Countercomp family: Difference between revisions
Name change following pythagorean -> compton |
Update optimal tuning to include the period |
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The '''countercomp family''' tempers out [[41-comma|Pythagorean countercomma]], {{monzo| 65 -41 }}, and hence the fifths form a closed 41-note circle of fifths, identical to [[41edo]]. | The '''countercomp family''' tempers out the [[41-comma|Pythagorean countercomma]], {{monzo| 65 -41 }}, and hence the fifths form a closed 41-note circle of fifths, identical to [[41edo]]. | ||
== Countercomp == | == Countercomp == | ||
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Mapping generators: ~531441/524288, ~5/1 | Mapping generators: ~531441/524288, ~5/1 | ||
[[Optimal tuning]] ([[POTE]]): ~5/4 = 386.668 | [[Optimal tuning]] ([[POTE]]): ~531441/524288 = 1\41, ~5/4 = 386.668 | ||
{{Val list|legend=1| 41, 123, 164, 205, 369, 574, 779, 2132bc }} | {{Val list|legend=1| 41, 123, 164, 205, 369, 574, 779, 2132bc }} | ||
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{{Multival|legend=1| 0 41 0 65 0 -115 }} | {{Multival|legend=1| 0 41 0 65 0 -115 }} | ||
[[Optimal tuning]] ([[POTE]]): ~5/4 = 385.731 | [[Optimal tuning]] ([[POTE]]): ~64/63 = 1\41, ~5/4 = 385.731 | ||
{{Val list|legend=1| 41, 123, 164, 205d, 246d, 451dd }} | {{Val list|legend=1| 41, 123, 164, 205d, 246d, 451dd }} | ||
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Mapping: [{{val| 41 65 0 115 237 }}, {{val| 0 0 1 0 -1 }}] | Mapping: [{{val| 41 65 0 115 237 }}, {{val| 0 0 1 0 -1 }}] | ||
Optimal tuning (POTE): ~5/4 = 385.871 | Optimal tuning (POTE): ~56/55 = 1\41, ~5/4 = 385.871 | ||
Optimal GPV sequence: {{Val list| 41, 123e, 164, 205d, 451dd }} | Optimal GPV sequence: {{Val list| 41, 123e, 164, 205d, 451dd }} | ||
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Mapping: [{{val| 41 65 0 115 237 247 }}, {{val| 0 0 1 0 -1 -1 }}] | Mapping: [{{val| 41 65 0 115 237 247 }}, {{val| 0 0 1 0 -1 -1 }}] | ||
Optimal tuning (POTE): ~5/4 = 386.604 | Optimal tuning (POTE): ~56/55 = 1\41, ~5/4 = 386.604 | ||
Optimal GPV sequence: {{Val list| 41, 123e, 164, 205d }} | Optimal GPV sequence: {{Val list| 41, 123e, 164, 205d }} | ||
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{{Multival|legend=1| 0 41 41 65 65 -20 }} | {{Multival|legend=1| 0 41 41 65 65 -20 }} | ||
[[Optimal tuning]] ([[POTE]]): ~5/4 = 385.667 | [[Optimal tuning]] ([[POTE]]): ~50/49 = 1\41, ~5/4 = 385.667 | ||
{{Val list|legend=1| 41, 123d, 164d, 205, 246, 451d, 697dd }} | {{Val list|legend=1| 41, 123d, 164d, 205, 246, 451d, 697dd }} | ||
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Mapping: [{{val| 41 65 0 20 237 }}, {{val| 0 0 1 1 -1 }}] | Mapping: [{{val| 41 65 0 20 237 }}, {{val| 0 0 1 1 -1 }}] | ||
Optimal tuning (POTE): ~5/4 = 385.309 | Optimal tuning (POTE): ~55/54 = 1\41, ~5/4 = 385.309 | ||
Optimal GPV sequence: {{Val list| 41, 164d, 205, 246 }} | Optimal GPV sequence: {{Val list| 41, 164d, 205, 246 }} | ||
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[[Mapping]]: [{{val| 41 65 1 68 }}, {{val| 0 0 2 1 }}] | [[Mapping]]: [{{val| 41 65 1 68 }}, {{val| 0 0 2 1 }}] | ||
Mapping generators: ~ | Mapping generators: ~100352/98415, ~567/256 | ||
[[Optimal tuning]] ([[POTE]]): ~567/512 = 178.7115 | [[Optimal tuning]] ([[POTE]]): ~100352/98415 = 1\41, ~567/512 = 178.7115 | ||
{{Val list|legend=1| 41, 328, 369, 779 }} | {{Val list|legend=1| 41, 328, 369, 779 }} | ||
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Mapping: [{{val| 41 65 1 68 189 }}, {{val| 0 0 2 1 -1 }}] | Mapping: [{{val| 41 65 1 68 189 }}, {{val| 0 0 2 1 -1 }}] | ||
POTE | Optimal tuning (POTE): ~56/55 = 1\41, ~567/512 = 178.9285 | ||
Optimal GPV sequence: {{Val list| 41, 328, 369 }} | Optimal GPV sequence: {{Val list| 41, 328, 369 }} | ||
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Mapping: [{{val| 41 65 1 68 236 }}, {{val| 0 0 2 1 -2 }}] | Mapping: [{{val| 41 65 1 68 236 }}, {{val| 0 0 2 1 -2 }}] | ||
Optimal tuning (POTE): ~ | Optimal tuning (POTE): ~55/54 = 1\41, ~256/231 = 178.3714 | ||
Optimal GPV sequence: {{Val list| 41, 328e, 369e, 410, 451, 861e, 2173bcee }} | Optimal GPV sequence: {{Val list| 41, 328e, 369e, 410, 451, 861e, 2173bcee }} | ||