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Schismatic family: Difference between revisions

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[[POTE generator]]: ~3/2 = 701.736
[[POTE generator]]: ~3/2 = 701.736
[[Mapping]]: [{{val| 1 0 15 }}, {{val| 0 1 -8 }}]


Mapping generators: ~2, ~3
Mapping generators: ~2, ~3
[[Mapping]]: [{{val| 1 0 15 }}, {{val| 0 1 -8 }}]


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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{{Vals|legend=1| 12, 29, 41, 53, 118, 171, 289, 460, 749, 3456bc, 4205bc, 4954bc, 5703bbc, 6452bbcc }}
{{Vals|legend=1| 12, 29, 41, 53, 118, 171, 289, 460, 749, 3456bc, 4205bc, 4954bc, 5703bbc, 6452bbcc }}


Badness: 0.00426
[[Badness]]: 0.00426


== Seven-limit extensions ==
== Seven-limit extensions ==
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= Garibaldi =
= Garibaldi =
{{main| Garibaldi temperament }}


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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[[Minimax tuning]]:
[[Minimax tuning]]:
* 7-odd-limit:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 1/15 0 -1/15 }}, {{monzo| 5/3 -8/15 0 8/15 }}, {{monzo| 5/3 -14/15 0 14/15 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 1/15 0 -1/15 }}, {{monzo| 5/3 -8/15 0 8/15 }}, {{monzo| 5/3 -14/15 0 14/15 }}]
: [[Eigenmonzo]]s: 2, 7/6
: [[Eigenmonzo]]s: 2, 7/6
* 9-odd-limit:
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 }}, {{monzo| 5/2 -1 0 1/2 }}, {{monzo| 25/8 -7/4 0 7/8 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 }}, {{monzo| 5/2 -1 0 1/2 }}, {{monzo| 25/8 -7/4 0 7/8 }}]
: Eigenmonzos: 2, 9/7
: Eigenmonzos: 2, 9/7
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Comma list: 225/224, 385/384, 2200/2187
Comma list: 225/224, 385/384, 2200/2187


[[POTE generator]]: ~3/2 = 702.157
POTE generator: ~3/2 = 702.157


Mapping: [{{val| 1 0 15 25 -33 }}, {{val| 0 1 -8 -14 23 }}]
Mapping: [{{val| 1 0 15 25 -33 }}, {{val| 0 1 -8 -14 23 }}]
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Minimax tuning:
Minimax tuning:
* 11-odd-limit:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 0 }}, {{monzo| 5/2 -1 0 1/2 0 }}, {{monzo| 25/8 -7/4 0 7/8 0 }}, {{monzo| 47/16 23/8 0 -23/16 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/16 1/8 0 -1/16 0 }}, {{monzo| 5/2 -1 0 1/2 0 }}, {{monzo| 25/8 -7/4 0 7/8 0 }}, {{monzo| 47/16 23/8 0 -23/16 0 }}]
: Eigenmonzos: 2, 9/7
: Eigenmonzos: 2, 9/7


{{Val list|legend=1| 41, 53, 94, 135, 229c, 323c, 417ce }}
{{Val list|legend=1| 41, 53, 94, 229c, 323c, 417ce }}


Badness: 0.0274
Badness: 0.0274
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Comma list: 225/224, 275/273, 325/324, 385/384
Comma list: 225/224, 275/273, 325/324, 385/384


[[POTE generator]]: ~3/2 = 702.113
POTE generator: ~3/2 = 702.113


Mapping: [{{val| 1 0 15 25 -33 -28 }}, {{val| 0 1 -8 -14 23 20 }}]
Mapping: [{{val| 1 0 15 25 -33 -28 }}, {{val| 0 1 -8 -14 23 20 }}]
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Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Val list|legend=1| 12e, 41, 53, 94, 135, 429cdef, 523cdef }}
{{Val list|legend=1| 41, 53, 94, 429cdef, 523cdef }}


Badness: 0.0207
Badness: 0.0207
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Comma list: 100/99, 105/104, 196/195, 245/242
Comma list: 100/99, 105/104, 196/195, 245/242


[[POTE generator]]: ~3/2 = 702.559
POTE generator: ~3/2 = 702.559


Mapping: [{{val| 1 0 15 25 32 37 }}, {{val| 0 1 -8 -14 -18 -21 }}]
Mapping: [{{val| 1 0 15 25 32 37 }}, {{val| 0 1 -8 -14 -18 -21 }}]
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Mapping generators: ~2, ~3
Mapping generators: ~2, ~3


{{Val list|legend=1| 12, 53, 118d, 171de }}
{{Val list|legend=1| 53, 118d, 171de }}


Badness: 0.0356
Badness: 0.0356
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: Eigenmonzos: 2, 10/9
: Eigenmonzos: 2, 10/9


{{Val list|legend=1| 53, 118, 171, 1079, 1250, 1421 }}
{{Val list|legend=1| 53, 118, 171, 1592c, 1763c, …, 2960cd, 3131bcd }}


[[Badness]]: 0.0141
[[Badness]]: 0.0141
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* [[9-odd-limit]] eigenmonzos: 2, 9/7
* [[9-odd-limit]] eigenmonzos: 2, 9/7


{{Val list|legend=1| 77, 89, 101, 166c, 243c }}
{{Val list|legend=1| 77, 166c, 243c }}


[[Badness]]: 0.0704
[[Badness]]: 0.0704
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Mapping generators: ~99/70, ~3
Mapping generators: ~99/70, ~3


{{Val list|legend=1| 12, 118, 130, 248 }}
{{Val list|legend=1| 118, 130, 248 }}


Badness: 0.0282
Badness: 0.0282
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Mapping: [{{val| 2 0 30 69 102 -75 }}, {{val| 0 1 -8 -20 -30 26 }}]
Mapping: [{{val| 2 0 30 69 102 -75 }}, {{val| 0 1 -8 -20 -30 26 }}]


{{Val list|legend=1| 12, 118, 130, 248, 378 }}
{{Val list|legend=1| 118, 130, 248, 378 }}


Badness: 0.0287
Badness: 0.0287
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{{Multival|legend=1| 4 -32 38 -60 49 178 }}
{{Multival|legend=1| 4 -32 38 -60 49 178 }}


{{Val list|legend=1| 24, 94, 118, 212, 330, 542d, 872cd }}
{{Val list|legend=1| 94, 118, 212, 330, 542d, 872cd }}


[[Badness]]: 0.1106
[[Badness]]: 0.1106
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Mapping generators: ~99/70, ~16/11
Mapping generators: ~99/70, ~16/11


{{Val list|legend=1| 24, 94, 118, 212, 330e, 542de }}
{{Val list|legend=1| 94, 118, 212, 330e, 542de }}


Badness: 0.0367
Badness: 0.0367
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Mapping generators: ~99/70, ~16/11
Mapping generators: ~99/70, ~16/11


{{Val list|legend=1| 24, 94, 118, 212f }}
{{Val list|legend=1| 94, 118, 212f }}


Badness: 0.0376
Badness: 0.0376
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: [[Eigenmonzo]]s: 2, 5/4
: [[Eigenmonzo]]s: 2, 5/4


{{Val list|legend=1| 41, 77, 118, 159, 200, 277d }}
{{Val list|legend=1| 36e, 41, 77, 118, 159, 277d }}


Badness: 0.0266
Badness: 0.0266
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Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}]
Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}]


{{Val list|legend=1| 41, 77, 118 }}
{{Val list|legend=1| 36e, 41, 77, 118 }}


Badness: 0.0284
Badness: 0.0284
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* [[9-odd-limit]] eigenmonzos: 2, 9/7
* [[9-odd-limit]] eigenmonzos: 2, 9/7


{{Val list|legend=1| 12, 171, 1038, 1209, 1380, 1551, 1722 }}
{{Val list|legend=1| 171, 867, 1038, 1209, 1380, 1551, 1722 }}


[[Badness]]: 0.0200
[[Badness]]: 0.0200
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* [[9-odd-limit]] eigenmonzos: 2, 9/7
* [[9-odd-limit]] eigenmonzos: 2, 9/7


{{Val list|legend=1| 41, 130, 171, 643, 2100 }}
{{Val list|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}


[[Badness]]: 0.0112
[[Badness]]: 0.0112
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Mapping generators: ~2, ~256/231
Mapping generators: ~2, ~256/231


{{Val list|legend=1| 41, 89, 130, 171 }}
{{Val list|legend=1| 41, 89, 130, 301e, 431e }}


Badness: 0.0293
Badness: 0.0293
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Mapping: [{{val| 2 2 14 10 23 }}, {{val| 0 4 -32 -15 -55 }}]
Mapping: [{{val| 2 2 14 10 23 }}, {{val| 0 4 -32 -15 -55 }}]


{{Val list|legend=1| 130, 212, 342, 1156, 1498 }}
{{Val list|legend=1| 82e, 130, 212, 342, 1156, 1498, 1840d }}


Badness: 0.0170
Badness: 0.0170
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Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20


{{Val list|legend=1| 29, 101, 130, 289, 419 }}
{{Val list|legend=1| 29, 72cd, 101, 130, 289, 419 }}


[[Badness]]: 0.1088
[[Badness]]: 0.1088
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Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20


{{Val list|legend=1| 29, 130, 159, 289 }}
{{Val list|legend=1| 29, 72cde, 101e, 130, 289 }}


Badness: 0.0455
Badness: 0.0455
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Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20


{{Val list|legend=1| 29, 130, 159, 289 }}
{{Val list|legend=1| 29, 72cdef, 101e, 130, 289 }}


Badness: 0.0253
Badness: 0.0253
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Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 540/539, 1375/1372, 4096/4095, 6656/6655
Comma list: 540/539, 729/728, 1375/1372, 4096/4095


POTE generator: ~56/45 = 380.351
POTE generator: ~56/45 = 380.351
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{{Multival|legend=1| 8 -64 88 -120 117 384 }}
{{Multival|legend=1| 8 -64 88 -120 117 384 }}


{{Val list|legend=1| 24, 224, 472, 696, 1168 }}
{{Val list|legend=1| 224, 472, 696, 1168 }}


Badness: 0.1572
Badness: 0.1572
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Mapping generators: ~12/11, ~3
Mapping generators: ~12/11, ~3


{{Val list|legend=1| 24, 224, 472, 696, 1168 }}
{{Val list|legend=1| 224, 472, 696, 1168 }}


Badness: 0.0448
Badness: 0.0448
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Mapping generators: ~12/11, ~3
Mapping generators: ~12/11, ~3


{{Val list|legend=1| 24, 224, 472, 696 }}
{{Val list|legend=1| 224, 472, 696 }}


Badness: 0.0304
Badness: 0.0304
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[[Category:Schismatic family| ]] <!-- main article -->
[[Category:Schismatic family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
{{todo| review | improve readability }}
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