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Meantone family: Difference between revisions

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Move subgroup extensions to the "subgroup extensions" section
→Dominant: +link; +CTE tunings
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== Dominant ==
== Dominant ==
{{Main| Dominant (temperament) }}
{{See also| Archytas clan }}
{{See also| Archytas clan }}


Line 1,319: Line 1,320:
{{Multival|legend=1| 1 4 -2 4 -6 -16 }}
{{Multival|legend=1| 1 4 -2 4 -6 -16 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.573
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 699.622
* [[POTE]]: ~2 = 1\1, ~3/2 = 701.573


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 1,341: Line 1,344:
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.254
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 703.334
* POTE: ~2 = 1\1, ~3/2 = 703.254


{{Optimal ET sequence|legend=1| 5, 12, 17c, 29cde }}
Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17c, 29cde }}


Badness: 0.024180
Badness: 0.024180
Line 1,354: Line 1,359:
Mapping: {{mapping| 1 0 -4 6 13 18 | 0 1 4 -2 -6 -9 }}
Mapping: {{mapping| 1 0 -4 6 13 18 | 0 1 4 -2 -6 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.636
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 704.847
* POTE: ~2 = 1\1, ~3/2 = 703.636


Tuning ranges:  
Tuning ranges:  
Line 1,360: Line 1,367:
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]


{{Optimal ET sequence|legend=1| 12f, 17c, 29cdef }}
Optimal ET sequence: {{Optimal ET sequence|12f, 17c, 29cdef }}


Badness: 0.024108
Badness: 0.024108
Line 1,371: Line 1,378:
Mapping: {{mapping| 1 0 -4 6 13 -9 | 0 1 4 -2 -6 8 }}
Mapping: {{mapping| 1 0 -4 6 13 -9 | 0 1 4 -2 -6 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.905
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 704.034
* POTE: ~2 = 1\1, ~3/2 = 704.905


{{Optimal ET sequence|legend=1| 5, 12, 17c, 46cde }}
Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17c, 46cde }}


Badness: 0.027295
Badness: 0.027295
Line 1,384: Line 1,393:
Mapping: {{mapping| 1 0 -4 6 -6 | 0 1 4 -2 6 }}
Mapping: {{mapping| 1 0 -4 6 -6 | 0 1 4 -2 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.776
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.240
* POTE: ~2 = 1\1, ~3/2 = 698.776


{{Optimal ET sequence|legend=1| 5e, 7, 12, 19d, 43de }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 7, 12, 19d, 43de }}


Badness: 0.021978
Badness: 0.021978
Line 1,397: Line 1,408:
Mapping: {{mapping| 1 0 -4 6 -6 10 | 0 1 4 -2 6 -4 }}
Mapping: {{mapping| 1 0 -4 6 -6 10 | 0 1 4 -2 6 -4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 695.762
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.315
* POTE: ~2 = 1\1, ~3/2 = 695.762


{{Optimal ET sequence|legend=1| 5ef, 7, 12, 19d, 31def }}
Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}


Badness: 0.027039
Badness: 0.027039
Line 1,410: Line 1,423:
Mapping: {{mapping| 1 0 -4 6 -6 10 12 | 0 1 4 -2 6 -4 -5 }}
Mapping: {{mapping| 1 0 -4 6 -6 10 12 | 0 1 4 -2 6 -4 -5 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.115
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.894
* POTE: ~2 = 1\1, ~3/2 = 696.115


{{Optimal ET sequence|legend=1| 5ef, 7, 12, 19d, 31def }}
Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}


Badness: 0.024539
Badness: 0.024539
Line 1,423: Line 1,438:
Mapping: {{mapping| 1 0 -4 6 -6 10 12 9 | 0 1 4 -2 6 -4 -5 -3 }}
Mapping: {{mapping| 1 0 -4 6 -6 10 12 9 | 0 1 4 -2 6 -4 -5 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.217
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.139
* POTE: ~2 = 1\1, ~3/2 = 696.217


{{Optimal ET sequence|legend=1| 5ef, 7, 12, 19d, 31def }}
Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}


Badness: 0.020398
Badness: 0.020398
Line 1,436: Line 1,453:
Mapping: {{mapping| 1 0 -4 6 -6 -1 | 0 1 4 -2 6 3 }}
Mapping: {{mapping| 1 0 -4 6 -6 -1 | 0 1 4 -2 6 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.544
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 694.840
* POTE: ~2 = 1\1, ~3/2 = 698.544


{{Optimal ET sequence|legend=1| 5e, 7, 12f, 19df }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 7, 12f, 19df }}


Badness: 0.018289
Badness: 0.018289
Line 1,449: Line 1,468:
Mapping: {{mapping| 1 0 -4 6 -14 | 0 1 4 -2 11 }}
Mapping: {{mapping| 1 0 -4 6 -14 | 0 1 4 -2 11 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.004
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 703.268
* POTE: ~2 = 1\1, ~3/2 = 705.004


{{Optimal ET sequence|legend=1| 5e, 12e, 17c, 46cd }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 12e, 17c, 46cd }}


Badness: 0.036562
Badness: 0.036562
Line 1,462: Line 1,483:
Mapping: {{mapping| 1 0 -4 6 -14 -9 | 0 1 4 -2 11 8 }}
Mapping: {{mapping| 1 0 -4 6 -14 -9 | 0 1 4 -2 11 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 705.496
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 703.719
* POTE: ~2 = 1\1, ~3/2 = 705.496


{{Optimal ET sequence|legend=1| 5e, 12e, 17c }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 12e, 17c }}


Badness: 0.027435
Badness: 0.027435
Line 1,475: Line 1,498:
Mapping: {{mapping| 1 0 -4 6 5 | 0 1 4 -2 -1 }}
Mapping: {{mapping| 1 0 -4 6 5 | 0 1 4 -2 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.491
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 698.546
* POTE: ~2 = 1\1, ~3/2 = 698.491


{{Optimal ET sequence|legend=1| 5, 7, 12e }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12e }}


Badness: 0.026141
Badness: 0.026141
Line 1,488: Line 1,513:
Mapping: {{mapping| 1 0 -4 6 5 -1 | 0 1 4 -2 -1 3 }}
Mapping: {{mapping| 1 0 -4 6 5 -1 | 0 1 4 -2 -1 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.743
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.929
* POTE: ~2 = 1\1, ~3/2 = 696.743


{{Optimal ET sequence|legend=1| 5, 7, 12ef, 19def }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}


Badness: 0.023300
Badness: 0.023300
Line 1,501: Line 1,528:
Mapping: {{mapping| 1 0 -4 6 5 -1 12 | 0 1 4 -2 -1 3 -5 }}
Mapping: {{mapping| 1 0 -4 6 5 -1 12 | 0 1 4 -2 -1 3 -5 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.978
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.683
* POTE: ~2 = 1\1, ~3/2 = 696.978


{{Optimal ET sequence|legend=1| 5, 7, 12ef, 19def }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}


Badness: 0.024535
Badness: 0.024535
Line 1,514: Line 1,543:
Mapping: {{mapping| 1 0 -4 6 5 -1 12 9 | 0 1 4 -2 -1 3 -5 -3 }}
Mapping: {{mapping| 1 0 -4 6 5 -1 12 9 | 0 1 4 -2 -1 3 -5 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 697.068
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.997
* POTE: ~2 = 1\1, ~3/2 = 697.068


{{Optimal ET sequence|legend=1| 5, 7, 12ef, 19def }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}


Badness: 0.021098
Badness: 0.021098
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