Schismatic family: Difference between revisions
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Move hemischis here |
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* [[#Bischismic]] adds {{monzo| -69 40 0 2 }} and has a fifth generator with a half-octave period. | * [[#Bischismic]] adds {{monzo| -69 40 0 2 }} and has a fifth generator with a half-octave period. | ||
* [[#Guiron]] adds [[1029/1024|{{monzo| -10 1 0 3 }}]], with an 8/7 generator, three of which give the fifth. | * [[#Hemischis]] adds {{monzo| -34 25 0 -2 }} and has a hemififth generator. | ||
* [[#Guiron]] adds [[1029/1024|{{monzo| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth. | |||
* [[#Term]] adds {{monzo| -94 54 0 3 }} with a 1/3 octave period. | * [[#Term]] adds {{monzo| -94 54 0 3 }} with a 1/3 octave period. | ||
* [[#Sesquiquartififths]] adds {{monzo| -35 15 0 4 }} and slices the fifth in four. | * [[#Sesquiquartififths]] adds {{monzo| -35 15 0 4 }} and slices the fifth in four. | ||
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* [[Sensamagic clan #Salsa|Salsa]] | * [[Sensamagic clan #Salsa|Salsa]] | ||
* [[Gamelismic clan #Guiron|Guiron]] | * [[Gamelismic clan #Guiron|Guiron]] | ||
Remarkable subgroup temperaments include | Remarkable subgroup temperaments include | ||
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Badness: 0.024734 | Badness: 0.024734 | ||
== Hemischis == | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 6144/6125, 19683/19600 | |||
[[Mapping]]: [{{val| 1 0 15 -17 }}, {{val| 0 2 -16 25 }}] | |||
{{Multival|legend=1| 2 -16 25 -30 34 103 }} | |||
[[POTE generator]]: ~81/70 = 249.203 | |||
{{Val list|legend=1| 24, 53, 130, 183, 313 }} | |||
[[Badness]]: 0.045817 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 5632/5625, 8019/8000 | |||
Mapping: [{{val| 1 0 15 -17 51 }}, {{val| 0 2 -16 25 -60 }}] | |||
POTE generator: ~81/70 = 249.199 | |||
Optimal GPV sequence: {{Val list| 24e, 53, 130, 183, 313 }} | |||
Badness: 0.036289 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 540/539, 676/675, 4096/4095 | |||
Mapping: [{{val| 1 0 15 -17 51 14 }}, {{val| 0 2 -16 25 -60 -13 }}] | |||
POTE generator: ~15/13 = 249.199 | |||
Optimal GPV sequence: {{Val list| 24e, 53, 130, 183, 313 }} | |||
Badness: 0.020816 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 351/350, 442/441, 561/560, 676/675, 4096/4095 | |||
Mapping: [{{val| 1 0 15 -17 51 14 -49 }}, {{val| 0 2 -16 25 -60 -13 67 }}] | |||
POTE generator: ~15/13 = 249.190 | |||
Optimal GPV sequence: {{Val list| 53, 130, 183, 679df }} | |||
Badness: 0.021073 | |||
== Squirrel == | == Squirrel == | ||