Meantone family: Difference between revisions

Yourmusic Productions (talk | contribs)
m →Superpine: Fix math error
Restore POTE tuning by request
Line 20: Line 20:
{{Multival|legend=1| 1 4 4 }}
{{Multival|legend=1| 1 4 4 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 697.2143
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 697.2143
* [[POTE]]: ~2 = 1\1, ~3/2 = 696.239


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 73: Line 75:
{{Multival|legend=1| 1 4 10 4 13 12 }}
{{Multival|legend=1| 1 4 10 4 13 12 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 696.9521
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 696.9521
* [[POTE]]: ~2 = 1\1, ~3/2 = 696.495


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 102: Line 106:
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.1676
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.1676
* POTE: ~2 = 1\1, ~3/2 = 696.967


Minimax tuning:  
Minimax tuning:  
Line 129: Line 135:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 | 0 1 4 10 18 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8552
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.8552
* POTE: ~2 = 1\1, ~3/2 = 696.642


Minimax tuning:  
Minimax tuning:  
Line 148: Line 156:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 | 0 1 4 10 18 15 26 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 | 0 1 4 10 18 15 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.6486
* POTE: ~2 = 1\1, ~3/2 = 696.377


{{Optimal ET sequence|legend=1| 12fg, 19eg, 31, 50e }}
{{Optimal ET sequence|legend=1| 12fg, 19eg, 31, 50e }}
Line 161: Line 171:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 -40 | 0 1 4 10 18 15 26 28 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -37 -40 | 0 1 4 10 18 15 26 28 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.5551
* POTE: ~2 = 1\1, ~3/2 = 696.273


{{Optimal ET sequence|legend=1| 12fghh, 19egh, 31, 50e }}
{{Optimal ET sequence|legend=1| 12fghh, 19egh, 31, 50e }}
Line 176: Line 188:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 | 0 1 4 10 18 15 7 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 | 0 1 4 10 18 15 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.0360
* POTE: ~2 = 1\1, ~3/2 = 696.448


{{Optimal ET sequence|legend=1| 12f, 19eg, 31g }}
{{Optimal ET sequence|legend=1| 12f, 19eg, 31g }}
Line 189: Line 203:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 -10 | 0 1 4 10 18 15 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 -7 -10 | 0 1 4 10 18 15 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.2161
* POTE: ~2 = 1\1, ~3/2 = 696.394


{{Optimal ET sequence|legend=1| 12f, 19egh, 31gh }}
{{Optimal ET sequence|legend=1| 12f, 19egh, 31gh }}
Line 204: Line 220:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.9080
* POTE: ~2 = 1\1, ~3/2 = 697.003


{{Optimal ET sequence|legend=1| 12f, 31 }}
{{Optimal ET sequence|legend=1| 12f, 31 }}
Line 217: Line 235:
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 9 | 0 1 4 10 18 15 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.9308
* POTE: ~2 = 1\1, ~3/2 = 697.140


{{Optimal ET sequence|legend=1| 12f, 31 }}
{{Optimal ET sequence|legend=1| 12f, 31 }}
Line 232: Line 252:
Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}
Mapping: {{mapping| 1 0 -4 -13 -25 29 | 0 1 4 10 18 -16 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2582
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.2582
* POTE: ~2 = 1\1, ~3/2 = 697.264


Minimax tuning:  
Minimax tuning:  
Line 253: Line 275:
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 | 0 1 4 10 18 -16 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.2996
* POTE: ~2 = 1\1, ~3/2 = 697.335


{{Optimal ET sequence|legend=1| 12, 31, 43, 74g }}
{{Optimal ET sequence|legend=1| 12, 31, 43, 74g }}
Line 266: Line 290:
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -25 29 12 9 | 0 1 4 10 18 -16 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.3271
* POTE: ~2 = 1\1, ~3/2 = 697.380


{{Optimal ET sequence|legend=1| 12, 31, 43, 74gh }}
{{Optimal ET sequence|legend=1| 12, 31, 43, 74gh }}
Line 281: Line 307:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 | 0 1 4 10 18 27 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5155
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.5155
* POTE: ~2 = 1\1, ~3/2 = 697.529


Minimax tuning:  
Minimax tuning:  
Line 298: Line 326:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 | 0 1 4 10 18 27 38 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 | 0 1 4 10 18 27 38 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.5076
* POTE: ~2 = 1\1, ~3/2 = 697.514


{{Optimal ET sequence|legend=1| 12fg, 31fg, 43 }}
{{Optimal ET sequence|legend=1| 12fg, 31fg, 43 }}
Line 311: Line 341:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 -59 | 0 1 4 10 18 27 38 40 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -56 -59 | 0 1 4 10 18 27 38 40 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.4848
* POTE: ~2 = 1\1, ~3/2 = 697.481


{{Optimal ET sequence|legend=1| 12fghh, 31fgh, 43 }}
{{Optimal ET sequence|legend=1| 12fghh, 31fgh, 43 }}
Line 324: Line 356:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 | 0 1 4 10 18 27 7 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 | 0 1 4 10 18 27 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.6098
* POTE: ~2 = 1\1, ~3/2 = 697.376


{{Optimal ET sequence|legend=1| 12f, 31fg, 43g }}
{{Optimal ET sequence|legend=1| 12f, 31fg, 43g }}
Line 337: Line 371:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 -10 | 0 1 4 10 18 27 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 -7 -10 | 0 1 4 10 18 27 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.7012
* POTE: ~2 = 1\1, ~3/2 = 697.316


{{Optimal ET sequence|legend=1| 12f, 19effgh, 31fgh, 43gh }}
{{Optimal ET sequence|legend=1| 12f, 19effgh, 31fgh, 43gh }}
Line 350: Line 386:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 | 0 1 4 10 18 27 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.5384
* POTE: ~2 = 1\1, ~3/2 = 697.644


{{Optimal ET sequence|legend=1| 12f, 43 }}
{{Optimal ET sequence|legend=1| 12f, 43 }}
Line 363: Line 401:
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -39 12 9 | 0 1 4 10 18 27 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.5550
* POTE: ~2 = 1\1, ~3/2 = 697.715


{{Optimal ET sequence|legend=1| 12f, 43 }}
{{Optimal ET sequence|legend=1| 12f, 43 }}
Line 378: Line 418:
: mapping generators: ~2, ~26/15
: mapping generators: ~2, ~26/15


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6109
Optimal tunings:
* CTE: ~2 = 1\1, ~26/15 = 948.6109
* POTE: ~2 = 1\1, ~26/15 = 948.465


{{Optimal ET sequence|legend=1| 19e, 43, 62 }}
{{Optimal ET sequence|legend=1| 19e, 43, 62 }}
Line 391: Line 433:
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 | 0 2 8 20 36 11 33 }}


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173
Optimal tunings:
* CTE: ~2 = 1\1, ~26/15 = 948.6173
* POTE: ~2 = 1\1, ~26/15 = 948.477


{{Optimal ET sequence|legend=1| 19eg, 43, 62 }}
{{Optimal ET sequence|legend=1| 19eg, 43, 62 }}
Line 404: Line 448:
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}
Mapping: {{mapping| 1 0 -4 -13 -25 -5 -22 -25 | 0 2 8 20 36 11 33 37 }}


Optimal tuning (CTE): ~2 = 1\1, ~19/11 = 948.6088
Optimal tunings:
* CTE: ~2 = 1\1, ~19/11 = 948.6088
* POTE: ~2 = 1\1, ~19/11 = 948.473


{{Optimal ET sequence|legend=1| 19egh, 43, 62 }}
{{Optimal ET sequence|legend=1| 19egh, 43, 62 }}
Line 419: Line 465:
: mapping generators: ~55/39, ~3
: mapping generators: ~55/39, ~3


Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 697.1678
Optimal tunings:
* CTE: ~55/39 = 1\2, ~3/2 = 697.1678
* POTE: ~55/39 = 1\2, ~3/2 = 697.005


{{Optimal ET sequence|legend=1| 12f, 38deefff, 50eff, 62, 136b }}
{{Optimal ET sequence|legend=1| 12f, 38deefff, 50eff, 62, 136b }}
Line 432: Line 480:
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 | 0 1 4 10 18 21 1 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740
Optimal tunings:
* CTE: ~17/12 = 1\2, ~3/2 = 697.1740
* POTE: ~17/12 = 1\2, ~3/2 = 696.927


{{Optimal ET sequence|legend=1| 12f, 50eff, 62, 136bg }}
{{Optimal ET sequence|legend=1| 12f, 50eff, 62, 136bg }}
Line 445: Line 495:
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}
Mapping: {{mapping| 2 0 -8 -26 -50 -59 5 -1 | 0 1 4 10 18 21 1 3 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871
Optimal tunings:
* CTE: ~17/12 = 1\2, ~3/2 = 697.1871
* POTE: ~17/12 = 1\2, ~3/2 = 696.906


{{Optimal ET sequence|legend=1| 12f, 50eff, 62 }}
{{Optimal ET sequence|legend=1| 12f, 50eff, 62 }}
Line 464: Line 516:
: mapping generator: ~2, ~3
: mapping generator: ~2, ~3


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5311
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.5311
* POTE: ~2 = 1\1, ~3/2 = 696.434


Minimax tuning:  
Minimax tuning:  
Line 492: Line 546:
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3563
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.3563
* POTE: ~2 = 1\1, ~3/2 = 696.211


Minimax tuning:  
Minimax tuning:  
Line 513: Line 569:
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 | 0 1 4 10 -13 15 26 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.3508
* POTE: ~2 = 1\1, ~3/2 = 696.194


{{Optimal ET sequence|legend=1| 19g, 31, 50, 81, 131bd }}
{{Optimal ET sequence|legend=1| 19g, 31, 50, 81, 131bd }}
Line 526: Line 584:
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 -37 -40 | 0 1 4 10 -13 15 26 28 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.3471
* POTE: ~2 = 1\1, ~3/2 = 696.188


{{Optimal ET sequence|legend=1| 19gh, 31, 50, 81 }}
{{Optimal ET sequence|legend=1| 19gh, 31, 50, 81 }}
Line 539: Line 599:
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 | 0 1 4 10 -13 15 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.4388
* POTE: ~2 = 1\1, ~3/2 = 696.408


{{Optimal ET sequence|legend=1| 19, 31 }}
{{Optimal ET sequence|legend=1| 19, 31 }}
Line 552: Line 614:
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 12 9 | 0 1 4 10 -13 15 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.4838
* POTE: ~2 = 1\1, ~3/2 = 696.499


{{Optimal ET sequence|legend=1| 12ef, 19, 31 }}
{{Optimal ET sequence|legend=1| 12ef, 19, 31 }}
Line 565: Line 629:
Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2827
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.2827
* POTE: ~2 = 1\1, ~3/2 = 696.202


Minimax tuning:  
Minimax tuning:  
Line 582: Line 648:
Mapping: {{mapping| 1 0 -4 -13 24 10 12 | 0 1 4 10 -13 -4 -5 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 12 | 0 1 4 10 -13 -4 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.4069
* POTE: ~2 = 1\1, ~3/2 = 696.414


{{Optimal ET sequence|legend=1| 12e, 19 }}
{{Optimal ET sequence|legend=1| 12e, 19 }}
Line 595: Line 663:
Mapping: {{mapping| 1 0 -4 -13 24 10 12 9 | 0 1 4 10 -13 -4 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 12 9 | 0 1 4 10 -13 -4 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.4731
* POTE: ~2 = 1\1, ~3/2 = 696.497


{{Optimal ET sequence|legend=1| 12e, 19 }}
{{Optimal ET sequence|legend=1| 12e, 19 }}
Line 608: Line 678:
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 | 0 1 4 10 -13 -4 7 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 | 0 1 4 10 -13 -4 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.6614
* POTE: ~2 = 1\1, ~3/2 = 696.415


{{Optimal ET sequence|legend=1| 12e, 19g, 31fg }}
{{Optimal ET sequence|legend=1| 12e, 19g, 31fg }}
Line 621: Line 693:
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 -10 | 0 1 4 10 -13 -4 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 -7 -10 | 0 1 4 10 -13 -4 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 697.0160
* POTE: ~2 = 1\1, ~3/2 = 696.583


{{Optimal ET sequence|legend=1| 12e, 19gh, 31fgh }}
{{Optimal ET sequence|legend=1| 12e, 19gh, 31fgh }}
Line 636: Line 710:
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1527
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.1527
* POTE: ~2 = 1\1, ~3/2 = 696.250


Tuning ranges:  
Tuning ranges:  
Line 653: Line 729:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.0983
* POTE: ~2 = 1\1, ~3/2 = 696.146


{{Optimal ET sequence|legend=1| 7df, 12f, 19, 31e }}
{{Optimal ET sequence|legend=1| 7df, 12f, 19, 31e }}
Line 666: Line 744:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 | 0 1 4 10 6 15 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.2161
* POTE: ~2 = 1\1, ~3/2 = 696.575


{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
Line 679: Line 759:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 12 9 | 0 1 4 10 6 15 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.2774
* POTE: ~2 = 1\1, ~3/2 = 696.706


{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
Line 692: Line 774:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 | 0 1 4 10 6 15 7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 | 0 1 4 10 6 15 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.4501
* POTE: ~2 = 1\1, ~3/2 = 696.025


{{Optimal ET sequence|legend=1| 7dfg, 12f, 19g }}
{{Optimal ET sequence|legend=1| 7dfg, 12f, 19g }}
Line 705: Line 789:
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 -10 | 0 1 4 10 6 15 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 -7 -10 | 0 1 4 10 6 15 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7925
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.7925
* POTE: ~2 = 1\1, ~3/2 = 696.121


{{Optimal ET sequence|legend=1| 7dfgh, 12f, 19gh }}
{{Optimal ET sequence|legend=1| 7dfgh, 12f, 19gh }}
Line 718: Line 804:
Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 | 0 1 4 10 6 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.7897
* POTE: ~2 = 1\1, ~3/2 = 695.060


{{Optimal ET sequence|legend=1| 7d, 12, 19 }}
{{Optimal ET sequence|legend=1| 7d, 12, 19 }}
Line 731: Line 819:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 | 0 1 4 10 6 -4 -5 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.0114
* POTE: ~2 = 1\1, ~3/2 = 695.858


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 744: Line 834:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 | 0 1 4 10 6 -4 -5 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.1196
* POTE: ~2 = 1\1, ~3/2 = 696.131


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 757: Line 849:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 | 0 1 4 10 6 -4 -5 -3 -6 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 | 0 1 4 10 6 -4 -5 -3 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0585
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.0585
* POTE: ~2 = 1\1, ~3/2 = 696.044


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 770: Line 864:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 | 0 1 4 10 6 -4 -5 -3 -6 -2 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 | 0 1 4 10 6 -4 -5 -3 -6 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.9824
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.9824
* POTE: ~2 = 1\1, ~3/2 = 695.913


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 783: Line 879:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7980
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.7980
* POTE: ~2 = 1\1, ~3/2 = 695.750


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 796: Line 894:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6746
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.6746
* POTE: ~2 = 1\1, ~3/2 = 695.603


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 809: Line 909:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7239
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.7239
* POTE: ~2 = 1\1, ~3/2 = 695.696


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 822: Line 924:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7160
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.7160
* POTE: ~2 = 1\1, ~3/2 = 695.688


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 835: Line 939:
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 4 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 1 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 12 9 14 8 16 -9 18 7 4 | 0 1 4 10 6 -4 -5 -3 -6 -2 -7 9 -8 -1 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6849
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.6849
* POTE: ~2 = 1\1, ~3/2 = 695.676


{{Optimal ET sequence|legend=1| 12, 19 }}
{{Optimal ET sequence|legend=1| 12, 19 }}
Line 848: Line 954:
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 | 0 1 4 10 6 -4 7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 | 0 1 4 10 6 -4 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.4125
* POTE: ~2 = 1\1, ~3/2 = 695.358


{{Optimal ET sequence|legend=1| 7dg, 12, 19g }}
{{Optimal ET sequence|legend=1| 7dg, 12, 19g }}
Line 861: Line 969:
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 -10 | 0 1 4 10 6 -4 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 10 -7 -10 | 0 1 4 10 6 -4 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.9500
* POTE: ~2 = 1\1, ~3/2 = 695.725


{{Optimal ET sequence|legend=1| 7dgh, 12, 19gh }}
{{Optimal ET sequence|legend=1| 7dgh, 12, 19gh }}
Line 874: Line 984:
Mapping: {{mapping| 1 0 -4 -13 -6 -1 | 0 1 4 10 6 3 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -1 | 0 1 4 10 6 3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 695.6202
* POTE: ~2 = 1\1, ~3/2 = 697.254


{{Optimal ET sequence|legend=1| 7d, 12f, 19f }}
{{Optimal ET sequence|legend=1| 7d, 12f, 19f }}
Line 887: Line 999:
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 | 0 1 4 10 6 3 7 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 | 0 1 4 10 6 3 7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.2789
* POTE: ~2 = 1\1, ~3/2 = 697.586


{{Optimal ET sequence|legend=1| 7dg, 12f }}
{{Optimal ET sequence|legend=1| 7dg, 12f }}
Line 900: Line 1,014:
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 -10 | 0 1 4 10 6 3 7 9 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -1 -7 -10 | 0 1 4 10 6 3 7 9 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.8486
* POTE: ~2 = 1\1, ~3/2 = 698.118


{{Optimal ET sequence|legend=1| 7dgh, 12f }}
{{Optimal ET sequence|legend=1| 7dgh, 12f }}
Line 915: Line 1,031:
Mapping: {{mapping| 1 0 -4 -13 5 | 0 1 4 10 -1 }}
Mapping: {{mapping| 1 0 -4 -13 5 | 0 1 4 10 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.7022
* POTE: ~2 = 1\1, ~3/2 = 694.689


{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
Line 928: Line 1,046:
Mapping: {{mapping| 1 0 -4 -13 5 10 | 0 1 4 10 -1 -4 }}
Mapping: {{mapping| 1 0 -4 -13 5 10 | 0 1 4 10 -1 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 696.2408
* POTE: ~2 = 1\1, ~3/2 = 694.764


{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
{{Optimal ET sequence|legend=1| 7d, 12e, 19e }}
Line 945: Line 1,065:
: mapping generators: ~63/44, ~3
: mapping generators: ~63/44, ~3


Optimal tuning (CTE): ~63/44 = 1\2, ~3/2 = 696.5199
Optimal tunings:
* CTE: ~63/44 = 1\2, ~3/2 = 696.5199
* POTE: ~63/44 = 1\2, ~3/2 = 696.016


{{Optimal ET sequence|legend=1| 12, 26de, 38d, 50 }}
{{Optimal ET sequence|legend=1| 12, 26de, 38d, 50 }}
Line 958: Line 1,080:
Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}
Mapping: {{mapping| 2 0 -8 -26 -31 -40 | 0 1 4 10 12 15 }}


Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410
Optimal tunings:
* CTE: ~55/39 = 1\2, ~3/2 = 696.3410
* POTE: ~55/39 = 1\2, ~3/2 = 695.836


{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
Line 971: Line 1,095:
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 | 0 1 4 10 12 15 1 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526
Optimal tunings:
* CTE: ~17/12 = 1\2, ~3/2 = 696.3526
* POTE: ~17/12 = 1\2, ~3/2 = 695.783


{{Optimal ET sequence|legend=1| 12f, 38df, 50 }}
{{Optimal ET sequence|legend=1| 12f, 38df, 50 }}
Line 984: Line 1,110:
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}
Mapping: {{mapping| 2 0 -8 -26 -31 -40 5 -1 | 0 1 4 10 12 15 1 3 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3837
Optimal tunings:
* CTE: ~17/12 = 1\2, ~3/2 = 696.3837
* POTE: ~17/12 = 1\2, ~3/2 = 695.752


{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
Line 999: Line 1,127:
: mapping generators: ~2, ~11/10
: mapping generators: ~2, ~11/10


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 167.7074
* POTE: ~2 = 1\1, ~11/10 = 167.805


{{Optimal ET sequence|legend=1| 7d, 36d, 43, 50, 93 }}
{{Optimal ET sequence|legend=1| 7d, 36d, 43, 50, 93 }}
Line 1,012: Line 1,142:
Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}
Mapping: {{mapping| 1 2 4 7 5 3 | 0 -3 -12 -30 -11 5 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 167.7121
* POTE: ~2 = 1\1, ~11/10 = 167.790


{{Optimal ET sequence|legend=1| 7d, 43, 50, 93 }}
{{Optimal ET sequence|legend=1| 7d, 43, 50, 93 }}
Line 1,025: Line 1,157:
Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}
Mapping: {{mapping| 1 2 4 7 5 3 8 | 0 -3 -12 -30 -11 5 -28 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 167.7047
* POTE: ~2 = 1\1, ~11/10 = 167.786


{{Optimal ET sequence|legend=1| 7dg, 43, 50, 93 }}
{{Optimal ET sequence|legend=1| 7dg, 43, 50, 93 }}