Canou family: Difference between revisions
Move some of the detailed descriptions to the main article |
+extension section (more to be added) and 13-limit synca extension |
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[[Complexity spectrum]]: 4/3, 9/7, 9/8, 7/6, 6/5, 10/9, 5/4, 8/7, 7/5 | [[Complexity spectrum]]: 4/3, 9/7, 9/8, 7/6, 6/5, 10/9, 5/4, 8/7, 7/5 | ||
=== Extensions === | |||
Canou has a neat extension to the 2.3.5.7.17.19 subgroup with virtually no additional errors. The comma basis is {1216/1215, 1225/1224, 1445/1444}. Otherwise, 11- and 13-limit extensions are somewhat less ideal. | |||
== Synca == | == Synca == | ||
Synca, for symbiotic canou, adds the [[symbiotic comma]] to the comma list. | Synca, for symbiotic canou, adds the [[symbiotic comma]] and the [[wilschisma]] to the comma list. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Comma list]]: 19712/19683, 42875/42768 | [[Comma list]]: 19712/19683, 42875/42768 | ||
[[Mapping]]: [{{val| 1 0 0 -1 -7 }}, {{val| 0 1 2 2 7 }}, {{val| 0 0 4 - | [[Mapping]]: [{{val| 1 0 0 -1 -7 }}, {{val| 0 1 2 2 7 }}, {{val| 0 0 -4 3 -3 }}] | ||
[[POTE generator]]s: ~3/2 = 702.2549, ~81/70 = 254.6291 | [[POTE generator]]s: ~3/2 = 702.2549, ~81/70 = 254.6291 | ||
{{Val list|legend=1| 94, 99e, 118, 193, 212, 311, 740 }} | {{Val list|legend=1| 94, 99e, 118, 193, 212, 311, 740, 1051d }} | ||
[[Badness]]: 2.042 × 10<sup>-3</sup> | [[Badness]]: 2.042 × 10<sup>-3</sup> | ||
[[Complexity spectrum]]: 4/3, 9/8, 9/7, 7/6, 5/4, 6/5, 10/9, 11/9, 8/7, 12/11, 11/10, 14/11, 11/8, 7/5 | [[Complexity spectrum]]: 4/3, 9/8, 9/7, 7/6, 5/4, 6/5, 10/9, 11/9, 8/7, 12/11, 11/10, 14/11, 11/8, 7/5 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2080/2079, 19712/19683, 42875/42768 | |||
Mapping: [{{val| 1 0 0 -1 -7 -13 }}, {{val| 0 1 2 2 7 10 }}, {{val| 0 0 -4 3 -3 4 }}] | |||
POTE generators: ~3/2 = 702.1807, ~81/70 = 254.6239 | |||
Vals: {{Val list| 94, 118f, 193f, 212, 217, 311, 740, 1051d }} | |||
Badness: 2.555 × 10<sup>-3</sup> | |||
== Semicanou == | == Semicanou == | ||
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[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Canou]] | [[Category:Canou family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||