Trisedodge family: Difference between revisions
m →13-limit: add POTE for symmetry/completeness |
m →Septimal trisedodge: explain generators |
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== Septimal trisedodge == | == Septimal trisedodge == | ||
The generator of this temperament, when reduced to be as small as possible (by using period-reduction and period-complement-reduction) is what is shown in the optimal tunings, however note that the generator is also interpretable as ~6/5 (reached by a period plus 25/24, that is, 144/125 * 25/24 = 6/5). Other possible generators are described below in the limits in which they appear. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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=== 11-limit === | === 11-limit === | ||
In the 11-limit the generator can be taken to be ~11/10 (reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10). Therefore, because a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Mapping: {{mapping| 5 1 7 21 15 | 0 3 2 -3 1 }} | Mapping: {{mapping| 5 1 7 21 15 | 0 3 2 -3 1 }} | ||
Optimal tunings: (all have 1\5 = ~55/48) | Optimal tunings: (all have 1\5 = ~[[63/55]]~[[55/48]]) | ||
* POTE: ~25/24 = 74.9401 | * POTE: ~25/24 = 74.9401 | ||
* CTE: ~25/24 = 74.466 | * CTE: ~25/24 = 74.466 | ||