No-fives subgroup temperaments: Difference between revisions
→Skidoo: I'm not the one who named it; unverified Tags: Mobile edit Mobile web edit |
Added Glacier and extensions |
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* [https://www.youtube.com/watch?v=bwGjN56iMM0 ''Moody Improvisation in the Shoal Temperament''] - [[Budjarn Lambeth]] (2025) | * [https://www.youtube.com/watch?v=bwGjN56iMM0 ''Moody Improvisation in the Shoal Temperament''] - [[Budjarn Lambeth]] (2025) | ||
=== Glacier === | |||
The 2.3.13 gene subgroup is not nearly as good as Shoal, but it can extend extremely well to other no-5 subgroups. It is very well represented in [[26edo]], where a pure 13/12 can serve as the generator, but [[94edo]] provides a much better tuning in higher subgroups. | |||
[[Subgroup]]: 2.3.13 | |||
[[Comma list]]: [[373248/371293]] | |||
{{Mapping|legend=2|1 1 3|0 5 6}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 140.360 | |||
{{Optimal ET sequence|legend=1|9, 17, 26, 43, 60, 77, 94, 111, 137, 171}} | |||
Badness (Sintel): 0.383 | |||
=== Glaceir === | |||
[[Subgroup]]: 2.3.11.13 | |||
[[Comma list]]: [[144/143]], [[1352/1331]] | |||
{{Mapping|legend=2|1 1 3 3|0 5 4 6}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 139.755 | |||
{{Optimal ET sequence|legend=1|9, 17, 26, 43, 60d}} | |||
Badness (Sintel): 0.420 | |||
==== 2.3.7.11.13 ==== | |||
[[Subgroup]]: 2.3.7.11.13 | |||
[[Comma list]]: [[78/77]], [[99/98]], [[144/143]] | |||
{{Mapping|legend=2|1 1 2 3 3|0 5 7 4 6}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 139.817 | |||
{{Optimal ET sequence|legend=1|9, 17, 26, 43, 60d}} | |||
Badness (Sintel): 0.400 | |||
=== Glaishur === | |||
[[Subgroup]]: 2.3.11.13 | |||
[[Comma list]]: [[352/351]], [[531674/531441]] | |||
{{Mapping|legend=2|1 1 0 3|0 5 21 6}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 140.537 | |||
{{Optimal ET sequence|legend=1|17, 77, 94, 111, 128, 145, 205}} | |||
Badness (Sintel): 0.400 | |||
==== 2.3.7.11.13 ==== | |||
[[Subgroup]]: 2.3.7.11.13 | |||
[[Comma list]]: [[352/351]], [[729/728]], [[1573/1568]] | |||
{{Mapping|legend=2|1 1 0 1 3|0 5 24 21 6}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 140.429 | |||
{{Optimal ET sequence|legend=1|17, 77, 94, 111, 128, 145, 205}} | |||
Badness (Sintel): 0.415 | |||
==== 2.3.7.11.13.23 ==== | |||
[[Subgroup]]: 2.3.7.11.13.23 | |||
[[Comma list]]: [[352/351]], [[729/728]], [[253/252]], [[1288/1287]] | |||
{{Mapping|legend=2|1 1 0 1 3 3|0 5 24 21 6 13}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 140.426 | |||
{{Optimal ET sequence|legend=1|17, 77, 94, 111, 205}} | |||
Badness (Sintel): 0.452 | |||
==== 2.3.7.11.13.23.29 ==== | |||
[[Subgroup]]: 2.3.7.11.13.23.29 | |||
[[Comma list]]: [[352/351]], [[729/728]], [[253/252]], [[1288/1287]], [[378/377]] | |||
{{Mapping|legend=2|1 1 0 1 3 3 1|0 5 24 21 6 13 33}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 140.426 | |||
{{Optimal ET sequence|legend=1|17, 77, 94, 111j}} | |||
Badness (Sintel): 0.511 | |||
==== 2.3.7.11.13.19.23.29 ==== | |||
[[Subgroup]]: 2.3.7.11.13.23.29 | |||
[[Comma list]]: [[352/351]], [[729/728]], [[209/208]], [[253/252]], [[1288/1287]], [[378/377]] | |||
{{Mapping|legend=2|1 1 0 1 3 -6 3 1|0 5 24 21 6 -15 13 33}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[13/12]] = 140.426 | |||
{{Optimal ET sequence|legend=1|17, 77, 94, 111j}} | |||
Badness (Sintel): 0.699 | |||
== Temperaments with a higher-limit gene == | == Temperaments with a higher-limit gene == | ||