Schismatic family: Difference between revisions
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== Pontiac == | == Pontiac == | ||
{{main|Pontiac}} | {{main| Pontiac }} | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Badness: 0.033677 | Badness: 0.033677 | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Badness: 0.028891 | Badness: 0.028891 | ||
==== Helena ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 169/168, 325/324, 385/384, 3146/3125 | |||
Mapping: [{{val|1 0 15 -59 51 -28}}, {{val|0 1 -8 39 -30 20}}] | |||
POTE generator: ~3/2 = 701.740 | |||
Optimal GPV sequence: {{Val list| 53, 118f, 171ef }} | |||
Badness: 0.036281 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 169/168, 273/272, 325/324, 385/384, 3146/3125 | |||
Mapping: [{{val|1 0 15 -59 51 -28 -91}}, {{val|0 1 -8 39 -30 20 60}}] | |||
POTE generator: ~3/2 = 701.730 | |||
Optimal GPV sequence: {{Val list| 53, 118f, 171ef, 289eff }} | |||
Badness: 0.030688 | |||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 169/168, 273/272, 286/285, 325/324, 385/384, 627/625 | |||
Mapping: [{{val|1 0 15 -59 51 -28 -91 9}}, {{val|0 1 -8 39 -30 20 60 -3}}] | |||
POTE generator: ~3/2 = 701.729 | |||
Optimal GPV sequence: {{Val list| 53, 118f, 171ef, 289effh }} | |||
Badness: 0.021892 | |||
=== Ponta === | === Ponta === | ||
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=== Semiterm === | === Semiterm === | ||
The ''semiterm'' temperament (12&342 | The ''semiterm'' temperament (12&342) has a period of 1/6 octave and tempers out [[9801/9800]] (kalisma) and 151263/151250 (odiheim comma). | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||