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Subgroup temperaments: Difference between revisions

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== 4.3.5 subgroup ==
== 4.3.5 subgroup ==
=== Tetrahanson ===
=== Tetrahanson ===
{{Main|Tetrahanson}}
{{Main| Tetrahanson }}


[[Subgroup]]: 4.3.5
[[Subgroup]]: 4.3.5
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[[Comma list]]: 15625/15552
[[Comma list]]: 15625/15552


{{Mapping|1 3 3|0 -6 - 5|legend=1}}
{{Mapping|legend=2| 1 3 3 | 0 -6 - 5 }}


: Mapping generators: ~4, ~5/3
: Mapping generators: ~4, ~5/3


[[CTE tuning]]: ~4 = 2\1, ~5/3 = 882.941
[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941


[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
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Mapping generators: ~4, ~9/64
Mapping generators: ~4, ~9/64


[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~[[9/]] = 1394.429
[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429


[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
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=== Halftone ===
=== Halftone ===
''Main article: [[Halftone]]''
{{Main| Halftone }}
 
[[Subgroup]]: 3/2.5/2.7/2
[[Subgroup]]: 3/2.5/2.7/2


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


=== Pythium ===
=== Meanquad aka pythium ===
Pythium is a [[Domain basis #Canonical form|noncanonical form]] of meanquad.
{{Main| Meanquad }}
 
[[Subgroup]]: 4.6.5


[[Subgroup]]: 3/2.4.5
[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}


[[Comma list]]: [[81/80]]
{{Mapping|legend=2| 1 0 -4| 0 1 4 }}


{{Mapping|legend=2|1 0 4|0 1 0}}
: mapping generators: ~4, ~6


[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\1edf, ~[[6/5]] = 294.135
[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214


[[Support]]ing [[ET]]s: *7, *5, *9, *12, *11, *8, *16, *13[+4], *19[+5], *17[+5], *15[+4], *23[+5], *20[+4, +5], *25[+4, +5]
[[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 3/2
<nowiki>*</nowiki> wart for 4


==== 3/2.4.5.7 ====
==== 4.6.5.7 subgroup (tetrominant) ====
[[Subgroup]]: 3/2.4.5.7
[[Subgroup]]: 4.6.5.7


[[Comma list]]: [[36/35]], [[64/63]]
[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}


{{Mapping|legend=2|1 0 4 4|0 1 0 2}}
{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}


[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\1edf, ~[[6/5]] = 286.062
[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622


[[Support]]ing [[ET]]s: *5, *7, *12, *9[+7], *8, *17[+5], *11[+7], *19[+5, +7], *13, *16[+7], *22[+5], *26[+5, +7], *29[+5, +7], *23[+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 3/2
<nowiki>*</nowiki> wart for 4


[[Category:Subgroup temperaments| ]] <!-- main article -->
[[Category:Subgroup temperaments| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"