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Schismatic family: Difference between revisions

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[[Badness]]: 0.0200
[[Badness]]: 0.0200


=Sesquiquartififths=
= Sesquiquartififths =
Commas: 2401/2400, 32805/32768
[[Comma list]]: 2401/2400, 32805/32768


7-limit minimax
[[POTE generator]]: ~448/405 = 175.434


Eigenmonzos: 2, 7/6
[[Mapping]]: [{{val| 1 1 7 5 }}, {{val| 0 4 -32 -15 }}]


9-limit minimax
Mapping generators: ~2, ~448/405


Eigenmonzos: 2, 9/7
{{Multival|legend=1| 4 -32 -15 -60 -35 55 }}


[[POTE_tuning|POTE generator]]: ~448/405 = 175.434
[[Minimax tuning]]:  
* [[7-odd-limit]] eigenmonzos: 2, 7/6
* [[9-odd-limit]] eigenmonzos: 2, 9/7


Mapping generator: ~448/405
{{Val list|legend=1| 41, 130, 171, 643, 2100 }}


Map: [<1 1 7 5|, <0 4 -32 -15|]
[[Badness]]: 0.0112


Wedgie: <<4 -32 -15 -60 -35 55||
== Sesquart ==
 
Comma list: 243/242, 441/440, 16384/16335
[[EDO|Edos]]: [[41edo|41]], [[130edo|130]], [[171edo|171]], [[643edo|643]], [[2100edo|2100edo]]
 
Badness: 0.0112
 
==Sesquart==
Commas: 243/242, 441/440, 16384/16335


POTE generator: ~256/231 = 175.406
POTE generator: ~256/231 = 175.406


Mapping generator: ~256/231
Mapping: [{{val| 1 1 7 5 2 }}, {{val| 0 4 -32 -15 10 }}]


Map: [<1 1 7 5 2|, <0 4 -32 -15 10|]
Mapping generators: ~2, ~256/231


EDOs: 41, 89, 130, 171
{{Val list|legend=1| 41, 89, 130, 171 }}


Badness: 0.0293
Badness: 0.0293


===13-limit===
=== 13-limit ===
Commas: 243/242, 364/363, 441/440, 3584/3575
Comma list: 243/242, 364/363, 441/440, 3584/3575


POTE generator: ~256/231 = 175.409
POTE generator: ~256/231 = 175.409


Map: [<1 1 7 5 2 -2|, <0 4 -32 -15 10 39|]
Mapping: [{{val| 1 1 7 5 2 -2 }}, {{val| 0 4 -32 -15 10 39 }}]


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


Badness: 0.0224
Badness: 0.0224


==Bisesqui==
== Bisesqui ==
Commas: 2401/2400, 9801/9800, 32805/32768
Comma list: 2401/2400, 9801/9800, 32805/32768


[[POTE_tuning|POTE generator]]: ~448/405 = 175.435
POTE generator: ~448/405 = 175.435


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


EDOs: 130, 212, 342, 1156, 1498
{{Val list|legend=1| 130, 212, 342, 1156, 1498 }}


Badness: 0.0170
Badness: 0.0170


=Sextilififths=
= Sextilififths =
Commas: 32768/32805, 235298/234375
[[Comma list]]: 32768/32805, 235298/234375


POTE generator: ~21/20 = 83.053
[[POTE generator]]: ~21/20 = 83.053


Mapping generator: ~21/20
[[Mapping]]: [{{val| 1 2 -1 -1 }}, {{val| 0 -6 48 55 }}]


Map: [<1 2 -1 -1|, <0 -6 48 55|]
Mapping generators: ~2, ~21/20


EDOs: 29, 101, 130, 289, 419
{{Val list|legend=1| 29, 101, 130, 289, 419 }}


Badness: 0.1088
[[Badness]]: 0.1088


==11-limit==
== 11-limit ==
Commas: 441/440, 4000/3993, 235298/234375
Comma list: 441/440, 4000/3993, 235298/234375


POTE generator: ~21/20 = 83.049
POTE generator: ~21/20 = 83.049


Mapping generator: ~21/20
Mapping: [{{val| 1 2 -1 -1 0 }}, {{val| 0 -6 48 55 50| }}]


Map: [<1 2 -1 -1 0|, <0 -6 48 55 50|]
Mapping generators: ~2, ~21/20


EDOs: 29, 130, 159, 289
{{Val list|legend=1| 29, 130, 159, 289 }}


Badness: 0.0455
Badness: 0.0455


==13-limit==
== 13-limit ==
Commas: 364/363, 441/440, 676/675, 10985/10976
Comma list: 364/363, 441/440, 676/675, 10985/10976


POTE generator: ~21/20 = 83.049
POTE generator: ~21/20 = 83.049


Mapping generator: ~21/20
Mapping: [{{val| 1 2 -1 -1 0 1 }}, {{val| 0 -6 48 55 50 39 }}]


Map: [<1 2 -1 -1 0 1|, <0 -6 48 55 50 39|]
Mapping generators: ~2, ~21/20


EDOs: 29, 130, 159, 289
{{Val list|legend=1| 29, 130, 159, 289 }}


Badness: 0.0253
Badness: 0.0253


=Tsaharuk=
= Tsaharuk =
Commas: 32805/32768, 420175/419904
[[Comma list]]: 32805/32768, 420175/419904


POTE generator: ~243/224 = 140.350
[[POTE generator]]: ~243/224 = 140.350


Mapping generator: ~243/224
[[Mapping]]: [{{val| 1 1 7 0 }}, {{val| 0 5 -40 24 }}]


Map: [<1 1 7 0|, <0 5 -40 24|]
Mapping generators: ~2, ~243/224


Wedgie: <<5 -40 24 -75 24 168||
{{Multival|legend=1| 5 -40 24 -75 24 168 }}


EDOs: 17, 60c, 77, 94, 171
{{Val list|legend=1| 17, 60c, 77, 94, 171 }}


Badness: 0.0307
[[Badness]]: 0.0307


=Quanharuk=
= Quanharuk =
Commas: 16875/16807, 32805/32768
[[Comma list]]: 16875/16807, 32805/32768


POTE generator: ~56/45 = 380.355
[[POTE generator]]: ~56/45 = 380.355


Mapping generator: ~56/45
[[Mapping]]: [{{val| 1 0 15 12 }}, {{val| 0 5 -40 -29 }}]


Map: [<1 0 15 12|, <0 5 -40 -29|]
Mapping generators: ~2, ~56/45


Wedgie: <<5 -40 -29 -75 -60 45||
{{Multival|legend=1| 5 -40 -29 -75 -60 45 }}


EDOs: 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd
{{Val list|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}


Badness: 0.0720
[[Badness]]: 0.0720


==11-limit==
== 11-limit ==
Commas: 540/539, 1375/1372, 32805/32768
Comma list: 540/539, 1375/1372, 32805/32768


POTE generator: ~56/45 = 380.352
POTE generator: ~56/45 = 380.352


Mapping generator: ~56/45
Mapping: [{{val| 1 0 15 12 -7 }}, {{val| 0 5 -40 -29 33 }}]


Map: [<1 0 15 12 -7|, <0 5 -40 -29 33|]
Mapping generators: ~2, ~56/45


EDOs: 41, 142, 183, 224, 631d, 855d, 1079d
{{Val list|legend=1| 41, 142, 183, 224, 631d, 855d, 1079d }}


Badness: 0.0315
Badness: 0.0315


==13-limit==
== 13-limit ==
Commas: 540/539, 1375/1372, 4096/4095, 6656/6655
Comma list: 540/539, 1375/1372, 4096/4095, 6656/6655


POTE generator: ~56/45 = 380.351
POTE generator: ~56/45 = 380.351


Map: [<1 0 15 12 -7 -15|, <0 5 -40 -29 33 59|]
Mapping: [{{val| 1 0 15 12 -7 -15 }}, {{val| 0 5 -40 -29 33 59 }}]


EDOs: 41, 142, 183, 224, 631d, 855d
Mapping generators: ~2, ~56/45
 
{{Val list|legend=1| 41, 142, 183, 224, 631d, 855d }}


Badness: 0.0214
Badness: 0.0214


=Octant=
= Octant =
Commas: 32805/32768, 2259436291848/2251875390625
Comma list: 32805/32768, 2259436291848/2251875390625


POTE generator: ~3/2 = 701.713
POTE generator: ~3/2 = 701.713


Mapping generator: ~3
Mapping: [{{val| 8 0 120 -117 }}, {{val| 0 1 -8 11 }}]


Map: [<8 0 120 -117|, <0 1 -8 11|]
Mapping generators: ~42875/39366, ~3


Wedgie: <<8 -64 88 -120 117 384||
{{Multival|legend=1| 8 -64 88 -120 117 384 }}


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


Badness: 0.1572
Badness: 0.1572


==11-limit==
== 11-limit ==
Commas: 9801/9800, 32805/32768, 46656/46585
Comma list: 9801/9800, 32805/32768, 46656/46585


POTE generator: ~3/2 = 701.713
POTE generator: ~3/2 = 701.713


Mapping generator: ~3
Mapping: [{{val| 8 0 120 -117 15 }}, {{val| 0 1 -8 11 1 }}]


Map: [<8 0 120 -117 15|, <0 1 -8 11 1|]
Mapping generators: ~12/11, ~3


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


Badness: 0.0448
Badness: 0.0448


==13-limit==
== 13-limit ==
Commas: 729/728, 1575/1573, 2200/2197, 6656/6655
Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655


POTE generator: ~3/2 = 701.725
POTE generator: ~3/2 = 701.725


Mapping generator: ~3
Mapping: [{{val| 8 0 120 -117 15 93 }}, {{val| 0 1 -8 11 1 -5 }}]


Map: [<8 0 120 -117 15 93|, <0 1 -8 11 1 -5|]
Mapping generators: ~12/11, ~3


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


Badness: 0.0304
Badness: 0.0304


[[Category:Theory]]
[[Category:Theory]]
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[[Category:Rank 2]]
[[Category:Rank 2]]


{{todo|review|improve readability}}
{{todo| review | improve readability }}
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