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Kleismic family: Difference between revisions

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= Catakleismic =
= Catakleismic =
[[Comma|Commas]]: 225/224, 4375/4374
[[Comma list]]: 225/224, 4375/4374


valid range: [315.789, 317.647] (19 to 34)
[[POTE generator]]: ~6/5 = 316.732


nice range: [315.641, 317.263]
[[Mapping]]: [{{val| 1 0 1 -3 }}, {{val| 0 6 5 22 }}]


strict range: [315.789, 317.263]
{{Multival|legend=1| 6 5 22 -6 18 37 }}


[[POTE tuning|POTE generator]]: 316.732
[[Tuning ranges]]:  
* valid range: [315.789, 317.647] (19 to 34)
* nice range: [315.641, 317.263]
* strict range: [315.789, 317.263]


Map: [<1 0 1 -3|, <0 6 5 22|]
{{Val list|legend=1| 19, 53, 72, 197, 269c }}
 
[[Wedgie]]: <<6 5 22 -6 18 37||
 
EDOs: {{EDOs| 19, 53, 72, 197, 269c }}


[[Badness]]: 0.0215
[[Badness]]: 0.0215


== 11-limit ==
== 11-limit ==
[[Comma|Commas]]: 225/224, 385/384, 4375/4374
Comma list: 225/224, 385/384, 4375/4374


valid range: [315.789, 316.981] (19 to 53)
POTE generator: ~6/5 = 316.719


nice range: [315.641, 317.263]
Mapping: [{{val| 1 0 1 -3 9 }}, {{val| 0 6 5 22 -21 }}]


strict range: [315.789, 316.981]
Tuning ranges:
* valid range: [315.789, 316.981] (19 to 53)
* nice range: [315.641, 317.263]
* strict range: [315.789, 316.981]


[[POTE tuning|POTE generator]]: 316.719
{{Val list|legend=1| 19, 53, 72, 197e, 269ce, 341ce, 610bce }}


Map: [<1 0 1 -3 9|, <0 6 5 22 -21|]
Badness: 0.0218
 
EDOs: {{EDOs| 19, 53, 72, 197e, 269ce, 341ce, 610bce }}
 
[[Badness]]: 0.0218


=== 13-limit ===
=== 13-limit ===
[[Comma|Commas]]: 169/168, 225/224, 325/324, 540/539
Comma list: 169/168, 225/224, 325/324, 540/539


valid range: [315.789, 316.981] (19 to 53)
POTE generator: ~6/5 = 316.738


nice range: [315.641, 318.309]
Mapping: [{{val| 1 0 1 -3 9 0 }}, {{val| 0 6 5 22 -21 14 }}]


strict range: [315.789, 316.981]
Tuning ranges:
* valid range: [315.789, 316.981] (19 to 53)
* nice range: [315.641, 318.309]
* strict range: [315.789, 316.981]


[[POTE tuning|POTE generator]]: 316.738
{{Val list|legend=1| 19, 53, 72, 125f, 197ef, 269cef }}


Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|]
Badness: 0.0169
 
EDOs: {{EDOs| 19, 53, 72, 125f, 197ef, 269cef }}
 
[[Badness]]: 0.0169


== Cataclysmic ==
== Cataclysmic ==
Commas: 99/98, 176/175, 2200/2187
Comma list: 99/98, 176/175, 2200/2187


POTE generator: ~6/5 = 317.042
POTE generator: ~6/5 = 317.042


Map: [<1 0 1 -3 -5|, <0 6 5 22 32|]
Mapping: [{{val| 1 0 1 -3 -5 }}, {{val| 0 6 5 22 32 }}]


EDOs: {{EDOs| 53, 87d, 140d, 171de, 181de, 193de, 224de, 246de, 277de }}
{{Val list|legend=1| 53, 87d, 140d, 171de, 181de, 193de, 224de, 246de, 277de }}


Badness: 0.0400
Badness: 0.0400


=== 13-limit ===
=== 13-limit ===
Commas: 99/98, 169/168, 176/175, 275/273
Comma list: 99/98, 169/168, 176/175, 275/273


POTE generator: ~6/5 = 317.036
POTE generator: ~6/5 = 317.036


Map: [<1 0 1 -3 -5 0|, <0 6 5 22 32 14|]
Mapping: [{{val| 1 0 1 -3 -5 0 }}, {{val| 0 6 5 22 32 14 }}]


EDOs: {{EDOs| 53, 87d, 140d, 193de, 246de }}
{{Val list|legend=1| 53, 87d, 140d, 193de, 246de }}


Badness: 0.0226
Badness: 0.0226


== Catalytic ==
== Catalytic ==
Commas: 225/224, 441/440, 4375/4374
Comma list: 225/224, 441/440, 4375/4374


POTE generator: ~6/5 = 316.653
POTE generator: ~6/5 = 316.653


Map: [<1 0 1 -3 -10|, <0 6 5 22 51|]
Mapping: [{{val| 1 0 1 -3 -10 }}, {{val| 0 6 5 22 51 }}]


EDOs: {{EDOs| 53e, 72 }}
{{Val list|legend=1| 53e, 72 }}


Badness: 0.0304
Badness: 0.0304


=== 13-limit ===
=== 13-limit ===
Commas: 169/168 225/224 325/324 1716/1715
Comma list: 169/168 225/224 325/324 1716/1715


POTE generator: ~6/5 = 316.639
POTE generator: ~6/5 = 316.639


Map: [<1 0 1 -3 -10 0|, <0 6 5 22 51 14|]
Mapping: [{{val| 1 0 1 -3 -10 0 }}, {{val| 0 6 5 22 51 14 }}]


EDOs: {{EDOs| 19e, 53e, 72 }}
{{Val list|legend=1| 19e, 53e, 72 }}


Badness: 0.0223
Badness: 0.0223


== Cataleptic ==
== Cataleptic ==
Commas: 100/99, 225/224, 864/847
Comma list: 100/99, 225/224, 864/847


POTE generator: ~6/5 = 317.083
POTE generator: ~6/5 = 317.083


Map: [<1 0 1 -3 4|, <0 6 5 22 -2|]
Mapping: [{{val| 1 0 1 -3 4 }}, {{val| 0 6 5 22 -2 }}]


EDOs: {{EDOs| 19, 34d, 53e }}
{{Val list|legend=1| 19, 34d, 53e }}


Badness: 0.0443
Badness: 0.0443


=== 13-limit ===
=== 13-limit ===
Commas: 78/77, 100/99, 144/143, 676/675
Comma list: 78/77, 100/99, 144/143, 676/675


POTE generator: ~6/5 = 317.118
POTE generator: ~6/5 = 317.118


Map: [<1 0 1 -3 4 0|, <0 6 5 22 -2 14|]
Mapping: [{{val| 1 0 1 -3 4 0 }}, {{val| 0 6 5 22 -2 14 }}]


EDOs: {{EDOs| 19, 34d, 53e, 87de }}
{{Val list|legend=1| 19, 34d, 53e, 87de }}


Badness: 0.0273
Badness: 0.0273


= Countercata =
= Countercata =
[[Comma|Commas]]: 5120/5103, 15625/15552
[[Comma list]]: 5120/5103, 15625/15552


[[POTE tuning|POTE generator]]: 317.121
[[POTE generator]]: ~6/5 = 317.121


Map: [<1 0 1 11|, <0 6 5 -31|]
[[Mapping]]: [{{val| 1 0 1 11 }}, {{val| 0 6 5 -31 }}]


[[Wedgie]]: <<6 5 -31 -6 -66 -86||
{{Multival|legend=1| 6 5 -31 -6 -66 -86 }}


EDOs: {{EDOs| 19d, 34, 53, 87, 140, 333, 473, 806b }}
{{Val list|legend=1| 19d, 34, 53, 87, 140, 333, 473, 806b }}


[[Badness]]: 0.0521
[[Badness]]: 0.0521


== 11-limit ==
== 11-limit ==
[[Comma]]s: 385/384, 2200/2187, 3388/3375
Comma list: 385/384, 2200/2187, 3388/3375


POTE generator: ~6/5 = 317.162
POTE generator: ~6/5 = 317.162


Map: [<1 0 1 11 -5|, <0 6 5 -31 32|]
Mapping: [{{val| 1 0 1 11 -5 }}, {{val| 0 6 5 -31 32 }}]


EDOs: {{EDOs| 34, 53, 87, 140, 227 }}
{{Val list|legend=1| 34, 53, 87, 140, 227 }}


[[Badness]]: 0.0398
Badness: 0.0398


== 13-limit ==
== 13-limit ==
[[Comma]]s: 325/324, 352/351, 385/384, 625/624
Comma list: 325/324, 352/351, 385/384, 625/624


POTE generator: ~6/5 = 317.162
POTE generator: ~6/5 = 317.162


Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|]
Mapping: [{{val| 1 0 1 11 -5 0 }}, {{val| 0 6 5 -31 32 14 }}]


EDOs: {{EDOs| 34, 53, 87, 140, 227, 367e, 507e }}
{{Val list|legend=1| 34, 53, 87, 140, 227, 367e, 507e }}


[[Badness]]: 0.0202
Badness: 0.0202


= Metakleismic =
= Metakleismic =
[[Comma]]s: 15625/15552, 179200/177147
[[Comma list]]: 15625/15552, 179200/177147


POTE generator: ~6/5 = 317.314
[[POTE generator]]: ~6/5 = 317.314


Map: [<1 0 1 -12|, <0 6 5 56|]
[[Mapping]]: [{{val| 1 0 1 -12 }}, {{val| 0 6 5 56 }}]


Wedgie: <<6 5 56 -6 72 116||
{{Multival|legend=1| 6 5 56 -6 72 116 }}


EDOs: {{EDOs| 34d, 53d, 87, 121, 208 }}
{{Val list|legend=1| 34d, 53d, 87, 121, 208 }}


[[Badness]]: 0.1635
[[Badness]]: 0.1635


== 11-limit ==
== 11-limit ==
[[Comma]]s: 896/891, 2200/2187, 14700/14641
Comma list: 896/891, 2200/2187, 14700/14641


POTE generator: ~6/5 = 317.311
POTE generator: ~6/5 = 317.311


Map: [<1 0 1 -12 -5|, <0 6 5 56 32|]
Mapping: [{{val| 1 0 1 -12 -5 }}, {{val| 0 6 5 56 32 }}]


EDOs: {{EDOs| 34d, 53d, 87, 121, 208 }}
{{Val list|legend=1| 34d, 53d, 87, 121, 208 }}


[[Badness]]: 0.0486
Badness: 0.0486


== 13-limit ==
== 13-limit ==
[[Comma]]s: 325/324, 352/351, 364/363, 625/624
Comma list: 325/324, 352/351, 364/363, 625/624


POTE generator: ~6/5 = 317.311
POTE generator: ~6/5 = 317.311


Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|]
Mapping: [{{val| 1 0 1 -12 -5 0 }}, {{val| 0 6 5 56 32 14 }}]


EDOs: {{EDOs| 34d, 53d, 87, 121, 208 }}
{{Val list|legend=1| 34d, 53d, 87, 121, 208 }}


[[Badness]]: 0.0244
Badness: 0.0244


= Hemikleismic =
= Hemikleismic =
Commas: 4000/3969, 6144/6125
[[Comma list]]: 4000/3969, 6144/6125


[[POTE tuning|POTE generator]]: 158.649
[[POTE generator]]: 158.649


Map: [<1 0 1 4|, <0 12 10 -9|]
Mapping: [{{val| 1 0 1 4 }}, {{val| 0 12 10 -9 }}]


EDOs: {{EDOs| 15, 53, 121 }}
{{Val list|legend=1| 15, 53, 121 }}


Badness: 0.0521
Badness: 0.0521


== 11-limit ==
== 11-limit ==
Commas: 121/120, 176/175, 4000/3969
Comma list: 121/120, 176/175, 4000/3969


POTE generator: ~11/10 = 158.677
POTE generator: ~11/10 = 158.677


Map: [<1 0 1 4 2|, <0 12 10 -9 11|]
Mapping: [{{val| 1 0 1 4 2 }}, {{val| 0 12 10 -9 11 }}]


EDOs: {{EDOs| 15, 38, 53, 68, 121e }}
{{Val list|legend=1| 15, 38, 53, 68, 121e }}


Badness: 0.0380
Badness: 0.0380


== 13-limit ==
== 13-limit ==
Commas: 121/120, 176/175, 275/273, 325/324
Comma list: 121/120, 176/175, 275/273, 325/324


POTE generator: ~11/10 = 158.655
POTE generator: ~11/10 = 158.655


Map: [<1 0 1 4 2 0|, <0 12 10 -9 11 28|]
Mapping: [{{val| 1 0 1 4 2 0 }}, {{val| 0 12 10 -9 11 28 }}]


EDOs: {{EDOs| 15, 53, 121e }}
{{Val list|legend=1| 15, 53, 121e }}


Badness: 0.0260
Badness: 0.0260


= Clyde =
= Clyde =
[[Comma|Commas]]: 245/243, 3136/3125
[[Comma list]]: 245/243, 3136/3125
 
7 and 9 limit minimax
 
[|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>]


[[Eigenmonzo|Eigenmonzos]]: 2, 7
[[POTE generator]]: ~9/7 = 441.335


[[POTE tuning|POTE generator]]: ~9/7 = 441.335
[[Mapping]]: [{{val| 1 6 6 12 }}, {{val| 0 -12 -10 -25 }}]


Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 [[cent|cents]]. Associated recurrence relationship quickly converges.
Mapping [[generator]]s: ~2, ~9/7


Map: [<1 6 6 12|, <0 -12 -10 -25|]
[[Minimax tuning]]:
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 }}]
* [[Eigenmonzo]]s: 2, 7


[[Generator|Generators]]: 2, 9/7
[[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.


[[EDO|EDOs]]: {{EDOs| 19, 49, 68, 87, 155 }}
{{Val list|legend=1| 19, 49, 68, 87, 155 }}


Badness: 0.0473
Badness: 0.0473


== 11-limit ==
== 11-limit ==
Commas: 245/243, 3136/3125, 385/384
Comma list: 245/243, 3136/3125, 385/384


POTE generator: ~9/7 = 441.355
POTE generator: ~9/7 = 441.355


Map: [&lt;1 6 6 12 -5|, &lt;0 -12 -10 -25 23|]
Mapping: [{{val| 1 6 6 12 -5 }}, {{val| 0 -12 -10 -25 23 }}]


EDOs: {{EDOs| 19, 68, 87, 329bd, 419bd, 503bd, 590bd }}
{{Val list|legend=1| 19, 68, 87, 329bd, 419bd, 503bd, 590bd }}


Badness: 0.0474
Badness: 0.0474


== 13-limit ==
== 13-limit ==
Commas: 196/195, 245/243, 385/384, 625/624
Comma list: 196/195, 245/243, 385/384, 625/624


POTE generator: ~9/7 = 441.363
POTE generator: ~9/7 = 441.363


Map: [&lt;1 6 6 12 -5 14|, &lt;0 -12 -10 -25 23 -28|]
Mapping: [{{val| 1 6 6 12 -5 14 }}, {{val| 0 -12 -10 -25 23 -28 }}]


EDOs: {{EDOs| 19, 68, 87, 503bdf, 590bdf }}
{{Val list|legend=1| 19, 68, 87, 503bdf, 590bdf }}


Badness: 0.0268
Badness: 0.0268


= Bikleismic =
= Bikleismic =
Commas: 225/224, 243/242, 4375/4356
Comma list: 225/224, 243/242, 4375/4356


POTE generator: ~6/5 = 316.721
POTE generator: ~6/5 = 316.721


Map: [&lt;2 0 2 -6 -1|, &lt;0 6 5 22 15|]
Mapping: [{{val| 2 0 2 -6 -1 }}, {{val| 0 6 5 22 15 }}]


EDOs: {{EDOs| 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc }}
{{Val list|legend=1| 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc }}


Badness: 0.0293
Badness: 0.0293


== 13-limit ==
== 13-limit ==
Commas: 169/168, 225/224, 243/242, 325/324
Comma list: 169/168, 225/224, 243/242, 325/324


POTE generator: ~6/5 = 316.726
POTE generator: ~6/5 = 316.726


Map: [&lt;2 0 2 -6 -1 0|, &lt;0 6 5 22 15 14|]
Mapping: [{{val| 2 0 2 -6 -1 0 }}, {{val| 0 6 5 22 15 14 }}]


EDOs: {{EDOs| 72, 106, 322cff, 394cff, 466bcff, 538bcfff }}
{{Val list|legend=1| 72, 106, 322cff, 394cff, 466bcff, 538bcfff }}


Badness: 0.0218
Badness: 0.0218


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


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