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Kleismic family: Difference between revisions

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Badness: 0.0273
Badness: 0.0273
== Bikleismic ==
Comma list: 225/224, 243/242, 4375/4356
POTE generator: ~6/5 = 316.721
Mapping: [{{val| 2 0 2 -6 -1 }}, {{val| 0 6 5 22 15 }}]
{{Val list|legend=1| 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc }}
Badness: 0.0293
=== 13-limit ===
Comma list: 169/168, 225/224, 243/242, 325/324
POTE generator: ~6/5 = 316.726
Mapping: [{{val| 2 0 2 -6 -1 0 }}, {{val| 0 6 5 22 15 14 }}]
{{Val list|legend=1| 72, 106, 322cff, 394cff, 466bcff, 538bcfff }}
Badness: 0.0218


= Countercata =
= Countercata =
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
7- and [[9-odd-limit]]:  
* 7- and [[9-odd-limit]]:  
* [{{monzo| 1 0 0 0 }}, {{monzo| 6/25 0 0 12/25 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 6/25 0 0 12/25 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
* [[Eigenmonzo]]s: 2, 7
: [[Eigenmonzo]]s: 2, 7


[[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges.
[[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges.
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Badness: 0.0268
Badness: 0.0268
= Bikleismic =
Comma list: 225/224, 243/242, 4375/4356
POTE generator: ~6/5 = 316.721
Mapping: [{{val| 2 0 2 -6 -1 }}, {{val| 0 6 5 22 15 }}]
{{Val list|legend=1| 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc }}
Badness: 0.0293
== 13-limit ==
Comma list: 169/168, 225/224, 243/242, 325/324
POTE generator: ~6/5 = 316.726
Mapping: [{{val| 2 0 2 -6 -1 0 }}, {{val| 0 6 5 22 15 14 }}]
{{Val list|legend=1| 72, 106, 322cff, 394cff, 466bcff, 538bcfff }}
Badness: 0.0218


= Tritikleismic =
= Tritikleismic =
{{see also| Gamelismic clan #Tritikleismic }}
{{see also| Gamelismic clan #Tritikleismic }}


[[Comma]]s: 1029/1024, 15625/15552
[[Comma list]]: 1029/1024, 15625/15552


[[POTE tuning|POTE generator]]: 316.872
[[POTE generator]]: 316.872


Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]
[[Mapping]]: [{{val| 3 0 3 10 }}, {{val| 0 6 5 -2 }}]


[[Wedgie]]: &lt;&lt;18 15 -6 -18 -60 -56||
{{Multival|legend=1| 18 15 -6 -18 -60 -56 }}


EDOs: {{EDOs| 15, 57, 72, 159, 231 }}
{{Val list|legend=1| 15, 57, 72, 159, 231 }}


[[Badness]]: 0.0563
[[Badness]]: 0.0563


== 11-limit ==
== 11-limit ==
[[Comma]]s: 385/384, 441/440, 4000/3993
Comma list: 385/384, 441/440, 4000/3993


[[POTE tuning|POTE generator]]: 316.881
POTE generator: ~6/5 = 316.881


Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]
Mapping: [{{val| 3 0 3 10 8 }}, {{val| 0 6 5 -2 3 }}]


EDOs: {{EDOs| 15, 57, 72, 159, 231 }}
{{Val list|legend=1| 15, 57, 72, 159, 231 }}


[[Badness]]: 0.0193
Badness: 0.0193


== 13-limit ==
== 13-limit ==
[[Comma]]s: 325/324, 364/363, 441/440, 625/624
Comma list: 325/324, 364/363, 441/440, 625/624


[[POTE tuning|POTE generator]]: 316.959
POTE generator: ~6/5 = 316.959


Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]
Mapping: [{{val| 3 0 3 10 8 0 }}, {{val| 0 6 5 -2 3 14 }}]


EDOs: {{EDOs| 15, 72, 87, 159, 867, 1026 }}
{{Val list|legend=1| 15, 72, 87, 159, 867, 1026 }}


[[Badness]]: 0.0157
[[Badness]]: 0.0157


= Quadritikleismic =
= Quadritikleismic =
[[Comma]]s: 2401/2400, 15625/15552
[[Comma list]]: 2401/2400, 15625/15552


[[POTE tuning|POTE generator]]: 316.9999
[[POTE generator]]: ~6/5 = 316.9999


Map: [&lt;4 0 4 7|, &lt;0 6 5 4|]
[[Mapping]]: [{{val| 4 0 4 7 }}, {{val| 0 6 5 4 }}]


Wedgie: &lt;&lt;24 20 16 -24 -42 -19||
{{Multival|legend=1| 24 20 16 -24 -42 -19 }}


EDOs: {{EDOs| 68, 72, 140, 212, 1200 }}
{{Val list|legend=1| 68, 72, 140, 212, 1200 }}


[[Badness]]: 0.0392
[[Badness]]: 0.0392


== 11-limit ==
== 11-limit ==
Commas: 385/384, 1375/1372, 6250/6237
Comma list: 385/384, 1375/1372, 6250/6237


[[POTE tuning|POTE generator]]: 316.925
POTE generator: ~6/5 = 316.925


Map: [&lt;4 0 4 7 17|, &lt;0 6 5 4 -3|]
Mapping: [{{val| 4 0 4 7 17 }}, {{val| 0 6 5 4 -3 }}]


EDOs: {{EDOs| 68, 72, 140, 212, 284, 496, 780 }}
{{Val list|legend=1| 68, 72, 140, 212, 284, 496, 780 }}


[[Badness]]: 0.0234
Badness: 0.0234


== 13-limit ==
== 13-limit ==
Commas: 325/324, 385/384, 625/624, 1573/1568
Comma list: 325/324, 385/384, 625/624, 1573/1568


[[POTE tuning|POTE generator]]: 316.989
POTE generator: ~6/5 = 316.989


Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]
Mapping: [{{val| 4 0 4 7 17 0 }}, {{val| 0 6 5 4 -3 14 }}]


EDOs: {{EDOs| 68, 72, 140, 212 }}
{{Val list|legend=1| 68, 72, 140, 212 }}


[[Badness]]: 0.0187
Badness: 0.0187


= Kleiboh =
= Kleiboh =
Commas: 1728/1715, 3125/3087
[[Comma list]]: 1728/1715, 3125/3087


POTE generator: ~25/21 = 294.303
[[POTE generator]]: ~25/21 = 294.303


Map: [&lt;1 6 6 6|, &lt;0 -18 -15 -13|]
[[Mapping]]: [{{val| 1 6 6 6 }}, {{val| 0 -18 -15 -13 }}]


Wedgie: &lt;&lt;18 15 13 -18 -30 -12||
{{Multival|legend=1| 18 15 13 -18 -30 -12 }}


EDOs: {{EDOs| 49, 53, 314d }}
{{Val list|legend=1| 49, 53, 314d }}


Badness: 0.0765
Badness: 0.0765


== 11-limit ==
== 11-limit ==
Commas: 176/175, 540/539, 3125/3087
Comma list: 176/175, 540/539, 3125/3087


POTE generator: ~25/21 = 294.181
POTE generator: ~25/21 = 294.181


Map: [&lt;1 6 6 6 14|, &lt;0 -18 -15 -13 -43|]
Mapping: [{{val| 1 6 6 6 14 }}, {{val| 0 -18 -15 -13 -43 }}]


EDOs: {{EDOs| 49, 53, 102d, 155d }}
{{Val list|legend=1| 49, 53, 102d, 155d }}


Badness: 0.0528
Badness: 0.0528


== 13-limit ==
== 13-limit ==
Commas: 176/175, 275/273, 325/324, 540/539
Comma list: 176/175, 275/273, 325/324, 540/539


POTE generator: ~13/11 = 294.187
POTE generator: ~13/11 = 294.187


Map: [&lt;1 6 6 6 14 14|, &lt;0 -18 -15 -13 -43 -42|]
Mapping: [{{val| 1 6 6 6 14 14 }}, {{val| 0 -18 -15 -13 -43 -42 }}]


EDOs: {{EDOs| 53, 102df, 155d }}
{{Val list|legend=1| 53, 102df, 155d }}


Badness: 0.0311
Badness: 0.0311


= Novemkleismic =
= Novemkleismic =
Commas: 15625/15552, 40353607/40310784
[[Comma list]]: 15625/15552, 40353607/40310784


POTE generator: ~6/5 = 317.005
[[POTE generator]]: ~6/5 = 317.005


Map: [&lt;9 0 9 11|, &lt;0 6 5 6|]
[[Mapping]]: [{{val| 9 0 9 11 }}, {{val| 0 6 5 6 }}]


Wedgie: &lt;&lt;54 45 54 -54 -66 -1||
{{Multival|legend=1| 54 45 54 -54 -66 -1 }}


EDOs: {{EDOs| 72, 261, 333, 405, 477c, 882c }}
{{Val list|legend=1| 72, 261, 333, 405, 477c, 882c }}


Badness: 0.1934
[[Badness]]: 0.1934


== 11-limit ==
== 11-limit ==
Commas: 1375/1372, 4000/3993, 15625/15552
Comma list: 1375/1372, 4000/3993, 15625/15552


POTE generator: ~6/5 = 317.010
POTE generator: ~6/5 = 317.010


Map: [&lt;9 0 9 11 24|, &lt;0 6 5 6 3|]
Mapping: [{{val| 9 0 9 11 24 }}, {{val| 0 6 5 6 3 }}]


EDOs: {{EDOs| 72, 261, 333, 405, 882c }}
{{Val list|legend=1| 72, 261, 333, 405, 882c }}


Badness: 0.05172
Badness: 0.05172


== 13-limit ==
== 13-limit ==
Commas: 325/324, 625/624, 1375/1372, 4000/3993
Comma list: 325/324, 625/624, 1375/1372, 4000/3993


POTE generator: ~6/5 = 317.086
POTE generator: ~6/5 = 317.086


Map: [&lt;9 0 9 11 24 0|, &lt;0 6 5 6 3 14|]
Mapping: [{{val| 9 0 9 11 24 0 }}, {{val| 0 6 5 6 3 14 }}]


EDOs: {{EDOs| 72, 261, 333, 738cf, 1071bcf }}
{{Val list|legend=1| 72, 261, 333, 738cf, 1071bcf }}


Badness: 0.0391
Badness: 0.0391


= Sqrtphi =
= Sqrtphi =
Commas: 15625/15552, 16875/16807
 
The just value of sqrt (φ) is 416.545 cents.
 
[[Comma list]]: 15625/15552, 16875/16807


[[POTE tuning|POTE generator]]: ~125/98 = 416.603 cents
[[POTE tuning|POTE generator]]: ~125/98 = 416.603 cents


Sqrt(phi) = 416.545 cents
[[Mapping]]: [{{val| 1 12 11 16 }}, {{val| 0 -30 -25 -38 }}]
 
Map: [&lt;1 12 11 16|, &lt;0 -30 -25 -38|]


EDOs: {{EDOs| 49, 72, 193, 265 }}
{{Val list|legend=1| 49, 72, 193, 265 }}


Badness: 0.0704
[[Badness]]: 0.0704


== 11-limit ==
== 11-limit ==
Commas: 540/539, 1375/1372, 4375/4356
Comma list: 540/539, 1375/1372, 4375/4356


POTE generator: ~14/11 = 416.604
POTE generator: ~14/11 = 416.604


Map: [&lt;1 12 11 16 17|, &lt;0 -30 -25 -38 -39|]
Mapping: [{{val| 1 12 11 16 17 }}, {{val| 0 -30 -25 -38 -39 }}]


EDOs: {{EDOs| 49, 72, 193, 265 }}
{{Val list|legend=1| 49, 72, 193, 265 }}


Badness: 0.0255
Badness: 0.0255


== 13-limit ==
== 13-limit ==
Commas: 325/324, 364/363, 625/624, 1375/1372
Comma list: 325/324, 364/363, 625/624, 1375/1372


POTE generator: ~14/11 = 416.585
POTE generator: ~14/11 = 416.585


Map: [&lt;1 12 11 16 17 28|, &lt;0 -30 -25 -38 -39 -70|]
Mapping: [{{val| 1 12 11 16 17 28 }}, {{val| 0 -30 -25 -38 -39 -70 }}]


EDOs: {{EDOs| 72, 121, 193 }}
{{Val list|legend=1| 72, 121, 193 }}


Badness: 0.0200
Badness: 0.0200


== 17-limit ==
== 17-limit ==
Commas: 325/324, 364/363, 375/374, 540/539, 595/594
Comma list: 325/324, 364/363, 375/374, 540/539, 595/594


POTE generator: ~14/11 = 416.585
POTE generator: ~14/11 = 416.585


Map: [&lt;1 12 11 16 17 28 27|, &lt;0 -30 -25 -38 -39 -70 -66|]
Mapping: [{{val| 1 12 11 16 17 28 27 }}, {{val| 0 -30 -25 -38 -39 -70 -66 }}]


EDOs: {{EDOs| 72, 121, 193 }}
{{Val list|legend=1| 72, 121, 193 }}


Badness: 0.0130
Badness: 0.0130


== 19-limit ==
== 19-limit ==
Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594
Comma list: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594


POTE generator: ~14/11 = 416.580
POTE generator: ~14/11 = 416.580


Map: [&lt;1 12 11 16 17 28 27 -2|, &lt;0 -30 -25 -38 -39 -70 -66 18|]
Mapping: [{{val| 1 12 11 16 17 28 27 -2 }}, {{val| 0 -30 -25 -38 -39 -70 -66 18 }}]


EDOs: {{EDOs| 72, 121, 193 }}
{{Val list|legend=1| 72, 121, 193 }}


Badness: 0.0147
Badness: 0.0147
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[[Category:Listen]]
[[Category:Listen]]


[[Category:Todo:add definition]]
{{todo| review | improve readability }}
[[Category:Todo:review]]
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