Catalog of rank-4 temperaments: Difference between revisions
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A '''rank-4 temperament''' has a period and three additional independent generators. Typical examples include [[7-limit]] [[JI]], full 11-limit temperament with a one-dimensional [[comma basis]], and full 13-limit temperament with a two-dimensional comma basis. | A '''rank-4 temperament''' has a period and three additional independent generators. Typical examples include [[7-limit]] [[JI]], full 11-limit temperament with a one-dimensional [[comma basis]], and full 13-limit temperament with a two-dimensional comma basis. | ||
== Mothwellsmic (99/98) == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: [[99/98]] | |||
{{Mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 700.306, ~5/4 = 386.314, ~7/4 = 974.000 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 700.060, ~5/4 = 385.931, ~7/4 = 973.388 | |||
{{Optimal ET sequence|legend=1| 5, 8d, 9, 12, 17c, 19e, 22, 31, 53, 84e, 96, 127 }} | |||
[[Badness]]: 0.0299 × 10<sup>-6</sup> | |||
== Ptolemismic (100/99) == | == Ptolemismic (100/99) == | ||
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[[Comma list]]: [[243/242]] | [[Comma list]]: [[243/242]] | ||
{{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0}} | {{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }} | ||
: mapping generators: ~2, ~11/9, ~5, ~7 | : mapping generators: ~2, ~11/9, ~5, ~7 | ||
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[[Badness]]: 0.0509 × 10<sup>-6</sup> | [[Badness]]: 0.0509 × 10<sup>-6</sup> | ||
== Frostmic (245/242) == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: [[245/242]] | |||
{{Mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }} | |||
: mapping generators: ~2, ~3, ~11/7, ~7 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.955, ~11/7 = 792.479, ~7/4 = 964.861 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.753, ~5/4 = 792.335, ~7/4 = 964.527 | |||
{{Optimal ET sequence|legend=1| 9, 12, 15, 23de, 24, 26, 27e, 38d, 41, 91, 106d }} | |||
[[Badness]]: 0.0897 × 10<sup>-6</sup> | |||
== Akua (352/351, 847/845) == | == Akua (352/351, 847/845) == | ||