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Schismic–commatic equivalence continuum: Difference between revisions

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| [[Marvel temperaments #Gracecordial|Gracecordial]]
| [[Marvel temperaments #Gracecordial|Gracecordial]]
| 17433922005/17179869184
| 17433922005/17179869184
| {{monzo|-34 20 1}}
| {{monzo| -34 20 1 }}
|-
|-
| 0
| 0
| [[Compton family|Compton]]
| [[Compton family|Compton]]
| 531441/524288
| 531441/524288
| {{monzo|-19 12}}
| {{monzo| -19 12 }}
|-
|-
| 1
| 1
| [[Meantone family|Meantone]]
| [[Meantone family|Meantone]]
| 81/80
| 81/80
| {{monzo|-4 4 -1}}
| {{monzo|-4 4 -1 }}
|-
|-
| 2
| 2
| [[Diaschismic family|Diaschismic]]
| [[Diaschismic family|Diaschismic]]
| 2048/2025
| 2048/2025
| {{monzo| 11 -4 -2}}
| {{monzo| 11 -4 -2 }}
|-
|-
| 3
| 3
| [[Misty family|Misty]]
| [[Misty family|Misty]]
| 67108864/66430125
| 67108864/66430125
| {{monzo| 26 -12 -3}}
| {{monzo| 26 -12 -3 }}
|-
|-
| 4
| 4
| [[Hemifamity temperaments|Undim]]
| [[Hemifamity temperaments|Undim]]
|  
|  
| {{monzo| 41 -20 -4}}
| {{monzo| 41 -20 -4 }}
|-
|-
| 5
| 5
| [[28ed5|Quindromeda]]
| [[Quindromeda family|Quindromeda]]
|  
|  
| {{monzo| 56 -28 -5}}
| {{monzo| 56 -28 -5 }}
|-
|-
| 6
| 6
| Sextile
| [[Sextile]]
|  
|  
| {{monzo| 71 -36 -6}}
| {{monzo| 71 -36 -6 }}
|-
|-
| 7
| 7
| Sepsa-sepgu (12&323)
| Sepsa-sepgu (12&323)
|  
|  
| {{monzo| 86 -44 -7}}
| {{monzo| 86 -44 -7 }}
|-
|-
| 8
| 8
| Tritrisa-quadbigu (12&388)
| Tritrisa-quadbigu (12&388)
|  
|  
| {{monzo| 101 -52 -8}}
| {{monzo| 101 -52 -8 }}
|-
|-
| 9
| 9
| Quinbisa-tritrigu (12&441)
| Quinbisa-tritrigu (12&441)
|  
|  
| {{monzo| 116 -60 -9}}
| {{monzo| 116 -60 -9 }}
|-
|-
| 10
| 10
| Lesa-quinbigu (12&494)
| Lesa-quinbigu (12&494)
|  
|  
| {{monzo| 131 -68 -10}}
| {{monzo| 131 -68 -10 }}
|-
|-
| 11
| 11
| Quadtrisa-legu (12&559)
| Quadtrisa-legu (12&559)
|  
|  
| {{monzo| 146 -76 -11}}
| {{monzo| 146 -76 -11 }}
|-
|-
| 12
| 12
| [[Very high accuracy temperaments #Atomic|Atomic]]
| [[Very high accuracy temperaments #Atomic|Atomic]]
|  
|  
| [[Kirnberger's atom|{{monzo|161 -84 -12}}]]
| [[Kirnberger's atom|{{monzo| 161 -84 -12 }}]]
|-
|-
| 13
| 13
| Quintrila-theyo (12&677)
| Quintrila-theyo (12&677)
|  
|  
| {{monzo|-176 92 13}}
| {{monzo| -176 92 13 }}
|-
|-
| …
| …
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| [[Schismic]]
| [[Schismic]]
| [[32805/32768]]
| [[32805/32768]]
| {{monzo| -15 8 1}}
| {{monzo| -15 8 1 }}
|}
|}


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* [[Augmented family|Augmented]] (''n'' = 3/2 = 1.5)
* [[Augmented family|Augmented]] (''n'' = 3/2 = 1.5)
* [[Passion family|Passion]] (''n'' = 5/3 = 1.{{overline|6}})
* [[Passion family|Passion]] (''n'' = 5/3 = 1.{{overline|6}})
* [[16ed5/2|Quintaleap]] / [[Octagar temperaments|Quintupole]] (''n'' = 5/2 = 2.5)
* [[Quintaleap family|Quintaleap]] (''n'' = 5/2 = 2.5)


== Compton temperament (12&72) ==
== Compton (12&72) ==
{{See also| Pythagorean comma }} ''and [[Compton family]]''
{{See also| Pythagorean comma }} ''and [[Compton family]]''
Subgroup: 2.3.5


Comma list: {{monzo| -19 12 }} = 531441/524288
Comma list: {{monzo| -19 12 }} = 531441/524288
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Mapping: [{{val| 12 19 28 }}, {{val| 0 0 -1 }}]
Mapping: [{{val| 12 19 28 }}, {{val| 0 0 -1 }}]


Wedgie: {{wedgie| 0 12 19 }}
{{Multival|legend=1| 0 12 19 }}


POTE generator: ~5/4 = 384.882
POTE generator: ~5/4 = 384.882
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== Lalagu (12&79) ==
== Lalagu (12&79) ==
Subgroup: 2.3.5
Comma list: {{monzo| -23 16 -1 }} = 43046721/41943040
Comma list: {{monzo| -23 16 -1 }} = 43046721/41943040


Mapping: [{{val| 1 2 9 }}, {{val| 0 -1 -16 }}]
Mapping: [{{val| 1 2 9 }}, {{val| 0 -1 -16 }}]


Wedgie: {{wedgie| 1 16 23 }}
{{Multival|legend=1| 1 16 23 }}


POTE generator: ~4/3 = 500.970
POTE generator: ~4/3 = 500.970
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Badness: 0.295079
Badness: 0.295079


== Quintaleap (12&121, trisa-quingu) ==
== Quintaleap (12&121) ==
{{See also| 16ed5/2 #Regular temperaments }}
{{See also| Quintaleap family }}
 
Subgroup: 2.3.5


Comma list: {{monzo| 37 -16 -5 }} = 137438953472/134521003125
Comma list: {{monzo| 37 -16 -5 }} = 137438953472/134521003125
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Mapping: [{{val| 1 2 1 }}, {{val| 0 -5 16 }}]
Mapping: [{{val| 1 2 1 }}, {{val| 0 -5 16 }}]


Wedgie: {{wedgie| 5 -16 -37 }}
{{Multival|legend=1| 5 -16 -37 }}


POTE generator: ~135/128 = 99.267
POTE generator: ~135/128 = 99.267
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== Undim (12&152) ==
== Undim (12&152) ==
{{see also| Hemifamity temperaments #Undim }}
{{see also| Hemifamity temperaments #Undim }}
Subgroup: 2.3.5


Comma list: {{monzo| 41 -20 -4 }}
Comma list: {{monzo| 41 -20 -4 }}
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Mapping: [{{val| 4 6 11 }}, {{val| 0 1 -5 }}]
Mapping: [{{val| 4 6 11 }}, {{val| 0 1 -5 }}]


Wedgie: {{wedgie| 4 -20 -41 }}
{{Multival|legend=1| 4 -20 -41 }}


POTE generator: ~3/2 = 702.6054
POTE generator: ~3/2 = 702.6054
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Badness: 0.241703
Badness: 0.241703


== Quindromeda (12&205, quinsa-quingu) ==
== Quindromeda (12&205) ==
{{see also| 28ed5 #Regular temperaments }}
{{See also| Quindromeda family }}
 
Subgroup: 2.3.5


Comma list: {{monzo| 56 -28 -5 }}
Comma list: {{monzo| 56 -28 -5 }}
Mapping: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]


POTE generator: ~4428675/4194304 = 99.526
POTE generator: ~4428675/4194304 = 99.526


Mapping: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]
{{Multival|legend=1| 5 -28 -56 }}
 
Wedgie: {{wedgie| 5 -28 -56 }}


Vals: {{Val list| 12, 193, 205, 217, 422 }}
Vals: {{Val list| 12, 193, 205, 217, 422 }}
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== Sextile (12&270) ==
== Sextile (12&270) ==
{{see also| Landscape microtemperaments #Sextile }}
{{See also| Landscape microtemperaments #Sextile }}
 
Subgroup: 2.3.5


Comma list: {{monzo| 71 -36 -6 }}
Comma list: {{monzo| 71 -36 -6 }}
Mapping: [{{val| 6 10 11 }}, {{val| 0 -1 6 }}]


POTE generator: ~3/2 = 702.2356
POTE generator: ~3/2 = 702.2356


Mapping: [{{val| 6 10 11 }}, {{val| 0 -1 6 }}]
{{Multival|legend=1| 6 -36 -77 }}
 
Wedgie: {{wedgie| 6 -36 -77 }}


Vals: {{Val list| 12, 258, 270, 1878 }}
Vals: {{Val list| 12, 258, 270, 1878 }}
Line 195: Line 207:


[[Category:12edo]]
[[Category:12edo]]
[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]
Retrieved from "https://en.xen.wiki/w/Schismic–commatic_equivalence_continuum"