Countercomp family: Difference between revisions
m Moving from Category:Temperament family to Category:Temperament families using Cat-a-lot |
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POTE generator: ~5/4 = 385.871 | POTE generator: ~5/4 = 385.871 | ||
Optimal GPV sequence: {{Val list| 41, 123e, 164, 205d, 451dd }} | |||
Badness: 0.076537 | Badness: 0.076537 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 196/195, 352/351, 385/384, 59150/59049 | |||
Mapping: [{{val| 41 65 0 115 237 247 }}, {{val| 0 0 1 0 -1 -1 }}] | |||
POTE generator: ~5/4 = 386.604 | |||
Optimal GPV sequence: {{Val list| 41, 123e, 164, 205d }} | |||
Badness: 0.054921 | |||
== Mermapyth == | == Mermapyth == | ||
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POTE generator: ~5/4 = 385.309 | POTE generator: ~5/4 = 385.309 | ||
Optimal GPV sequence: {{Val list| 41, 164d, 205, 246 }} | |||
Badness: 0.076588 | Badness: 0.076588 | ||
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POTE generator: ~567/512 = 178.9285 | POTE generator: ~567/512 = 178.9285 | ||
Optimal GPV sequence: {{Val list| 41, 328, 369 }} | |||
Badness: 0.064400 | Badness: 0.064400 | ||
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POTE generator: ~567/512 = 178.3714 | POTE generator: ~567/512 = 178.3714 | ||
Optimal GPV sequence: {{Val list| 41, 328e, 369e, 410, 451, 861e, 2173bcee }} | |||
Badness: 0.100152 | Badness: 0.100152 | ||
Revision as of 12:34, 3 March 2022
The counterpyth family tempers out counterpyth comma, [65 -41⟩, and hence the fifths form a closed 41-note circle of fifths, identical to 41EDO.
Counterpyth
Subgroup: 2.3.5
Comma list: [65 -41⟩
Mapping: [⟨41 65 0], ⟨0 0 1]]
Mapping generators: ~531441/524288, ~5/1
POTE generator: ~5/4 = 386.668
Badness: 0.934310
Gamelapyth
Subgroup: 2.3.5.7
Comma list: 1029/1024, 537824/531441
Mapping: [⟨41 65 0 115], ⟨0 0 1 0]]
Wedgie: ⟨⟨ 0 41 0 65 0 -115 ]]
POTE generator: ~5/4 = 385.731
Badness: 0.161056
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 537824/531441
Mapping: [⟨41 65 0 115 237], ⟨0 0 1 0 -1]]
POTE generator: ~5/4 = 385.871
Optimal GPV sequence: Template:Val list
Badness: 0.076537
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 59150/59049
Mapping: [⟨41 65 0 115 237 247], ⟨0 0 1 0 -1 -1]]
POTE generator: ~5/4 = 386.604
Optimal GPV sequence: Template:Val list
Badness: 0.054921
Mermapyth
Subgroup: 2.3.5.7
Comma list: 5120/5103, 2500000/2470629
Mapping: [⟨41 65 0 20], ⟨0 0 1 1]]
Wedgie: ⟨⟨ 0 41 41 65 65 -20 ]]
POTE generator: ~5/4 = 385.667
Badness: 0.142344
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5120/5103, 75625/75264
Mapping: [⟨41 65 0 20 237], ⟨0 0 1 1 -1]]
POTE generator: ~5/4 = 385.309
Optimal GPV sequence: Template:Val list
Badness: 0.076588
Hemicounterpyth
Subgroup: 2.3.5.7
Comma list: 2401/2400, 52613349376/52301766015
Mapping: [⟨41 65 1 68], ⟨0 0 2 1]]
Mapping generators: ~531441/524288, ~567/256
POTE generator: ~567/512 = 178.7115
Badness: 0.134559
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 16384/16335, 19712/19683
Mapping: [⟨41 65 1 68 189], ⟨0 0 2 1 -1]]
POTE generator: ~567/512 = 178.9285
Optimal GPV sequence: Template:Val list
Badness: 0.064400
Hemermapyth
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 59290/59049, 131072/130977
Mapping: [⟨41 65 1 68 236], ⟨0 0 2 1 -2]]
POTE generator: ~567/512 = 178.3714
Optimal GPV sequence: Template:Val list
Badness: 0.100152