Schismatic family: Difference between revisions

→Hemischis: music collection
→Bischismic: tuning; review optimal ET sequence
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{{Multival|legend=1| 2 -16 -40 -30 -69 -48 }}
{{Multival|legend=1| 2 -16 -40 -30 -69 -48 }}


[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~3/2 = 701.592
[[Optimal tuning]] ([[CTE]]): ~567/400 = 1\2, ~3/2 = 701.5899


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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* [[9-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.9/7
* [[9-odd-limit]] eigenmonzo (unchanged-interval) basis: 2.9/7


{{Optimal ET sequence|legend=1| 12, 106d, 118, 130, 248, 378, 508 }}
{{Optimal ET sequence|legend=1| 12, 106d, 118, 130, 248, 378 }}


[[Badness]]: 0.054744
[[Badness]]: 0.054744
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Mapping: {{mapping| 2 0 30 69 102 | 0 1 -8 -20 -30 }}
Mapping: {{mapping| 2 0 30 69 102 | 0 1 -8 -20 -30 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.612
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.6077


{{Optimal ET sequence|legend=1| 12, 106de, 118, 130, 248 }}
{{Optimal ET sequence|legend=1| 12, 106de, 118, 130, 248 }}
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Mapping: {{mapping| 2 0 30 69 102 -75 | 0 1 -8 -20 -30 26 }}
Mapping: {{mapping| 2 0 30 69 102 -75 | 0 1 -8 -20 -30 26 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.590
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.5949


{{Optimal ET sequence|legend=1| 12, 106def, 118, 130, 248, 378 }}
{{Optimal ET sequence|legend=1| 12, 106def, 118, 130, 248, 378 }}
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Mapping: {{mapping| 2 0 30 69 102 -75 5 | 0 1 -8 -20 -30 26 1 }}
Mapping: {{mapping| 2 0 30 69 102 -75 5 | 0 1 -8 -20 -30 26 1 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.600
Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.5959


{{Optimal ET sequence|legend=1| 12, 106def, 118, 130, 248g }}
{{Optimal ET sequence|legend=1| 12, 106def, 118, 130, 248g }}
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Mapping: {{mapping| 2 0 30 69 102 131 | 0 1 -8 -20 -30 -39 }}
Mapping: {{mapping| 2 0 30 69 102 131 | 0 1 -8 -20 -30 -39 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~3/2 = 701.565
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 701.5708


{{Optimal ET sequence|legend=1| 12f, 106deff, 118f, 130 }}
{{Optimal ET sequence|legend=1| 12f, 106deff, 118f, 130 }}
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Mapping: {{mapping| 2 0 30 69 102 131 5 | 0 1 -8 -20 -30 -39 1 }}
Mapping: {{mapping| 2 0 30 69 102 131 5 | 0 1 -8 -20 -30 -39 1 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~3/2 = 701.595
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 701.5717


{{Optimal ET sequence|legend=1| 12f, 106deff, 118f, 130, 248fg, 378fgg }}
{{Optimal ET sequence|legend=1| 12f, 106deff, 118f, 130, 248fg }}


Badness: 0.026894
Badness: 0.026894