Pentacircle clan: Difference between revisions
m +link to parahemif |
+etypyth and terrapyth as proposed by Scott Dakota and found in the temperament finder |
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* ''[[Uni]]'', {540/539, 896/891} → [[Hemimage family #Uni|Hemimage family]] | * ''[[Uni]]'', {540/539, 896/891} → [[Hemimage family #Uni|Hemimage family]] | ||
Considered below, in addition to the no-5 subgroup temperament ''parapyth'', | Considered below, in addition to the no-5 subgroup temperament ''parapyth'', are ''tolerant'' and ''terrapyth''. | ||
== Pentacircle == | == Pentacircle == | ||
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Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
Comma list: 352/351, 364/363 | |||
Sval mapping: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 -4 -7 }}, {{val| 0 0 0 1 1 1 }}] | |||
POTE generators: ~3/2 = 703.8563, ~7/4 = 969.9074 | |||
{{Val list | Optimal GPV sequence: {{Val list| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }} | ||
[ | Badness: 0.101 × 10<sup>-3</sup> | ||
=== Etypyth === | |||
Subgroup: 2.3.7.11.13.17 | |||
Comma list: 352/351, 364/363, 442/441 | |||
Sval mapping: [{{val| 1 0 0 0 7 12 -13 }}, {{val| 0 1 0 0 -4 -7 9 }}, {{val| 0 0 0 1 1 1 1 }}] | |||
POTE generators: ~3/2 = 704.0315, ~7/4 = 970.6051 | |||
Optimal GPV sequence: {{Val list| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }} | |||
Badness: 0.325 × 10<sup>-3</sup> | |||
== Tolerant == | == Tolerant == | ||
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Mapping: [{{val| 1 0 0 -10 -3 2 }}, {{val| 0 1 0 11 7 4 }}, {{val| 0 0 1 -2 -2 -2 }}] | Mapping: [{{val| 1 0 0 -10 -3 2 }}, {{val| 0 1 0 11 7 4 }}, {{val| 0 0 1 -2 -2 -2 }}] | ||
POTE generators: ~3/2 = 703.9605, ~5/4 = 386.9831 | |||
Vals: {{Val list| 41, 46, 80, 87, 121, 167, 208, 375be, 583bef }} | Vals: {{Val list| 41, 46, 80, 87, 121, 167, 208, 375be, 583bef }} | ||
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Badness: 0.982 × 10<sup>-3</sup> | Badness: 0.982 × 10<sup>-3</sup> | ||
== Terrapyth == | |||
Terrapyth tempers out the leapday comma, and can be described as 29 & 46 & 121. | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 896/891, 585640/583443 | |||
[[Mapping]]: [{{val| 1 0 -31 0 7 }}, {{val| 0 1 21 0 -4 }}, {{val| 0 0 0 1 1 }}] | |||
Mapping generators: ~2, ~3, ~7 | |||
[[POTE generator]]s: ~3/2 = 704.1814, ~7/4 = 970.6217 | |||
{{Val list|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }} | |||
[[Badness]]: 5.35 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 364/363, 9295/9261 | |||
Mapping: [{{val| 1 0 -31 0 7 12 }}, {{val| 0 1 0 11 7 4 -7 }}, {{val| 0 0 1 -2 -2 -2 1 }}] | |||
POTE generators: ~3/2 = 704.1691, ~7/4 = 970.8432 | |||
Vals: {{Val list| 17c, 29, 46, 75e, 92def, 121, 167, 288be }} | |||
Badness: 2.48 × 10<sup>-3</sup> | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 352/351, 364/363, 442/441, 715/714 | |||
Mapping: [{{val| 1 0 -31 0 7 12 -13 }}, {{val| 0 1 0 11 7 4 -7 9 }}, {{val| 0 0 1 -2 -2 -2 1 1 }}] | |||
POTE generators: ~3/2 = 704.1628, ~7/4 = 970.6620 | |||
Vals: {{Val list| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }} | |||
Badness: 1.52 × 10<sup>-3</sup> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||