Xenharmonic Wiki

Unicorn family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m recat
m Cleanup
Line 1: Line 1:
__FORCETOC__
The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo| -2 13 -8 }}.  
The unicorn family tempers out the unicorn comma, 1594323/1562500 = |-2 13 -8>.


=Unicorn=
= Unicorn =
Comma: 1594323/1562500


POTE generator: ~250/243 = 62.458
Subgroup: 2.3.5


Map: [<1 2 3|, <0 -8 -13|]
[[Comma list]]: 1594323/1562500


EDOs: 19, 58, 77, 96, 173, 269
[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -8 -13 }}]


Badness: 0.1505
[[POTE generator]]: ~250/243 = 62.458


=Alicorn=
{{Val list|legend=1| 19, 58, 77, 96, 173, 269 }}
Commas: 126/125, 10976/10935


POTE generator: ~28/27 = 62.279
[[Badness]]: 0.1505


Map: [<1 2 3 4|, <0 -8 -13 -23|]
= Alicorn =
{{see also| Starling temperaments #Alicorn }}


EDOs: 19, 58, 77, 96d
Subgroup: 2.3.5.7


Badness: 0.0409
[[Comma list]]: 126/125, 10976/10935


==11-limit==
[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -8 -13 -23 }}]
Commas: 126/125, 540/539, 896/891
 
[[POTE generator]]: ~28/27 = 62.279
 
{{Val list|legend=1| 19, 58, 77, 96d }}
 
[[Badness]]: 0.0409
 
== 11-limit ==
 
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 540/539, 896/891
 
Mapping: [{{val| 1 2 3 4 3 }}, {{val| 0 -8 -13 -23 9 }}]


POTE generator: ~28/27 = 62.101
POTE generator: ~28/27 = 62.101


Map: [<1 2 3 4 3|, <0 -8 -13 -23 9|]
{{Val list|legend=1| 19, 58 }}
 
Badness: 0.0392
 
=== 13-limit ===


EDOs: 19, 58
Subgroup: 2.3.5.7.11.13


Badness: 0.0392
Comma list: 126/125, 144/143, 196/195, 676/675


==13-limit==
Mapping: [{{val| 1 2 3 4 3 5 }}, {{val| 0 -8 -13 -23 9 -25 }}]
Commas: 126/125, 144/143, 196/195, 676/675


POTE generator: ~28/27 = 62.119
POTE generator: ~28/27 = 62.119


Map: [<1 2 3 4 3 5|, <0 -8 -13 -23 9 -25|]
{{Val list|legend=1| 19, 58 }}


EDOs: 19, 58
Badness: 0.0237


Badness: 0.0237
== Camahueto ==
 
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 10976/10935, 385/384


==Camahueto==
Mapping: [{{val| 1 2 3 4 2 }}, {{val| 0 -8 -13 -23 28 }}]
Commas: 126/125, 10976/10935, 385/384


POTE generator: ~28/27 = 62.431
POTE generator: ~28/27 = 62.431


Map: [<1 2 3 4 2|, <0 -8 -13 -23 28|]
{{Val list|legend=1| 19, 58, 77, 96d }}
 
Badness: 0.0659
 
=== 13-limit ===


EDOs: 19, 58, 77, 96d
Subgroup: 2.3.5.7.11.13


Badness: 0.0659
Comma list: 126/125, 196/195, 385/384, 676/675


==13-limit==
Mapping: [{{val| 1 2 3 4 2 5 }}, {{val| 0 -8 -13 -23 28 -25 }}]
Commas: 126/125, 196/195, 385/384, 676/675


POTE generator: ~28/27 = 62.434
POTE generator: ~28/27 = 62.434


Map: [<1 2 3 4 2 5|, <0 -8 -13 -23 28 -25|]
{{Val list|legend=1| 19, 58, 77, 96d }}
 
Badness: 0.0362
 
== Qilin ==
 
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 176/175, 10976/10935
 
Mapping: [{{val| 1 2 3 4 6 }}, {{val| 0 -8 -13 -23 -49 }}]
 
POTE generator: ~28/27 = 62.196
 
{{Val list|legend=1| 58, 77, 135c, 193c, 328c }}
 
Badness: 0.0414
 
=== 13-limit ===


EDOs: 19, 58, 77, 96d
Subgroup: 2.3.5.7.11.13


Badness: 0.0362
Comma list: 126/125, 176/175, 196/195, 2200/2197
 
Mapping: [{{val| 1 2 3 4 6 5 }}, {{val| 0 -8 -13 -23 -49 -25 }}]
 
POTE generator: ~28/27 = 62.197


=Monocerus=
{{Val list|legend=1| 58, 77, 135c, 193cf, 328cf }}
Commas: 126/125, 243/242, 5488/5445


POTE generator: ~28/27 = 62.292
Badness: 0.0228


Map: [<2 4 6 8 9|, <0 -8 -13 -23 -20|]
== Monocerus ==


EDOs: 58, 96d, 154, 212ce, 366de
Subgroup: 2.3.5.7.11


Badness: 0.0528
Comma list: 126/125, 243/242, 5488/5445


==13-limit==
Mapping: [{{val| 2 4 6 8 9 }}, {{val| 0 -8 -13 -23 -20 }}]
Commas: 126/125, 196/195, 364/363, 676/675


POTE generator: ~28/27 = 62.301
POTE generator: ~28/27 = 62.292


Map: [<2 4 6 8 9 10|, <0 -8 -13 -23 -20 -25|]
{{Val list|legend=1| 58, 96d, 154, 212ce, 366de }}


EDOs: 58, 96d, 154, 366cef
Badness: 0.0528


Badness: 0.0288
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13


=Qilin=
Comma list: 126/125, 196/195, 364/363, 676/675
Commas: 126/125, 176/175, 10976/10935


POTE generator: ~28/27 = 62.196
Mapping: [{{val| 2 4 6 8 9 10 }}, {{val| 0 -8 -13 -23 -20 -25 }}]


Map: [<1 2 3 4 6|, <0 -8 -13 -23 -49|]
POTE generator: ~28/27 = 62.301


EDOs: 58, 77, 135c, 193c, 328c
{{Val list|legend=1| 58, 96d, 154, 366cef }}


Badness: 0.0414
Badness: 0.0288


==13-limit==
= Rhinoceros =
Commas: 126/125, 176/175, 196/195, 2200/2197


POTE generator: ~28/27 = 62.197
Subgroup: 2.3.5.7


Map: [<1 2 3 4 6 5|, <0 -8 -13 -23 -49 -25|]
[[Comma list]]: 49/48, 4375/4374


EDOs: 58, 77, 135c, 193cf, 328cf
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -8 -13 -4 }}]


Badness: 0.0228
{{Multival|legend=1| 8 13 4 2 -16 -27 }}


=Rhinoceros=
[[POTE generator]]: ~21/20 = 62.920
Commas: 49/48, 4375/4374


POTE generator: ~21/20 = 62.920
{{Val list|legend=1| 19 }}


Map: [<1 2 3 3]|, <0 -8 -13 -4|]
[[Badness]]: 0.0819


Wedgie: <<8 13 4 2 -16 -27||
== 11-limit ==


EDOs: 19
Subgroup: 2.3.5.7.11


Badness: 0.0819
Comma list: 49/48, 100/99, 126/121


==11-limit==
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -8 -13 -4 -10 }}]
Commas: 49/48, 100/99, 126/121


POTE generator: ~21/20 = 62.874
POTE generator: ~21/20 = 62.874


Map: [<1 2 3 3 4]|, <0 -8 -13 -4 -10|]
{{Val list|legend=1| 19 }}
 
Badness: 0.0593
 
== 13-limit ==


EDOs: 19
Subgroup: 2.3.5.7.11.13


Badness: 0.0593
Comma list: 49/48, 78/77, 100/99, 126/121


==13-limit==
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -8 -13 -4 -10 -6 }}]
Commas: 49/48, 78/77, 100/99, 126/121


POTE generator: ~21/20 = 63.043
POTE generator: ~21/20 = 63.043


Map: [<1 2 3 3 4 4]|, <0 -8 -13 -4 -10 -6|]
{{Val list|legend=1| 19 }}
 
EDOs: 19


Badness: 0.0393
Badness: 0.0393


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Unicorn]]
[[Category:Unicorn]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Unicorn_family"