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Ditonmic family: Difference between revisions

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{{Technical data page}}
The '''ditonmic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo|legend=1| -27 -2 13 }}).
The '''ditonmic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo|legend=1| -27 -2 13 }}).


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{{Mapping|legend=1| 1 6 3 | 0 -13 -2 }}
{{Mapping|legend=1| 1 6 3 | 0 -13 -2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~15625/12288 = 407.574
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~15625/12288 = 407.534
: [[error map]]: {{val| 0.000 +0.099 -1.382 }}
* [[POTE]]: ~2 = 1200.000, ~15625/12288 = 407.574
: error map: {{val| 0.000 -0.416 -1.462 }}


{{Optimal ET sequence|legend=1| 3, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}
{{Optimal ET sequence|legend=1| 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}


[[Badness]] (Smith): 0.167086
[[Badness]] (Smith): 0.167086
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{{Mapping|legend=1| 1 6 3 13 | 0 -13 -2 -30 }}
{{Mapping|legend=1| 1 6 3 13 | 0 -13 -2 -30 }}


{{Multival|legend=1| 13 2 30 -27 11 64 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.000, ~1225/972 = 407.642
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~1225/972 = 407.690
: [[error map]]: {{val| 0.000 -1.298 -1.597 +1.921 }}
* [[POTE]]: ~2 = 1200.000, ~1225/972 = 407.690
: error map: {{val| 0.000 -1.921 -1.693 +0.483 }}


{{Optimal ET sequence|legend=1| 3d, 50, 53, 103, 156 }}
{{Optimal ET sequence|legend=1| 3d, 50, 53, 103, 156 }}
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Mapping: {{mapping| 1 6 3 13 -3 | 0 -13 -2 -30 19 }}
Mapping: {{mapping| 1 6 3 13 -3 | 0 -13 -2 -30 19 }}


Optimal tuning (POTE): ~2 = 1200.000, ~1225/972 = 407.741
Optimal tunings:
* CTE: ~2 = 1200.000, ~1225/972 = 407.688
* POTE: ~2 = 1200.000, ~1225/972 = 407.741


{{Optimal ET sequence|legend=0| 50, 53, 103 }}
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
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Mapping: {{mapping| 1 6 3 13 -3 2 | 0 -13 -2 -30 19 5 }}
Mapping: {{mapping| 1 6 3 13 -3 2 | 0 -13 -2 -30 19 5 }}


Optimal tuning (POTE): ~2 = 1200.000, ~325/256 = 407.736
Optimal tunings:
* CTE: ~2 = 1200.000, ~325/256 = 407.691
* POTE: ~2 = 1200.000, ~325/256 = 407.736


{{Optimal ET sequence|legend=0| 50, 53, 103 }}
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
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Mapping: {{mapping| 1 6 3 13 15 | 0 -13 -2 -30 -34 }}
Mapping: {{mapping| 1 6 3 13 15 | 0 -13 -2 -30 -34 }}


Optimal tuning (POTE): ~2 = 1200.000, ~242/189 = 407.567
Optimal tunings:
* CTE: ~2 = 1200.000, ~242/189 = 407.528
* POTE: ~2 = 1200.000, ~242/189 = 407.567


{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
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Mapping: {{mapping| 1 6 3 13 15 20 | 0 -13 -2 -30 -34 -48 }}
Mapping: {{mapping| 1 6 3 13 15 20 | 0 -13 -2 -30 -34 -48 }}


Optimal tuning (POTE): ~2 = 1200.000, ~33/26 = 407.541
Optimal tunings:
* CTE: ~2 = 1200.000, ~242/189 = 407.514
* POTE: ~2 = 1200.000, ~33/26 = 407.541


{{Optimal ET sequence|legend=0| 3def, 53 }}
{{Optimal ET sequence|legend=0| 3def, 50eff, 53 }}


Badness (Smith): 0.043989
Badness (Smith): 0.043989
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{{Mapping|legend=1| 1 6 3 -4 | 0 -13 -2 20 }}
{{Mapping|legend=1| 1 6 3 -4 | 0 -13 -2 20 }}


{{Multival|legend=1| 13 2 -20 -27 -68 -52 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.000, ~2625/2048 = 407.922
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~2625/2048 = 407.954
: [[error map]]: {{val| 0.000 -4.939 -2.157 -10.388 }}
* [[POTE]]: ~2 = 1200.000, ~2625/2048 = 407.954
: error map: {{val| 0.000 -5.353 -2.221 -9.751 }}


{{Optimal ET sequence|legend=1| 3, 47, 50 }}
{{Optimal ET sequence|legend=1| 3, 47, 50 }}
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Mapping: {{mapping| 1 6 3 -4 -3 | 0 -13 -2 20 19 }}
Mapping: {{mapping| 1 6 3 -4 -3 | 0 -13 -2 20 19 }}


Optimal tuning (POTE): ~2 = 1200.000, ~14/11 = 407.892
Optimal tunings:
* CTE: ~2 = 1200.000, ~14/11 = 407.930
* POTE: ~2 = 1200.000, ~14/11 = 407.892


{{Optimal ET sequence|legend=0| 3, 47, 50, 53d }}
{{Optimal ET sequence|legend=0| 3, 47, 50 }}


Badness (Smith): 0.100884
Badness (Smith): 0.100884
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Mapping: {{mapping| 1 6 3 -4 -3 2 | 0 -13 -2 20 19 5 }}
Mapping: {{mapping| 1 6 3 -4 -3 2 | 0 -13 -2 20 19 5 }}


Optimal tuning (POTE): ~2 = 1200.000, ~14/11 = 407.887
Optimal tunings:
* CTE: ~2 = 1200.000, ~14/11 = 407.933
* POTE: ~2 = 1200.000, ~14/11 = 407.887


{{Optimal ET sequence|legend=0| 3, 47, 50, 53d }}
{{Optimal ET sequence|legend=0| 3, 47, 50 }}


Badness (Smith): 0.054997
Badness (Smith): 0.054997
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Ditonmic family| ]] <!-- main article -->
[[Category:Ditonmic family| ]] <!-- main article -->
[[Category:Ditonmic]]
[[Category:Ditonmic]]
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Ditonmic_family"