Countercomp family: Difference between revisions
m FloraC moved page Counterpyth family to Countercomp family: Name change following pythagorean -> compton |
Name change following pythagorean -> compton |
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The ''' | 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]]. | ||
== | == Countercomp == | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
[[Comma list]]: {{monzo| 65 -41 }} | [[Comma list]]: {{monzo| 65 -41 }} | ||
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Mapping generators: ~531441/524288, ~5/1 | Mapping generators: ~531441/524288, ~5/1 | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~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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[[Badness]]: 0.934310 | [[Badness]]: 0.934310 | ||
== | == Gamelacomp == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 1029/1024, 537824/531441 | [[Comma list]]: 1029/1024, 537824/531441 | ||
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{{Multival|legend=1| 0 41 0 65 0 -115 }} | {{Multival|legend=1| 0 41 0 65 0 -115 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~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 }}] | ||
POTE | Optimal tuning (POTE): ~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 }}] | ||
POTE | Optimal tuning (POTE): ~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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Badness: 0.054921 | Badness: 0.054921 | ||
== | == Mermacomp == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 5120/5103, 2500000/2470629 | [[Comma list]]: 5120/5103, 2500000/2470629 | ||
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{{Multival|legend=1| 0 41 41 65 65 -20 }} | {{Multival|legend=1| 0 41 41 65 65 -20 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~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 }}] | ||
POTE | Optimal tuning (POTE): ~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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Badness: 0.076588 | Badness: 0.076588 | ||
== | == Hemicountercomp == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 2401/2400, 52613349376/52301766015 | [[Comma list]]: 2401/2400, 52613349376/52301766015 | ||
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Mapping generators: ~531441/524288, ~567/256 | Mapping generators: ~531441/524288, ~567/256 | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~567/512 = 178.7115 | ||
{{Val list|legend=1| 41, 328, 369, 779 }} | {{Val list|legend=1| 41, 328, 369, 779 }} | ||
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Badness: 0.064400 | Badness: 0.064400 | ||
=== | === Hemermacomp === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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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 }}] | ||
POTE | Optimal tuning (POTE): ~567/512 = 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 }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Countercomp family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||