1,599:
[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]
[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]


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


==== 3/2.5/2.7/2.11/2.13/2 ====
==== 3/2.5/2.7/2.11/2.13/2 ====
Line 1,612: Line 1,612:
[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]
[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]


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


=== Semiwolf ===
=== Semiwolf ===
Line 1,679: Line 1,679:
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]
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
<nowiki />* Wart for 3/2


=== Doubleton ===
=== Doubleton ===
Line 1,694: Line 1,694:
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]
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
<nowiki />* Wart for 3/2


== 5/2-equave subgroups ==
== 5/2-equave subgroups ==
Line 1,711: Line 1,711:
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]
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
<nowiki />* Wart for 5/2


= Related temperament collections =
= Related temperament collections =
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"