Semicanousmic clan: Difference between revisions
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* ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]] | * ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]] | ||
Considered below | Considered below are deuteromere, the no-7 subgroup temperament, and vonacimes, but we can begin by looking at the rank-4 temperament. | ||
== Semicanousmic == | == Semicanousmic == | ||
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Badness: 0.403 × 10<sup>-3</sup> | Badness: 0.403 × 10<sup>-3</sup> | ||
== Vonacimes == | |||
Vonacimes (''semicanou'' spelt backwards) is in a certain sense dual to semicanou. It splits the perfect twelfth into two, whereas semicanou splits the octave. | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 14641/14580, 160083/160000 | |||
[[Mapping]]: [{{val| 1 0 2 7 1 }}, {{val| 0 2 0 -6 3 }}, {{val| 0 0 4 7 1 }}] | |||
Mapping generators: ~2, ~400/231, ~200/189 | |||
[[POTE generator]]s: ~400/231 = 951.1931, ~200/189 = 96.5791 | |||
{{Val list|legend=1| 87, 111, 125, 198, 212, 323, 410 }} | |||
[[Badness]]: 3.946 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 676/675, 1001/1000, 14641/14580 | |||
Mapping: [{{val| 1 0 2 7 1 1 }}, {{val| 0 2 0 -6 3 3 }}, {{val| 0 0 4 7 1 4 }}] | |||
POTE generators: ~26/15 = 951.2412, ~55/52 = 96.6292 | |||
Optimal GPV sequence: {{val list| 87, 111, 198, 323, 410 }} | |||
Badness: 1.893 × 10<sup>-3</sup> | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 676/675, 715/714, 1001/1000, 14641/14580 | |||
Mapping: [{{val| 1 0 2 7 1 1 -4 }}, {{val| 0 2 0 -6 3 3 10 }}, {{val| 0 0 4 7 1 4 2 }}] | |||
POTE generators: ~26/15 = 951.1985, ~55/52 = 96.5941 | |||
Optimal GPV sequence: {{val list| 87, 111, 198g, 212g, 299, 323, 410 }} | |||
Badness: 1.903 × 10<sup>-3</sup> | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 1445/1444 | |||
Mapping: [{{val| 1 0 2 7 1 1 -4 -4 }}, {{val| 0 2 0 -6 3 3 10 10 }}, {{val| 0 0 4 7 1 4 2 4 }}] | |||
POTE generators: ~26/15 = 951.1592, ~55/52 = 96.5502 | |||
Optimal GPV sequence: {{val list| 87, 111, 198gh, 212gh, 299, 323, 410, 622ef }} | |||
Badness: 1.733 × 10<sup>-3</sup> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Semicanousmic clan| ]] <!-- main article --> | [[Category:Semicanousmic clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||