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Pythagorean family: Difference between revisions

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{{Val list|legend=1| 12, 36, 48, 132, 180 }}
{{Val list|legend=1| 12, 36, 48, 132, 180 }}


==11-limit==
== 11-limit ==
Commas: 81/80, 99/98, 128/125
Comma list: 81/80, 99/98, 128/125


POTE generator: ~36/35 = 22.723
POTE generator: ~64/63 = 22.723


Map: [<12 19 28 0 -26|, <0 0 0 1 2|]
Mapping: [{{val| 12 19 28 0 -26 }}, {{val| 0 0 0 1 2 }}]


EDOs: 12, 48c, 108cd
{{Val list|legend=1| 12, 48c, 108cd }}


Badness: 0.0582
Badness: 0.0582


==Catlat==
== Catlat ==
Commas: 81/80, 128/125, 540/539
Comma list: 81/80, 128/125, 540/539


POTE generator: ~36/35 = 27.864
POTE generator: ~64/63 = 27.864


Map: [<12 19 28 0 109|, <0 0 0 1 -2|]
Mapping: [{{val| 12 19 28 0 109 }}, {{val| 0 0 0 1 -2 }}]


EDOs: 36, 48c, 84c
{{Val list|legend=1| 36, 48c, 84c }}


Badness: 0.0819
Badness: 0.0819


==Catcall==
== Catcall ==
Commas: 56/55, 81/80, 128/125
Comma list: 56/55, 81/80, 128/125


POTE generator: ~36/35 = 32.776
POTE generator: ~36/35 = 32.776


Map: [<12 19 28 0 8|, <0 0 0 1 1|]
Mapping: [{{val| 12 19 28 0 8 }}, {{val| 0 0 0 1 1 }}]


EDOs: 12, 24, 36, 72ce
{{Val list|legend=1| 12, 24, 36, 72ce }}


Badness: 0.0345
Badness: 0.0345


===13-limit===
=== 13-limit ===
Commas: 56/55, 66/65, 81/80, 105/104
Comma list: 56/55, 66/65, 81/80, 105/104


POTE generator: ~36/35 = 37.232
POTE generator: ~36/35 = 37.232


Map: [<12 19 28 0 8 11|, <0 0 0 1 1 1|]
Mapping: [{{val| 12 19 28 0 8 11 }}, {{val| 0 0 0 1 1 1 }}]


EDOs: 12f, 24, 36f, 60cf
{{Val list|legend=1| 12f, 24, 36f, 60cf }}


Badness: 0.0284
Badness: 0.0284


==Duodecic==
=== Duodecic ===
Commas: 56/55, 81/80, 91/90, 128/125
Comma list: 56/55, 81/80, 91/90, 128/125


POTE generator: ~36/35 = 37.688
POTE generator: ~36/35 = 37.688


Map: [<12 19 28 0 8 78|, <0 0 0 1 1 -1|]
Mapping: [{{val| 12 19 28 0 8 78 }}, {{val| 0 0 0 1 1 -1 }}]


EDOs: 12, 24, 36, 60c
{{Val list|legend=1| 12, 24, 36, 60c }}


Badness: 0.0383
Badness: 0.0383


===17-limit===
==== 17-limit ====
Commas: 51/50, 56/55, 81/80, 91/90, 128/125
Comma list: 51/50, 56/55, 81/80, 91/90, 128/125


POTE generator: ~36/35 = 38.097
POTE generator: ~36/35 = 38.097


Map: [<12 19 28 0 8 78 49|, <0 0 0 1 1 -1 0|]
Mapping: [{{val| 12 19 28 0 8 78 49 }}, {{val| 0 0 0 1 1 -1 0 }}]


EDOs: 12, 24, 36, 60c
{{Val list|legend=1| 12, 24, 36, 60c }}


Badness: 0.0275
Badness: 0.0275


===19-limit===
==== 19-limit ====
Commas: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95


POTE generator: ~36/35 = 38.080
POTE generator: ~36/35 = 38.080


Map: [<12 19 28 0 8 78 49 51|, <0 0 0 1 1 -1 0 0|]
Mapping: [{{val| 12 19 28 0 8 78 49 51 }}, {{val| 0 0 0 1 1 -1 0 0 }}]


EDOs: 12, 24, 36, 60c
{{Val list|legend=1| 12, 24, 36, 60c }}


Badness: 0.0209
Badness: 0.0209


==Duodecim==
= Duodecim =
Commas: 36/35, 50/49, 64/63
Comma list: 36/35, 50/49, 64/63


POTE generator: ~45/44 = 34.977
POTE generator: ~45/44 = 34.977


Map: [<12 19 28 34 0|, <0 0 0 0 1|]
Mapping: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]


EDOs: 12, 24d
{{Val list|legend=1| 12, 24d }}


=Omicronbeta temperament=
= Omicronbeta =
Commas: 225/224, 243/242, 441/440, 4375/4356
Comma list: 225/224, 243/242, 441/440, 4375/4356


Generator: ~13/8 = 837.814
POTE generator: ~13/8 = 837.814


Map: [<72 114 167 202 249 266|, <0 0 0 0 0 1|]
Mapping: [{{val| 72 114 167 202 249 266 }}, {{val| 0 0 0 0 0 1 }}]


EDOs: 72, 144, 216c, 288cdf, 504bcdef
{{Val list|legend=1| 72, 144, 216c, 288cdf, 504bcdef }}


Badness: 0.0300
Badness: 0.0300
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