Hemifamity family: Difference between revisions
Expand, +overview to extensions, +counterpyth, +17-limit pele |
→Laka: rework into mainly a 2.3.5.7.11.13.19 subgroup temperament |
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== Laka == | == Laka == | ||
{{Main| Laka }} | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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{{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }} | {{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }} | ||
[[Badness]]: 0.825 × 10<sup>-3</sup> | |||
[[Projection pair]]s: 5120/729 11 14348907/1310720 | [[Projection pair]]s: 5120/729 11 14348907/1310720 | ||
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Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 352/351, 540/539, | Comma list: 352/351, 540/539, 729/728 | ||
Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }} | Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }} | ||
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: eigenmonzo (unchanged-interval) basis: 2.11.13/7 | : eigenmonzo (unchanged-interval) basis: 2.11.13/7 | ||
{{Optimal ET sequence|legend=1| 41, 53, 58, 94, 111, 152f, | {{Optimal ET sequence|legend=1| 41, 53, 58, 94, 111, 152f, 415dff }}* | ||
<nowiki>*</nowiki> optimal patent val: [[205edo|205]] | |||
Badness: 0.822 × 10<sup>-3</sup> | |||
=== 2.3.5.7.11.13.19 subgroup === | |||
Subgroup: 2.3.5.7.11.13.19 | |||
Comma list: 352/351, 400/399, 495/494, 540/539 | |||
Mapping: {{mapping| 1 0 0 10 -18 -13 -6 | 0 1 0 -6 15 12 5 | 0 0 1 1 -1 -1 1 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.4062, ~5/4 = 385.5254 | |||
Optimal ET sequence: {{Optimal ET sequence| 41, 53, 58h, 94, 111, 152f, 415dffhh }}* | |||
<nowiki>*</nowiki> optimal patent val: [[205edo|205]] | <nowiki>*</nowiki> optimal patent val: [[205edo|205]] | ||
Badness: 0.661 × 10<sup>-3</sup> | |||
=== 17-limit === | === 17-limit === | ||
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: eigenmonzo (unchanged-interval) basis: 2.11.13/7 | : eigenmonzo (unchanged-interval) basis: 2.11.13/7 | ||
{{Optimal ET sequence | Optimal ET sequence: {{Optimal ET sequence| 58, 94, 111, 152f, 205, 263df }} | ||
Badness: 1.19 × 10<sup>-3</sup> | |||
== Akea == | == Akea == | ||