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. | ||
== Cake (45/44) == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: [[45/44]] | |||
{{Mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 694.823, ~5/4 = 378.660, ~7/4 = 968.826 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 693.197, ~5/4 = 376.082, ~7/4 = 965.060 | |||
{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 26, 45 }} | |||
[[Badness]]: 0.0219 × 10<sup>-6</sup> | |||
== Mothwellsmic (99/98) == | == Mothwellsmic (99/98) == | ||