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Würschmidt family: Difference between revisions

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{{Mapping|legend=1| 1 -1 2 | 0 8 1 }}
{{Mapping|legend=1| 1 -1 2 | 0 8 1 }}
: mapping generators: ~2, ~5/4
: mapping generators: ~2, ~5/4


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 387.734
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.734{{c}}
* [[POTE]]: ~2 = 1\1, ~5/4 = 387.799
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.799{{c}}


{{Optimal ET sequence|legend=1| 3, …, 28, 31, 34, 65, 99, 164, 721c, 885c, 1049cc, 1213ccc }}
{{Optimal ET sequence|legend=1| 3, …, 28, 31, 34, 65, 99, 164, 721c, 885c, 1049cc, 1213ccc }}
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Comma list: 576/575, 12167/12150
Comma list: 576/575, 12167/12150


Sval mapping: {{mapping| 1 -1 2 0 | 0 8 1 14 }}
Subgroup-val mapping: {{mapping| 1 -1 2 0 | 0 8 1 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 387.734
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.734{{c}}
* POTE: ~2 = 1\1, ~5/4 = 387.805
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.805{{c}}


Optimal ET sequence: {{optimal ET sequence| 3, …, 28i, 31, 34, 65, 99, 164 }}
{{Optimal ET sequence|legend=0| 3, …, 28i, 31, 34, 65, 99, 164 }}


Badness (Smith): 0.00530
Badness (Smith): 0.00530
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Comma list: 243/242, 276/275, 529/528
Comma list: 243/242, 276/275, 529/528


Sval mapping: {{mapping| 1 -1 2 -3 0 | 0 8 1 20 14 }}
Subgroup-val mapping: {{mapping| 1 -1 2 -3 0 | 0 8 1 20 14 }}


Optimal tuning:  
Optimal tuning:  
* CTE: ~2 = 1\1, ~5/4 = 387.652
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.652{{c}}
* POTE: ~2 = 1\1, ~5/4 = 387.690
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.690{{c}}


Optimal ET sequence: {{optimal ET sequence| 31, 34, 65 }}
{{Optimal ET sequence|legend=0| 31, 34, 65 }}


Badness (Smith): 0.00660
Badness (Smith): 0.00660
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 387.379
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.379{{c}}
* [[POTE]]: ~2 = 1\1, ~5/4 = 387.383
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.383{{c}}


{{Optimal ET sequence|legend=1| 31, 96, 127 }}
{{Optimal ET sequence|legend=1| 31, 96, 127 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 387.441
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.441{{c}}
* POTE: ~2 = 1\1, ~5/4 = 387.447
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.447{{c}}


Optimal ET sequence: {{optimal ET sequence| 31, 65d, 96, 127 }}
{{Optimal ET sequence|legend=0| 31, 65d, 96, 127 }}


Badness (Smith): 0.024413
Badness (Smith): 0.024413
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 387.469
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.469{{c}}
* POTE: ~2 = 1\1, ~5/4 = 387.626
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.626{{c}}


Optimal ET sequence: {{optimal ET sequence| 31, 65d }}
{{Optimal ET sequence|legend=0| 31, 65d }}


Badness (Smith): 0.023593
Badness (Smith): 0.023593
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 387.179
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.179{{c}}
* POTE: ~2 = 1\1, ~5/4 = 387.099
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.099{{c}}


Optimal ET sequence: {{optimal ET sequence| 3def, 28def, 31 }}
{{Optimal ET sequence|legend=0| 3def, 28def, 31 }}


Badness (Smith): 0.034382
Badness (Smith): 0.034382
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 387.406
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.406{{c}}
* [[POTE]]: ~2 = 1\1, ~5/4 = 387.392
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.392{{c}}


{{Optimal ET sequence|legend=1| 31, 96d, 127d }}
{{Optimal ET sequence|legend=1| 31, 96d, 127d }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 387.472
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.472{{c}}
* POTE: ~2 = 1\1, ~5/4 = 387.407
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.407{{c}}


Optimal ET sequence: {{optimal ET sequence| 31, 65, 96d, 127d }}
{{Optimal ET sequence|legend=0| 31, 65, 96d, 127d }}


Badness (Smith): 0.033436
Badness (Smith): 0.033436
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 387.853
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.853
* [[POTE]]: ~2 = 1\1, ~5/4 = 387.881
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 387.881


{{Optimal ET sequence|legend=1| 34d, 65, 99 }}
{{Optimal ET sequence|legend=1| 34d, 65, 99 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 387.829
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 387.829
* POTE: ~2 = 1\1, ~5/4 = 387.882
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 387.882


Optimal ET sequence: {{optimal ET sequence| 34d, 65, 99e }}
{{Optimal ET sequence|legend=0| 34d, 65, 99e }}


Badness (Smith): 0.058325
Badness (Smith): 0.058325
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[[Category:Würschmidt family| ]] <!-- main article -->
[[Category:Würschmidt family| ]] <!-- main article -->
[[Category:Würschmidt| ]] <!-- key article -->
[[Category:Würschmidt| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Catalogs of rank-2 temperaments]]
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