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Schismic–commatic equivalence continuum: Difference between revisions

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Tunings
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| [[Gracecordial]]
| [[Gracecordial]]
| (22 digits)
| (22 digits)
| {{monzo| -34 20 1 }}
| {{Monzo| -34 20 1 }}
|-
|-
| 0
| 0
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| [[Compton]]
| [[Compton]]
| [[531441/524288]]
| [[531441/524288]]
| {{monzo| -19 12 }}
| {{Monzo| -19 12 }}
|-
|-
| 1
| 1
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| [[Meantone]]
| [[Meantone]]
| [[81/80]]
| [[81/80]]
| {{monzo| -4 4 -1 }}
| {{Monzo| -4 4 -1 }}
|-
|-
| 2
| 2
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| [[Diaschismic]]
| [[Diaschismic]]
| [[2048/2025]]
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| {{Monzo| 11 -4 -2 }}
|-
|-
| 3
| 3
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| [[Misty]]
| [[Misty]]
| [[67108864/66430125]]
| [[67108864/66430125]]
| {{monzo| 26 -12 -3 }}
| {{Monzo| 26 -12 -3 }}
|-
|-
| 4
| 4
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| [[Undim]]
| [[Undim]]
| (26 digits)
| (26 digits)
| {{monzo| 41 -20 -4 }}
| {{Monzo| 41 -20 -4 }}
|-
|-
| 5
| 5
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| [[Quindromeda]]
| [[Quindromeda]]
| (34 digits)
| (34 digits)
| {{monzo| 56 -28 -5 }}
| {{Monzo| 56 -28 -5 }}
|-
|-
| 6
| 6
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| [[Sextile]]
| [[Sextile]]
| (44 digits)
| (44 digits)
| {{monzo| 71 -36 -6 }}
| {{Monzo| 71 -36 -6 }}
|-
|-
| 7
| 7
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| [[Heptacot]]
| [[Heptacot]]
| (52 digits)
| (52 digits)
| {{monzo| 86 -44 -7 }}
| {{Monzo| 86 -44 -7 }}
|-
|-
| 8
| 8
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| [[World calendar]]
| [[World calendar]]
| (62 digits)
| (62 digits)
| {{monzo| 101 -52 -8 }}
| {{Monzo| 101 -52 -8 }}
|-
|-
| 9
| 9
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| Quinbisa-tritrigu (12 & 441)
| Quinbisa-tritrigu (12 & 441)
| (70 digits)
| (70 digits)
| {{monzo| 116 -60 -9 }}
| {{Monzo| 116 -60 -9 }}
|-
|-
| 10
| 10
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| Lesa-quinbigu (12 & 494)
| Lesa-quinbigu (12 & 494)
| (80 digits)
| (80 digits)
| {{monzo| 131 -68 -10 }}
| {{Monzo| 131 -68 -10 }}
|-
|-
| 11
| 11
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| Quadtrisa-legu (12 & 559)
| Quadtrisa-legu (12 & 559)
| (88 digits)
| (88 digits)
| {{monzo| 146 -76 -11 }}
| {{Monzo| 146 -76 -11 }}
|-
|-
| 12
| 12
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| [[Atomic]]
| [[Atomic]]
| (98 digits)
| (98 digits)
| [[Kirnberger's atom|{{monzo| 161 -84 -12 }}]]
| [[Kirnberger's atom|{{Monzo| 161 -84 -12 }}]]
|-
|-
| 13
| 13
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| Quintrila-theyo (12 & 677)
| Quintrila-theyo (12 & 677)
| (106 digits)
| (106 digits)
| {{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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| [[Python]]
| [[Python]]
| [[43046721/41943040]]
| [[43046721/41943040]]
| {{monzo| -23 16 -1 }}
| {{Monzo| -23 16 -1 }}
|-
|-
| 0
| 0
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| [[Compton]]
| [[Compton]]
| [[531441/524288]]
| [[531441/524288]]
| {{monzo| -19 12 }}
| {{Monzo| -19 12 }}
|-
|-
| 1
| 1
Line 156: Line 156:
| [[Schismic]]
| [[Schismic]]
| [[32805/32768]]
| [[32805/32768]]
| {{monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
|-
|-
| 2
| 2
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| [[Diaschismic]]
| [[Diaschismic]]
| [[2048/2025]]
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| {{Monzo| 11 -4 -2 }}
|-
|-
| 3
| 3
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| [[Augmented (temperament)|Augmented]]
| [[Augmented (temperament)|Augmented]]
| [[128/125]]
| [[128/125]]
| {{monzo| 7 0 -3 }}
| {{Monzo| 7 0 -3 }}
|-
|-
| 4
| 4
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| [[Diminished (temperament)|Diminished]]
| [[Diminished (temperament)|Diminished]]
| [[648/625]]
| [[648/625]]
| {{monzo| 3 4 -4 }}
| {{Monzo| 3 4 -4 }}
|-
|-
| 5
| 5
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| [[Ripple]]
| [[Ripple]]
| [[6561/6250]]
| [[6561/6250]]
| {{monzo| -1 8 -5 }}
| {{Monzo| -1 8 -5 }}
|-
|-
| 6
| 6
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| [[Wronecki]]
| [[Wronecki]]
| [[531441/500000]]
| [[531441/500000]]
| {{monzo| -5 12 -6 }}
| {{Monzo| -5 12 -6 }}
|-
|-
| …
| …
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| [[Meantone]]
| [[Meantone]]
| [[81/80]]
| [[81/80]]
| {{monzo| -4 4 -1 }}
| {{Monzo| -4 4 -1 }}
|}
|}


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{{Mapping|legend=1| 1 0 34 | 0 1 -20 }}
{{Mapping|legend=1| 1 0 34 | 0 1 -20 }}
: mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.691{{c}}
* [[WE]]: ~2 = 1200.3986{{c}}, ~3/2 = 700.9665{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.734{{c}}
: [[error map]]: {{val| +0.399 -0.590 -0.064 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.7202{{c}}
: error map: {{val| 0.000 -1.235 -0.718 }}


{{Optimal ET sequence|legend=1| 12, 113, 125, 137, 1221bbcc }}
{{Optimal ET sequence|legend=1| 12, 113, 125, 137, 1221bbcc }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~10/9 = 200.000{{c}}, ~3/2 = 696.229{{c}}
* [[WE]]: ~10/9 = 200.1488{{c}}, ~3/2 = 695.5574{{c}}
* [[POTE]]: ~10/9 = 200.000{{c}}, ~3/2 = 695.040{{c}}
: [[error map]]: {{val| +0.893 -5.505 +5.843 }}
* [[CWE]]: ~10/9 = 1200.0000{{c}}, ~3/2 = 695.6109{{c}}
: error map: {{val| 0.000 -6.344 +4.908 }}


{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b }}
{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b }}
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