Subgroup temperaments: Difference between revisions

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{{Optimal ET sequence|legend=1| 5, 13, 31 }}
{{Optimal ET sequence|legend=1| 5, 13, 31 }}


== 2.9.25 subgroup ==
== 4.9.25 subgroup ==
=== Squared meantone ===
=== Meansquared ===
[[Subgroup]]: 2.9.25
[[Subgroup]]: 4.9.25


[[Comma list]]: [[6561/6400]]
[[Comma list]]: [[6561/6400]]
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{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
{{Mapping|legend=2| 1 3 4 | 0 1 4 }}


[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 194.429
Mapping generators: ~4, ~9/64


[[Support]]ing [[ET]]s: 6, 7[-25], 13, 19, 5[+25], 25, 31, 11[+25], 8[-25], 37, 20[-25], 32[-25], 17[+25], 43
[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~[[9/]] = 1394.429


==== Squared dominant ====
[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
[[Subgroup]]: 2.9.25.49


[[Comma list]]: 1296/1225, 4096/3969
== 4.9.49 subgroup ==
=== Archsquared ===
[[Subgroup]]: 4.9.49


{{Mapping|legend=2| 1 3 4 6 | 0 1 4 -2 }}
[[Comma list]]: 4096/3969


[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 199.244
{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}


[[Support]]ing [[ET]]s: 6, 5[+25], 11[+25], 17[+25, +49], 23[+25, +49], 29[+25, +49]
Mapping generators: ~4, ~9/64


==== Squared septimal meantone ====
[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190
[[Subgroup]]: 2.9.25.49
 
[[Comma list]]: [[6561/6400]], 50625/50176
 
{{Mapping|legend=2| 1 3 4 4 | 0 1 4 10 }}
 
[[Optimal tuning]] ([[CTE]]): ~[[9/8 ]]= 193.904
 
[[Support]]ing [[ET]]s: 6, 25, 19[-49], 31, 13[-49], 7[-25, -49], 37, 56[-9], 44[-49], 43[+49], 32[-25, --49], 68[-9], 81[-9, -49], 69[-9, -49]
 
==== Squared flattone ====
[[Subgroup]]: 2.9.25.49
 
[[Comma list]]: [[6561/6400]], 765625/746496


{{Mapping|legend=2| 1 3 4 7 | 0 1 4 -9 }}
[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
 
[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 187.104
 
[[Support]]ing [[ET]]s:  13, 6[-49], 19[-49], 32[-25, -49], 45[-9, -25, -49], 51[-9, -25, -49], 58[-9, -25, -49], 70[-9, -25, --49], 77[-9, --25, -49], 83[-9, -25, --49], 109[--9, --25, --49], 115[--9, --25, ---49], 122[--9, ---25, --49], 141[--9, ---25, ---49]
 
== 2.9.49 subgroup ==
=== Squared archy ===
[[Subgroup]]: 2.9.49
 
[[Comma list]]: 5, 11, 6, 16, 17[+49], 7[+49], 27, 21, 9[-49], 28[+49], 23[+49], 13[+49], 26[+9], 38[+9, +49]
 
{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
 
[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190


[[Support]]ing [[ET]]s: 5, 11, 6, 16, 17[+49], 7[+49], 27, 21, 9[-49], 28[+49], 23[+49], 13[+49], 26[+9], 38[+9, +49]


== 8.9.7 subgroup ==
== 8.9.7 subgroup ==