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Breedsmic temperaments: Difference between revisions

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m →Tertiaseptal: mention relation to 311
→Hemififths: +CTE tunings
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{{Mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}
{{Mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}


: Mapping generators: ~2, ~49/40
: mapping generators: ~2, ~49/40


{{Multival|legend=1| 2 25 13 35 15 -40 }}
{{Multival|legend=1| 2 25 13 35 15 -40 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 351.477
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~49/40 = 351.4464
* [[POTE]]: ~2 = 1\1, ~49/40 = 351.477


[[Minimax tuning]]:
[[Minimax tuning]]:
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Mapping: {{mapping| 1 1 -5 -1 2 | 0 2 25 13 5 }}
Mapping: {{mapping| 1 1 -5 -1 2 | 0 2 25 13 5 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.521
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 351.4289
* POTE: ~2 = 1\1, ~11/9 = 351.521


Optimal ET sequence: {{Optimal ET sequence| 17c, 41, 58, 99e }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 41, 58, 99e }}
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Mapping: {{mapping| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}
Mapping: {{mapping| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.573
Optimal tunings:
* CTE: ~2 = 1\1, ~11/9 = 351.4331
* POTE: ~2 = 1\1, ~11/9 = 351.573


Optimal ET sequence: {{Optimal ET sequence| 17c, 41, 58, 99ef, 157eff }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 41, 58, 99ef, 157eff }}
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Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}
Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}


: Mapping generators: ~99/70, ~49/40
: mapping generators: ~99/70, ~400/231


Optimal tuning (POTE): ~99/70 = 1\2, ~49/40 = 351.505
Optimal tunings:
* CTE: ~99/70 = 1\2, ~49/40 = 351.4722
* POTE: ~99/70 = 1\2, ~49/40 = 351.505


Optimal ET sequence: {{Optimal ET sequence| 58, 140, 198 }}
Optimal ET sequence: {{Optimal ET sequence| 58, 140, 198 }}
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Mapping: {{mapping| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}
Mapping: {{mapping| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~49/40 = 351.502
Optimal tunings:
* CTE: ~99/70 = 1\2, ~49/40 = 351.4674
* POTE: ~99/70 = 1\2, ~49/40 = 351.502


Optimal ET sequence: {{Optimal ET sequence| 58, 140, 198, 536f }}
Optimal ET sequence: {{Optimal ET sequence| 58, 140, 198, 536f }}
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: Mapping generators: ~2, ~243/220
: Mapping generators: ~2, ~243/220


Optimal tuning (POTE): ~2 = 1\1, ~243/220 = 175.7378
Optimal tunings:
* CTE: ~2 = 1\1, ~243/220 = 175.7284
* POTE: ~2 = 1\1, ~243/220 = 175.7378


Optimal ET sequence: {{Optimal ET sequence| 41, 157, 198, 239, 676b, 915be }}
Optimal ET sequence: {{Optimal ET sequence| 41, 157, 198, 239, 676b, 915be }}
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Mapping: {{mapping| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}
Mapping: {{mapping| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}


Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.7470
Optimal tunings:
* CTE: ~2 = 1\1, ~72/65 = 175.7412
* POTE: ~2 = 1\1, ~72/65 = 175.7470


Optimal ET sequence: {{Optimal ET sequence| 41, 157, 198, 437f, 635bcff }}
Optimal ET sequence: {{Optimal ET sequence| 41, 157, 198, 437f, 635bcff }}
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