Countercomp family: Difference between revisions
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→Hemicounterpyth: normalize mappings and generators |
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[[Comma list]]: 2401/2400, 52613349376/52301766015 | [[Comma list]]: 2401/2400, 52613349376/52301766015 | ||
[[Mapping]]: [{{val| 41 65 | [[Mapping]]: [{{val| 41 65 1 68 }}, {{val| 0 0 2 1 }}] | ||
[[POTE generator]]: ~ | Mapping generators: ~531441/524288, ~567/256 | ||
[[POTE generator]]: ~567/512 = 178.7115 | |||
{{Val list|legend=1| 41, 328, 369, 779 }} | {{Val list|legend=1| 41, 328, 369, 779 }} | ||
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Comma list: 2401/2400, 16384/16335, 19712/19683 | Comma list: 2401/2400, 16384/16335, 19712/19683 | ||
Mapping: [{{val| 41 65 | Mapping: [{{val| 41 65 1 68 189 }}, {{val| 0 0 2 1 -1 }}] | ||
POTE generator: ~ | POTE generator: ~567/512 = 178.9285 | ||
Vals: {{Val list| 41, 328, 369 }} | Vals: {{Val list| 41, 328, 369 }} | ||
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Comma list: 2401/2400, 59290/59049, 131072/130977 | Comma list: 2401/2400, 59290/59049, 131072/130977 | ||
Mapping: [{{val| 41 65 | Mapping: [{{val| 41 65 1 68 236 }}, {{val| 0 0 2 1 -2 }}] | ||
POTE generator: ~ | POTE generator: ~567/512 = 178.3714 | ||
Vals: {{Val list| 41, 328e, 369e, 410, 451, 861e, 2173bcee }} | Vals: {{Val list| 41, 328e, 369e, 410, 451, 861e, 2173bcee }} | ||
Revision as of 15:22, 29 December 2021
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
Vals: Template:Val list
Badness: 0.076537
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
Vals: 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
Vals: 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
Vals: Template:Val list
Badness: 0.100152