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Meantone family: Difference between revisions

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Cents for octave fractions. Unify cents to 3 decimal places, which should be enough. Adopt template: Mapping. -redundant links
Line 21: Line 21:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 697.2143
* [[CTE]]: ~2 = 1200.000, ~3/2 = 697.214
* [[POTE]]: ~2 = 1\1, ~3/2 = 696.239
* [[POTE]]: ~2 = 1200.000, ~3/2 = 696.239


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 75: Line 75:
* [[Mothra]] → [[Gamelismic clan #Mothra|Gamelismic clan]]
* [[Mothra]] → [[Gamelismic clan #Mothra|Gamelismic clan]]
* [[Mohaha]] → [[Rastmic clan #Mohaha|Rastmic clan]]
* [[Mohaha]] → [[Rastmic clan #Mohaha|Rastmic clan]]
* [[No-sevens subgroup temperaments#Dequarter|Dequarter]] → [[No-sevens subgroup temperaments#Dequarter|No-sevens subgroup temperaments]]


The rest are considered below.
The rest are considered below.
Line 95: Line 94:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 696.9521
* [[CTE]]: ~2 = 1200.000, ~3/2 = 696.952
* [[POTE]]: ~2 = 1\1, ~3/2 = 696.495
* [[POTE]]: ~2 = 1200.000, ~3/2 = 696.495


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{monzo| 0 0 1/4 }} (1/4-comma)
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~3/2 = {{monzo| 0 0 1/4 }} (1/4-comma)
: [[projection map]]: {{monzo list| 1 0 0 0 | 1 0 1/4 0 | 0 0 1 0 | -3 0 5/2 0 }}
: [[projection map]]: {{monzo list| 1 0 0 0 | 1 0 1/4 0 | 0 0 1 0 | -3 0 5/2 0 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 126: Line 125:
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}


{{Multival|legend=1| 1 4 10 18 4 13 25 12 28 16 }}
Wedgie: {{multival| 1 4 10 18 4 13 25 12 28 16 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.1676
* CTE: ~2 = 1200.000, ~3/2 = 697.168
* POTE: ~2 = 1\1, ~3/2 = 696.967
* POTE: ~2 = 1200.000, ~3/2 = 696.967


Minimax tuning:  
Minimax tuning:  
Line 143: Line 142:
Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.


{{Optimal ET sequence|legend=1| 12, 19e, 31, 105, 136b }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19e, 31, 105, 136b }}


Badness: 0.017027
Badness: 0.017027
Line 158: Line 157:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.8552
* CTE: ~2 = 1200.000, ~3/2 = 696.855
* POTE: ~2 = 1\1, ~3/2 = 696.642
* POTE: ~2 = 1200.000, ~3/2 = 696.642


Minimax tuning:  
Minimax tuning:  
Line 165: Line 164:
: eigenmonzo (unchanged-interval) basis: 2.11/9
: eigenmonzo (unchanged-interval) basis: 2.11/9


{{Optimal ET sequence|legend=1| 12f, 19e, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19e, 31 }}


Badness: 0.018048
Badness: 0.018048
Line 179: Line 178:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.6486
* CTE: ~2 = 1200.000, ~3/2 = 696.649
* POTE: ~2 = 1\1, ~3/2 = 696.377
* POTE: ~2 = 1200.000, ~3/2 = 696.377


{{Optimal ET sequence|legend=1| 12fg, 19eg, 31, 50e }}
Optimal ET sequence: {{Optimal ET sequence| 12fg, 19eg, 31, 50e }}


Badness: 0.019037
Badness: 0.019037
Line 194: Line 193:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.5551
* CTE: ~2 = 1200.000, ~3/2 = 696.555
* POTE: ~2 = 1\1, ~3/2 = 696.273
* POTE: ~2 = 1200.000, ~3/2 = 696.273


{{Optimal ET sequence|legend=1| 12fghh, 19egh, 31, 50e }}
Optimal ET sequence: {{Optimal ET sequence| 12fghh, 19egh, 31, 50e }}


Badness: 0.017846
Badness: 0.017846
Line 211: Line 210:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.0360
* CTE: ~2 = 1200.000, ~3/2 = 697.036
* POTE: ~2 = 1\1, ~3/2 = 696.448
* POTE: ~2 = 1200.000, ~3/2 = 696.448


{{Optimal ET sequence|legend=1| 12f, 19eg, 31g }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19eg, 31g }}


Badness: 0.019433
Badness: 0.019433
Line 226: Line 225:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.2161
* CTE: ~2 = 1200.000, ~3/2 = 697.216
* POTE: ~2 = 1\1, ~3/2 = 696.394
* POTE: ~2 = 1200.000, ~3/2 = 696.394


{{Optimal ET sequence|legend=1| 12f, 19egh, 31gh }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19egh, 31gh }}


Badness: 0.017437
Badness: 0.017437
Line 243: Line 242:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.9080
* CTE: ~2 = 1200.000, ~3/2 = 696.908
* POTE: ~2 = 1\1, ~3/2 = 697.003
* POTE: ~2 = 1200.000, ~3/2 = 697.003


{{Optimal ET sequence|legend=1| 12f, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 31 }}


Badness: 0.019982
Badness: 0.019982
Line 258: Line 257:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.9308
* CTE: ~2 = 1200.000, ~3/2 = 696.931
* POTE: ~2 = 1\1, ~3/2 = 697.140
* POTE: ~2 = 1200.000, ~3/2 = 697.140


{{Optimal ET sequence|legend=1| 12f, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 31 }}


Badness: 0.018047
Badness: 0.018047
Line 275: Line 274:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.2582
* CTE: ~2 = 1200.000, ~3/2 = 697.258
* POTE: ~2 = 1\1, ~3/2 = 697.264
* POTE: ~2 = 1200.000, ~3/2 = 697.264


Minimax tuning:  
Minimax tuning:  
Line 286: Line 285:
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)


{{Optimal ET sequence|legend=1| 12, 31, 43, 74 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 31, 43, 74 }}


Badness: 0.025899
Badness: 0.025899
Line 298: Line 297:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.2996
* CTE: ~2 = 1200.000, ~3/2 = 697.300
* POTE: ~2 = 1\1, ~3/2 = 697.335
* POTE: ~2 = 1200.000, ~3/2 = 697.335


{{Optimal ET sequence|legend=1| 12, 31, 43, 74g }}
Optimal ET sequence: {{Optimal ET sequence| 12, 31, 43, 74g }}


Badness: 0.020889
Badness: 0.020889
Line 313: Line 312:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.3271
* CTE: ~2 = 1200.000, ~3/2 = 697.327
* POTE: ~2 = 1\1, ~3/2 = 697.380
* POTE: ~2 = 1200.000, ~3/2 = 697.380


{{Optimal ET sequence|legend=1| 12, 31, 43, 74gh }}
Optimal ET sequence: {{Optimal ET sequence| 12, 31, 43, 74gh }}


Badness: 0.017611
Badness: 0.017611
Line 330: Line 329:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.5155
* CTE: ~2 = 1200.000, ~3/2 = 697.516
* POTE: ~2 = 1\1, ~3/2 = 697.529
* POTE: ~2 = 1200.000, ~3/2 = 697.529


Minimax tuning:  
Minimax tuning:  
Line 337: Line 336:
: eigenmonzo (unchanged-interval) basis: 2.13/9
: eigenmonzo (unchanged-interval) basis: 2.13/9


{{Optimal ET sequence|legend=1| 12f, 31f, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 31f, 43 }}


Badness: 0.026421
Badness: 0.026421
Line 349: Line 348:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.5076
* CTE: ~2 = 1200.000, ~3/2 = 697.508
* POTE: ~2 = 1\1, ~3/2 = 697.514
* POTE: ~2 = 1200.000, ~3/2 = 697.514


{{Optimal ET sequence|legend=1| 12fg, 31fg, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 12fg, 31fg, 43 }}


Badness: 0.027706
Badness: 0.027706
Line 364: Line 363:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.4848
* CTE: ~2 = 1200.000, ~3/2 = 697.485
* POTE: ~2 = 1\1, ~3/2 = 697.481
* POTE: ~2 = 1200.000, ~3/2 = 697.481


{{Optimal ET sequence|legend=1| 12fghh, 31fgh, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 12fghh, 31fgh, 43 }}


Badness: 0.025315
Badness: 0.025315
Line 379: Line 378:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.6098
* CTE: ~2 = 1200.000, ~3/2 = 697.610
* POTE: ~2 = 1\1, ~3/2 = 697.376
* POTE: ~2 = 1200.000, ~3/2 = 697.376


{{Optimal ET sequence|legend=1| 12f, 31fg, 43g }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 31fg, 43g }}


Badness: 0.027518
Badness: 0.027518
Line 394: Line 393:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.7012
* CTE: ~2 = 1200.000, ~3/2 = 697.701
* POTE: ~2 = 1\1, ~3/2 = 697.316
* POTE: ~2 = 1200.000, ~3/2 = 697.316


{{Optimal ET sequence|legend=1| 12f, 19effgh, 31fgh, 43gh }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19effgh, 31fgh, 43gh }}


Badness: 0.023613
Badness: 0.023613
Line 409: Line 408:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.5384
* CTE: ~2 = 1200.000, ~3/2 = 697.538
* POTE: ~2 = 1\1, ~3/2 = 697.644
* POTE: ~2 = 1200.000, ~3/2 = 697.644


{{Optimal ET sequence|legend=1| 12f, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 43 }}


Badness: 0.023881
Badness: 0.023881
Line 424: Line 423:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.5550
* CTE: ~2 = 1200.000, ~3/2 = 697.555
* POTE: ~2 = 1\1, ~3/2 = 697.715
* POTE: ~2 = 1200.000, ~3/2 = 697.715


{{Optimal ET sequence|legend=1| 12f, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 43 }}


Badness: 0.020540
Badness: 0.020540
Line 441: Line 440:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~26/15 = 948.6109
* CTE: ~2 = 1200.000, ~26/15 = 948.611
* POTE: ~2 = 1\1, ~26/15 = 948.465
* POTE: ~2 = 1200.000, ~26/15 = 948.465


{{Optimal ET sequence|legend=1| 19e, 43, 62 }}
Optimal ET sequence: {{Optimal ET sequence| 19e, 43, 62 }}


Badness: 0.031433
Badness: 0.031433
Line 456: Line 455:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~26/15 = 948.6173
* CTE: ~2 = 1200.000, ~26/15 = 948.617
* POTE: ~2 = 1\1, ~26/15 = 948.477
* POTE: ~2 = 1200.000, ~26/15 = 948.477


{{Optimal ET sequence|legend=1| 19eg, 43, 62 }}
Optimal ET sequence: {{Optimal ET sequence| 19eg, 43, 62 }}


Badness: 0.023380
Badness: 0.023380
Line 471: Line 470:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~19/11 = 948.6088
* CTE: ~2 = 1200.000, ~19/11 = 948.609
* POTE: ~2 = 1\1, ~19/11 = 948.473
* POTE: ~2 = 1200.000, ~19/11 = 948.473


{{Optimal ET sequence|legend=1| 19egh, 43, 62 }}
Optimal ET sequence: {{Optimal ET sequence| 19egh, 43, 62 }}


Badness: 0.018952
Badness: 0.018952
Line 488: Line 487:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 1\2, ~3/2 = 697.1678
* CTE: ~55/39 = 600.000, ~3/2 = 697.168
* POTE: ~55/39 = 1\2, ~3/2 = 697.005
* POTE: ~55/39 = 600.000, ~3/2 = 697.005


{{Optimal ET sequence|legend=1| 12f, 38deefff, 50eff, 62, 136b }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 38deefff, 50eff, 62, 136b }}


Badness: 0.040668
Badness: 0.040668
Line 503: Line 502:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~3/2 = 697.1740
* CTE: ~17/12 = 600.000, ~3/2 = 697.174
* POTE: ~17/12 = 1\2, ~3/2 = 696.927
* POTE: ~17/12 = 600.000, ~3/2 = 696.927


{{Optimal ET sequence|legend=1| 12f, 50eff, 62, 136bg }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 50eff, 62, 136bg }}


Badness: 0.031491
Badness: 0.031491
Line 518: Line 517:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~3/2 = 697.1871
* CTE: ~17/12 = 600.000, ~3/2 = 697.187
* POTE: ~17/12 = 1\2, ~3/2 = 696.906
* POTE: ~17/12 = 600.000, ~3/2 = 696.906


{{Optimal ET sequence|legend=1| 12f, 50eff, 62 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 50eff, 62 }}


Badness: 0.024206
Badness: 0.024206
Line 541: Line 540:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.5311
* CTE: ~2 = 1200.000, ~3/2 = 696.531
* POTE: ~2 = 1\1, ~3/2 = 696.434
* POTE: ~2 = 1200.000, ~3/2 = 696.434


Minimax tuning:  
Minimax tuning:  
Line 555: Line 554:
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.


{{Optimal ET sequence|legend=1| 12e, 19, 31, 81, 112b }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19, 31, 81, 112b }}


Badness: 0.021543
Badness: 0.021543
Line 570: Line 569:
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 }}


{{Multival|legend=1| 1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100 }}
Wedgie: {{multival| 1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.3563
* CTE: ~2 = 1200.000, ~3/2 = 696.356
* POTE: ~2 = 1\1, ~3/2 = 696.211
* POTE: ~2 = 1200.000, ~3/2 = 696.211


Minimax tuning:  
Minimax tuning:  
Line 584: Line 583:
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955] (1/2-comma to Pyth.)


{{Optimal ET sequence|legend=1| 19, 31, 50, 81 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 31, 50, 81 }}


Badness: 0.020883
Badness: 0.020883
Line 596: Line 595:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.3508
* CTE: ~2 = 1200.000, ~3/2 = 696.351
* POTE: ~2 = 1\1, ~3/2 = 696.194
* POTE: ~2 = 1200.000, ~3/2 = 696.194


{{Optimal ET sequence|legend=1| 19g, 31, 50, 81, 131bd }}
Optimal ET sequence: {{Optimal ET sequence| 19g, 31, 50, 81, 131bd }}


Badness: 0.019953
Badness: 0.019953
Line 611: Line 610:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.3471
* CTE: ~2 = 1200.000, ~3/2 = 696.347
* POTE: ~2 = 1\1, ~3/2 = 696.188
* POTE: ~2 = 1200.000, ~3/2 = 696.188


{{Optimal ET sequence|legend=1| 19gh, 31, 50, 81 }}
Optimal ET sequence: {{Optimal ET sequence| 19gh, 31, 50, 81 }}


Badness: 0.017791
Badness: 0.017791
Line 626: Line 625:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.4388
* CTE: ~2 = 1200.000, ~3/2 = 696.439
* POTE: ~2 = 1\1, ~3/2 = 696.408
* POTE: ~2 = 1200.000, ~3/2 = 696.408


{{Optimal ET sequence|legend=1| 19, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 31 }}


Badness: 0.022870
Badness: 0.022870
Line 641: Line 640:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.4838
* CTE: ~2 = 1200.000, ~3/2 = 696.484
* POTE: ~2 = 1\1, ~3/2 = 696.499
* POTE: ~2 = 1200.000, ~3/2 = 696.499


{{Optimal ET sequence|legend=1| 12ef, 19, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 12ef, 19, 31 }}


Badness: 0.020488
Badness: 0.020488
Line 658: Line 657:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.2827
* CTE: ~2 = 1200.000, ~3/2 = 696.283
* POTE: ~2 = 1\1, ~3/2 = 696.202
* POTE: ~2 = 1200.000, ~3/2 = 696.202


Minimax tuning:  
Minimax tuning:  
Line 665: Line 664:
: Eigenmonzo (unchanged-interval) basis: 2.11
: Eigenmonzo (unchanged-interval) basis: 2.11


{{Optimal ET sequence|legend=1| 12e, 19, 31f }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19, 31f }}


Badness: 0.027666
Badness: 0.027666
Line 677: Line 676:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.4069
* CTE: ~2 = 1200.000, ~3/2 = 696.407
* POTE: ~2 = 1\1, ~3/2 = 696.414
* POTE: ~2 = 1200.000, ~3/2 = 696.414


{{Optimal ET sequence|legend=1| 12e, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19 }}


Badness: 0.026836
Badness: 0.026836
Line 692: Line 691:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.4731
* CTE: ~2 = 1200.000, ~3/2 = 696.473
* POTE: ~2 = 1\1, ~3/2 = 696.497
* POTE: ~2 = 1200.000, ~3/2 = 696.497


{{Optimal ET sequence|legend=1| 12e, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19 }}


Badness: 0.023540
Badness: 0.023540
Line 707: Line 706:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.6614
* CTE: ~2 = 1200.000, ~3/2 = 696.661
* POTE: ~2 = 1\1, ~3/2 = 696.415
* POTE: ~2 = 1200.000, ~3/2 = 696.415


{{Optimal ET sequence|legend=1| 12e, 19g, 31fg }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19g, 31fg }}


Badness: 0.026094
Badness: 0.026094
Line 722: Line 721:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 697.0160
* CTE: ~2 = 1200.000, ~3/2 = 697.016
* POTE: ~2 = 1\1, ~3/2 = 696.583
* POTE: ~2 = 1200.000, ~3/2 = 696.583


{{Optimal ET sequence|legend=1| 12e, 19gh, 31fgh }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 19gh, 31fgh }}


Badness: 0.023104
Badness: 0.023104
Line 741: Line 740:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.1527
* CTE: ~2 = 1200.000, ~3/2 = 696.153
* POTE: ~2 = 1\1, ~3/2 = 696.250
* POTE: ~2 = 1200.000, ~3/2 = 696.250


Tuning ranges:  
Tuning ranges:  
Line 748: Line 747:
* 11-odd-limit diamond tradeoff: ~3/2 = [682.502, 704.377]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.502, 704.377]


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


Badness: 0.021423
Badness: 0.021423
Line 762: Line 761:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.0983
* CTE: ~2 = 1200.000, ~3/2 = 696.098
* POTE: ~2 = 1\1, ~3/2 = 696.146
* POTE: ~2 = 1200.000, ~3/2 = 696.146


{{Optimal ET sequence|legend=1| 7df, 12f, 19, 31e }}
Optimal ET sequence: {{Optimal ET sequence| 7df, 12f, 19, 31e }}


Badness: 0.021182
Badness: 0.021182
Line 777: Line 776:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.2161
* CTE: ~2 = 1200.000, ~3/2 = 696.216
* POTE: ~2 = 1\1, ~3/2 = 696.575
* POTE: ~2 = 1200.000, ~3/2 = 696.575


{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19, 31e }}


Badness: 0.022980
Badness: 0.022980
Line 792: Line 791:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.2774
* CTE: ~2 = 1200.000, ~3/2 = 696.277
* POTE: ~2 = 1\1, ~3/2 = 696.706
* POTE: ~2 = 1200.000, ~3/2 = 696.706


{{Optimal ET sequence|legend=1| 12f, 19, 31e }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 19, 31e }}


Badness: 0.020293
Badness: 0.020293
Line 807: Line 806:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.4501
* CTE: ~2 = 1200.000, ~3/2 = 696.450
* POTE: ~2 = 1\1, ~3/2 = 696.025
* POTE: ~2 = 1200.000, ~3/2 = 696.025


{{Optimal ET sequence|legend=1| 7dfg, 12f, 19g }}
Optimal ET sequence: {{Optimal ET sequence| 7dfg, 12f, 19g }}


Badness: 0.020171
Badness: 0.020171
Line 822: Line 821:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.7925
* CTE: ~2 = 1200.000, ~3/2 = 696.793
* POTE: ~2 = 1\1, ~3/2 = 696.121
* POTE: ~2 = 1200.000, ~3/2 = 696.121


{{Optimal ET sequence|legend=1| 7dfgh, 12f, 19gh }}
Optimal ET sequence: {{Optimal ET sequence| 7dfgh, 12f, 19gh }}


Badness: 0.018045
Badness: 0.018045
Line 837: Line 836:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.7897
* CTE: ~2 = 1200.000, ~3/2 = 695.790
* POTE: ~2 = 1\1, ~3/2 = 695.060
* POTE: ~2 = 1200.000, ~3/2 = 695.060


{{Optimal ET sequence|legend=1| 7d, 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 12, 19 }}


Badness: 0.024763
Badness: 0.024763
Line 852: Line 851:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.0114
* CTE: ~2 = 1200.000, ~3/2 = 696.011
* POTE: ~2 = 1\1, ~3/2 = 695.858
* POTE: ~2 = 1200.000, ~3/2 = 695.858


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.025535
Badness: 0.025535
Line 867: Line 866:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.1196
* CTE: ~2 = 1200.000, ~3/2 = 696.120
* POTE: ~2 = 1\1, ~3/2 = 696.131
* POTE: ~2 = 1200.000, ~3/2 = 696.131


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.022302
Badness: 0.022302
Line 882: Line 881:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.0585
* CTE: ~2 = 1200.000, ~3/2 = 696.059
* POTE: ~2 = 1\1, ~3/2 = 696.044
* POTE: ~2 = 1200.000, ~3/2 = 696.044


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.020139
Badness: 0.020139
Line 897: Line 896:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.9824
* CTE: ~2 = 1200.000, ~3/2 = 695.982
* POTE: ~2 = 1\1, ~3/2 = 695.913
* POTE: ~2 = 1200.000, ~3/2 = 695.913


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.018168
Badness: 0.018168
Line 912: Line 911:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.7980
* CTE: ~2 = 1200.000, ~3/2 = 695.798
* POTE: ~2 = 1\1, ~3/2 = 695.750
* POTE: ~2 = 1200.000, ~3/2 = 695.750


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.017069
Badness: 0.017069
Line 927: Line 926:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.6746
* CTE: ~2 = 1200.000, ~3/2 = 695.675
* POTE: ~2 = 1\1, ~3/2 = 695.603
* POTE: ~2 = 1200.000, ~3/2 = 695.603


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.016129
Badness: 0.016129
Line 942: Line 941:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.7239
* CTE: ~2 = 1200.000, ~3/2 = 695.724
* POTE: ~2 = 1\1, ~3/2 = 695.696
* POTE: ~2 = 1200.000, ~3/2 = 695.696


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.015356
Badness: 0.015356
Line 957: Line 956:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.7160
* CTE: ~2 = 1200.000, ~3/2 = 695.716
* POTE: ~2 = 1\1, ~3/2 = 695.688
* POTE: ~2 = 1200.000, ~3/2 = 695.688


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.013906
Badness: 0.013906
Line 972: Line 971:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.6849
* CTE: ~2 = 1200.000, ~3/2 = 695.685
* POTE: ~2 = 1\1, ~3/2 = 695.676
* POTE: ~2 = 1200.000, ~3/2 = 695.676


{{Optimal ET sequence|legend=1| 12, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 19 }}


Badness: 0.013818
Badness: 0.013818
Line 987: Line 986:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.4125
* CTE: ~2 = 1200.000, ~3/2 = 696.412
* POTE: ~2 = 1\1, ~3/2 = 695.358
* POTE: ~2 = 1200.000, ~3/2 = 695.358


{{Optimal ET sequence|legend=1| 7dg, 12, 19g }}
Optimal ET sequence: {{Optimal ET sequence| 7dg, 12, 19g }}


Badness: 0.022099
Badness: 0.022099
Line 1,002: Line 1,001:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.9500
* CTE: ~2 = 1200.000, ~3/2 = 696.950
* POTE: ~2 = 1\1, ~3/2 = 695.725
* POTE: ~2 = 1200.000, ~3/2 = 695.725


{{Optimal ET sequence|legend=1| 7dgh, 12, 19gh }}
Optimal ET sequence: {{Optimal ET sequence| 7dgh, 12, 19gh }}


Badness: 0.019904
Badness: 0.019904
Line 1,017: Line 1,016:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.6202
* CTE: ~2 = 1200.000, ~3/2 = 695.620
* POTE: ~2 = 1\1, ~3/2 = 697.254
* POTE: ~2 = 1200.000, ~3/2 = 697.254


{{Optimal ET sequence|legend=1| 7d, 12f, 19f }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 12f, 19f }}


Badness: 0.024243
Badness: 0.024243
Line 1,032: Line 1,031:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.2789
* CTE: ~2 = 1200.000, ~3/2 = 696.279
* POTE: ~2 = 1\1, ~3/2 = 697.586
* POTE: ~2 = 1200.000, ~3/2 = 697.586


{{Optimal ET sequence|legend=1| 7dg, 12f }}
Optimal ET sequence: {{Optimal ET sequence| 7dg, 12f }}


Badness: 0.021400
Badness: 0.021400
Line 1,047: Line 1,046:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.8486
* CTE: ~2 = 1200.000, ~3/2 = 696.849
* POTE: ~2 = 1\1, ~3/2 = 698.118
* POTE: ~2 = 1200.000, ~3/2 = 698.118


{{Optimal ET sequence|legend=1| 7dgh, 12f }}
Optimal ET sequence: {{Optimal ET sequence| 7dgh, 12f }}


Badness: 0.018996
Badness: 0.018996
Line 1,064: Line 1,063:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.7022
* CTE: ~2 = 1200.000, ~3/2 = 696.702
* POTE: ~2 = 1\1, ~3/2 = 694.689
* POTE: ~2 = 1200.000, ~3/2 = 694.689


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


Badness: 0.031539
Badness: 0.031539
Line 1,079: Line 1,078:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.2408
* CTE: ~2 = 1200.000, ~3/2 = 696.241
* POTE: ~2 = 1\1, ~3/2 = 694.764
* POTE: ~2 = 1200.000, ~3/2 = 694.764


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


Badness: 0.026288
Badness: 0.026288
Line 1,098: Line 1,097:


Optimal tunings:  
Optimal tunings:  
* CTE: ~63/44 = 1\2, ~3/2 = 696.5199
* CTE: ~63/44 = 600.000, ~3/2 = 696.520
* POTE: ~63/44 = 1\2, ~3/2 = 696.016
* POTE: ~63/44 = 600.000, ~3/2 = 696.016


{{Optimal ET sequence|legend=1| 12, 26de, 38d, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 26de, 38d, 50 }}


Badness: 0.038122
Badness: 0.038122
Line 1,113: Line 1,112:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 1\2, ~3/2 = 696.3410
* CTE: ~55/39 = 600.000, ~3/2 = 696.341
* POTE: ~55/39 = 1\2, ~3/2 = 695.836
* POTE: ~55/39 = 600.000, ~3/2 = 695.836


{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 26deff, 38df, 50 }}


Badness: 0.028817
Badness: 0.028817
Line 1,128: Line 1,127:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~3/2 = 696.3526
* CTE: ~17/12 = 600.000, ~3/2 = 696.353
* POTE: ~17/12 = 1\2, ~3/2 = 695.783
* POTE: ~17/12 = 600.000, ~3/2 = 695.783


{{Optimal ET sequence|legend=1| 12f, 38df, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 38df, 50 }}


Badness: 0.022666
Badness: 0.022666
Line 1,143: Line 1,142:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 1\2, ~3/2 = 696.3837
* CTE: ~17/12 = 600.000, ~3/2 = 696.384
* POTE: ~17/12 = 1\2, ~3/2 = 695.752
* POTE: ~17/12 = 600.000, ~3/2 = 695.752


{{Optimal ET sequence|legend=1| 12f, 26deff, 38df, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 26deff, 38df, 50 }}


Badness: 0.017785
Badness: 0.017785
Line 1,160: Line 1,159:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 167.7074
* CTE: ~2 = 1200.000, ~11/10 = 167.707
* POTE: ~2 = 1\1, ~11/10 = 167.805
* POTE: ~2 = 1200.000, ~11/10 = 167.805


{{Optimal ET sequence|legend=1| 7d, 36d, 43, 50, 93 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 36d, 43, 50, 93 }}


Badness: 0.050729
Badness: 0.050729
Line 1,175: Line 1,174:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 167.7121
* CTE: ~2 = 1200.000, ~11/10 = 167.712
* POTE: ~2 = 1\1, ~11/10 = 167.790
* POTE: ~2 = 1200.000, ~11/10 = 167.790


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


Badness: 0.035445
Badness: 0.035445
Line 1,190: Line 1,189:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 167.7047
* CTE: ~2 = 1200.000, ~11/10 = 167.705
* POTE: ~2 = 1\1, ~11/10 = 167.786
* POTE: ~2 = 1200.000, ~11/10 = 167.786


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


Badness: 0.025221
Badness: 0.025221
Line 1,211: Line 1,210:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 693.5520
* [[CTE]]: ~2 = 1200.000, ~3/2 = 693.552
* [[POTE]]: ~2 = 1\1, ~3/2 = 693.779
* [[POTE]]: ~2 = 1200.000, ~3/2 = 693.779


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,241: Line 1,240:


Optimal tuning:  
Optimal tuning:  
* CTE: ~2 = 1\1, ~3/2 = 693.2511
* CTE: ~2 = 1200.000, ~3/2 = 693.251
* POTE: ~2 = 1\1, ~3/2 = 693.126
* POTE: ~2 = 1200.000, ~3/2 = 693.126


Tuning ranges:  
Tuning ranges:  
Line 1,248: Line 1,247:
* 11-odd-limit diamond tradeoff: ~3/2 = [682.502, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.502, 701.955]


{{Optimal ET sequence|legend=1| 7, 19, 26, 45, 71bc, 116bcde }}
Optimal ET sequence: {{Optimal ET sequence| 7, 19, 26, 45, 71bc, 116bcde }}


Badness: 0.033839
Badness: 0.033839
Line 1,260: Line 1,259:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 693.0293
* CTE: ~2 = 1200.000, ~3/2 = 693.029
* POTE: ~2 = 1\1, ~3/2 = 693.058
* POTE: ~2 = 1200.000, ~3/2 = 693.058


Tuning ranges:  
Tuning ranges:  
Line 1,267: Line 1,266:
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.502, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.502, 701.955]


{{Optimal ET sequence|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }}
Optimal ET sequence: {{Optimal ET sequence| 7, 19, 26, 45f, 71bcf, 116bcdef }}


Badness: 0.022260
Badness: 0.022260
Line 1,283: Line 1,282:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 692.6984
* [[CTE]]: ~2 = 1200.000, ~3/2 = 692.698
* [[CWE]]: ~2 = 1\1, ~3/2 = 692.0479
* [[CWE]]: ~2 = 1200.000, ~3/2 = 692.0479


{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
Line 1,301: Line 1,300:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 692.642
* [[CTE]]: ~2 = 1200.000, ~3/2 = 692.642
* [[CWE]]: ~2 = 1\1, ~3/2 = 692.042
* [[CWE]]: ~2 = 1200.000, ~3/2 = 692.042


{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 19d, 26, 59bcd, 85bccd }}


'''Music'''
'''Music'''
Line 1,326: Line 1,325:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 699.622
* [[CTE]]: ~2 = 1200.000, ~3/2 = 699.622
* [[POTE]]: ~2 = 1\1, ~3/2 = 701.573
* [[POTE]]: ~2 = 1200.000, ~3/2 = 701.573


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 1,350: Line 1,349:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 703.334
* CTE: ~2 = 1200.000, ~3/2 = 703.334
* POTE: ~2 = 1\1, ~3/2 = 703.254
* POTE: ~2 = 1200.000, ~3/2 = 703.254


Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17c, 29cde }}
Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17c, 29cde }}
Line 1,365: Line 1,364:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.847
* CTE: ~2 = 1200.000, ~3/2 = 704.847
* POTE: ~2 = 1\1, ~3/2 = 703.636
* POTE: ~2 = 1200.000, ~3/2 = 703.636


Tuning ranges:  
Tuning ranges:  
Line 1,384: Line 1,383:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.034
* CTE: ~2 = 1200.000, ~3/2 = 704.034
* POTE: ~2 = 1\1, ~3/2 = 704.905
* POTE: ~2 = 1200.000, ~3/2 = 704.905


Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17c, 46cde }}
Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17c, 46cde }}
Line 1,399: Line 1,398:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.240
* CTE: ~2 = 1200.000, ~3/2 = 696.240
* POTE: ~2 = 1\1, ~3/2 = 698.776
* POTE: ~2 = 1200.000, ~3/2 = 698.776


Optimal ET sequence: {{Optimal ET sequence| 5e, 7, 12, 19d, 43de }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 7, 12, 19d, 43de }}
Line 1,414: Line 1,413:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.315
* CTE: ~2 = 1200.000, ~3/2 = 695.315
* POTE: ~2 = 1\1, ~3/2 = 695.762
* POTE: ~2 = 1200.000, ~3/2 = 695.762


Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}
Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}
Line 1,429: Line 1,428:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.894
* CTE: ~2 = 1200.000, ~3/2 = 695.894
* POTE:  ~2 = 1\1, ~3/2 = 696.115
* POTE:  ~2 = 1200.000, ~3/2 = 696.115


Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}
Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}
Line 1,444: Line 1,443:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.139
* CTE: ~2 = 1200.000, ~3/2 = 696.139
* POTE: ~2 = 1\1, ~3/2 = 696.217
* POTE: ~2 = 1200.000, ~3/2 = 696.217


Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}
Optimal ET sequence: {{Optimal ET sequence| 5ef, 7, 12, 19d, 31def }}
Line 1,459: Line 1,458:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 694.840
* CTE: ~2 = 1200.000, ~3/2 = 694.840
* POTE: ~2 = 1\1, ~3/2 = 698.544
* POTE: ~2 = 1200.000, ~3/2 = 698.544


Optimal ET sequence: {{Optimal ET sequence| 5e, 7, 12f, 19df }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 7, 12f, 19df }}
Line 1,474: Line 1,473:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 703.268
* CTE: ~2 = 1200.000, ~3/2 = 703.268
* POTE: ~2 = 1\1, ~3/2 = 705.004
* POTE: ~2 = 1200.000, ~3/2 = 705.004


Optimal ET sequence: {{Optimal ET sequence| 5e, 12e, 17c, 46cd }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 12e, 17c, 46cd }}
Line 1,489: Line 1,488:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 703.719
* CTE: ~2 = 1200.000, ~3/2 = 703.719
* POTE: ~2 = 1\1, ~3/2 = 705.496
* POTE: ~2 = 1200.000, ~3/2 = 705.496


Optimal ET sequence: {{Optimal ET sequence| 5e, 12e, 17c }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 12e, 17c }}
Line 1,504: Line 1,503:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 698.546
* CTE: ~2 = 1200.000, ~3/2 = 698.546
* POTE: ~2 = 1\1, ~3/2 = 698.491
* POTE: ~2 = 1200.000, ~3/2 = 698.491


Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12e }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12e }}
Line 1,519: Line 1,518:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 695.929
* CTE: ~2 = 1200.000, ~3/2 = 695.929
* POTE: ~2 = 1\1, ~3/2 = 696.743
* POTE: ~2 = 1200.000, ~3/2 = 696.743


Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}
Line 1,534: Line 1,533:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.683
* CTE: ~2 = 1200.000, ~3/2 = 696.683
* POTE: ~2 = 1\1, ~3/2 = 696.978
* POTE: ~2 = 1200.000, ~3/2 = 696.978


Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}
Line 1,549: Line 1,548:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 696.996
* CTE: ~2 = 1200.000, ~3/2 = 696.996
* POTE: ~2 = 1\1, ~3/2 = 697.068
* POTE: ~2 = 1200.000, ~3/2 = 697.068


Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7, 12ef, 19def }}
Line 1,568: Line 1,567:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 703.732
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.732
* [[POTE]]: ~2 = 1\1, ~3/2 = 700.140
* [[POTE]]: ~2 = 1200.000, ~3/2 = 700.140


{{Optimal ET sequence|legend=1| 5, 7d, 12d }}
{{Optimal ET sequence|legend=1| 5, 7d, 12d }}
Line 1,583: Line 1,582:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 702.730
* CTE: ~2 = 1200.000, ~3/2 = 702.730
* POTE: ~2 = 1\1, ~3/2 = 696.615
* POTE: ~2 = 1200.000, ~3/2 = 696.615


Optimal ET sequence: {{Optimal ET sequence| 5, 7d, 12de }}
Optimal ET sequence: {{Optimal ET sequence| 5, 7d, 12de }}
Line 1,598: Line 1,597:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 703.811
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.811
* [[POTE]]: ~2 = 1\1, ~3/2 = 704.889
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.889


{{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }}
{{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }}
Line 1,613: Line 1,612:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.016
* CTE: ~2 = 1200.000, ~3/2 = 704.016
* POTE: ~2 = 1\1, ~3/2 = 705.096
* POTE: ~2 = 1200.000, ~3/2 = 705.096


Optimal ET sequence: {{Optimal ET sequence| 5de, 12de, 17c, 29c }}
Optimal ET sequence: {{Optimal ET sequence| 5de, 12de, 17c, 29c }}
Line 1,628: Line 1,627:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 704.121
* CTE: ~2 = 1200.000, ~3/2 = 704.121
* POTE: ~2 = 1\1, ~3/2 = 705.094
* POTE: ~2 = 1200.000, ~3/2 = 705.094


Optimal ET sequence: {{Optimal ET sequence| 5de, 12de, 17c, 29c }}
Optimal ET sequence: {{Optimal ET sequence| 5de, 12de, 17c, 29c }}
Line 1,644: Line 1,643:
[[Comma list]]: 81/80, 6144/6125
[[Comma list]]: 81/80, 6144/6125


[[Mapping]]: [{{val| 1 1 0 6 }}, {{val| 0 2 8 -11 }}]
{{Mapping|legend=1| 1 1 0 6 | 0 2 8 -11 }}


: mapping generators: ~2, ~128/105
: mapping generators: ~2, ~128/105
Line 1,650: Line 1,649:
{{Multival|legend=1| 2 8 -11 8 -23 -48 }}
{{Multival|legend=1| 2 8 -11 8 -23 -48 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 348.415
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 348.415


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,675: Line 1,674:
Comma list: 81/80, 121/120, 176/175
Comma list: 81/80, 121/120, 176/175


Mapping: [{{val| 1 1 0 6 2 }}, {{val| 0 2 8 -11 5 }}]
Mapping: {{mapping| 1 1 0 6 2 | 0 2 8 -11 5 }}


{{Multival|legend=1| 2 8 -11 5 8 -23 1 -48 -16 52 }}
Wedgie: {{multival| 2 8 -11 5 8 -23 1 -48 -16 52 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.477
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.477


Minimax tuning:  
Minimax tuning:  
Line 1,690: Line 1,689:
* 11-odd-limit diamond tradeoff: ~11/9 = [344.999, 350.978]
* 11-odd-limit diamond tradeoff: ~11/9 = [344.999, 350.978]


{{Optimal ET sequence|legend=1| 7, 24, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31 }}


Badness: 0.026064
Badness: 0.026064
Line 1,701: Line 1,700:
Comma list: 66/65, 81/80, 105/104, 121/120
Comma list: 66/65, 81/80, 105/104, 121/120


Mapping: [{{val| 1 1 0 6 2 4 }}, {{val| 0 2 8 -11 5 -1 }}]
Mapping: {{mapping| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.558
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.558


{{Optimal ET sequence|legend=1| 7, 24, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31 }}


Badness: 0.023388
Badness: 0.023388
Line 1,716: Line 1,715:
Comma list: 66/65, 81/80, 105/104, 121/120, 154/153
Comma list: 66/65, 81/80, 105/104, 121/120, 154/153


Mapping: [{{val| 1 1 0 6 2 4 7 }}, {{val| 0 2 8 -11 5 -1 -10 }}]
Mapping: {{mapping| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.736
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.736


{{Optimal ET sequence|legend=1| 7, 24, 31, 86ef }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31, 86ef }}


Badness: 0.020576
Badness: 0.020576
Line 1,731: Line 1,730:
Comma list: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152
Comma list: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152


Mapping: [{{val| 1 1 0 6 2 4 7 6 }}, {{val| 0 2 8 -11 5 -1 -10 -6 }}]
Mapping: {{mapping| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.810
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 348.810


{{Optimal ET sequence|legend=1| 7, 24, 31, 55, 86efh }}
Optimal ET sequence: {{Optimal ET sequence| 7, 24, 31, 55, 86efh }}


Badness: 0.017302
Badness: 0.017302
Line 1,746: Line 1,745:
[[Comma list]]: 81/80, 392/375
[[Comma list]]: 81/80, 392/375


[[Mapping]]: [{{val| 1 1 0 -1 }}, {{val| 0 2 8 13 }}]
{{Mapping|legend=1| 1 1 0 -1 | 0 2 8 13 }}


: mapping generators: ~2, ~25/21
: mapping generators: ~2, ~25/21


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 350.586
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~25/21 = 350.586


{{Optimal ET sequence|legend=1| 7d, 17c, 24, 65cc, 89ccd }}
{{Optimal ET sequence|legend=1| 7d, 17c, 24, 65cc, 89ccd }}
Line 1,763: Line 1,762:
Comma list: 56/55, 77/75, 243/242
Comma list: 56/55, 77/75, 243/242


Mapping: [{{val| 1 1 0 -1 2 }}, {{val| 0 2 8 13 5 }}]
Mapping: {{mapping| 1 1 0 -1 2 | 0 2 8 13 5 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.565
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 350.565


{{Optimal ET sequence|legend=1| 7d, 17c, 24, 65cc, 89ccd }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 17c, 24, 65cc, 89ccd }}


Badness: 0.036207
Badness: 0.036207
Line 1,778: Line 1,777:
Comma list: 56/55, 66/65, 77/75, 243/242
Comma list: 56/55, 66/65, 77/75, 243/242


Mapping: [{{val| 1 1 0 -1 2 4 }}, {{val| 0 2 8 13 5 -1 }}]
Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.745
Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 350.745


{{Optimal ET sequence|legend=1| 7d, 17c, 24, 41c, 65cc }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 17c, 24, 41c, 65cc }}


Badness: 0.028738
Badness: 0.028738
Line 1,797: Line 1,796:
[[Comma list]]: 81/80, 686/675
[[Comma list]]: 81/80, 686/675


[[Mapping]]: [{{val| 1 0 -4 -3 }}, {{val| 0 3 12 11 }}]
{{Mapping|legend=1| 1 0 -4 -3 | 0 3 12 11 }}


: mapping generators: ~2, ~10/7
: mapping generators: ~2, ~10/7
Line 1,803: Line 1,802:
{{Multival|legend=1| 3 12 11 12 9 -8 }}
{{Multival|legend=1| 3 12 11 12 9 -8 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/7 = 632.406
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10/7 = 632.406


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,821: Line 1,820:
Comma list: 56/55, 81/80, 540/539
Comma list: 56/55, 81/80, 540/539


Mapping: [{{val| 1 0 -4 -3 4 }}, {{val| 0 3 12 11 -1 }}]
Mapping: {{mapping| 1 0 -4 -3 4 | 0 3 12 11 -1 }}


{{Multival|legend=1| 3 12 11 -1 12 9 -12 -8 -44 -41 }}
Wedgie: {{multival| 3 12 11 -1 12 9 -12 -8 -44 -41 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/7 = 633.073
Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 633.073


{{Optimal ET sequence|legend=1| 17c, 19, 36, 91cee }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19, 36, 91cee }}


Badness: 0.040721
Badness: 0.040721
Line 1,838: Line 1,837:
Comma list: 56/55, 78/77, 81/80, 91/90
Comma list: 56/55, 78/77, 81/80, 91/90


Mapping: [{{val| 1 0 -4 -3 4 0 }}, {{val| 0 3 12 11 -1 7 }}]
Mapping: {{mapping| 1 0 -4 -3 4 0 | 0 3 12 11 -1 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/7 = 633.042
Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 633.042


{{Optimal ET sequence|legend=1| 17c, 19, 36, 91ceef }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19, 36, 91ceef }}


Badness: 0.027304
Badness: 0.027304
Line 1,851: Line 1,850:
Comma list: 77/75, 81/80, 99/98
Comma list: 77/75, 81/80, 99/98


Mapping: [{{val| 1 0 -4 -3 -5 }}, {{val| 0 3 12 11 16 }}]
Mapping: {{mapping| 1 0 -4 -3 -5 | 0 3 12 11 16 }}


Wedgie: {{multival| 3 12 11 16 12 9 15 -8 -4 7 }}


{{Multival|legend=1| 3 12 11 16 12 9 15 -8 -4 7 }}
Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 633.061


Optimal tuning (POTE): ~2 = 1\1, ~10/7 = 633.061
Optimal ET sequence: {{Optimal ET sequence| 17c, 19e, 36e }}
 
{{Optimal ET sequence|legend=1| 17c, 19e, 36e }}


Badness: 0.041592
Badness: 0.041592
Line 1,867: Line 1,865:
Comma list: 66/65, 77/75, 81/80, 99/98
Comma list: 66/65, 77/75, 81/80, 99/98


Mapping: [{{val| 1 0 -4 -3 -5 0 }}, {{val| 0 3 12 11 16 7 }}]
Mapping: {{mapping| 1 0 -4 -3 -5 0 | 0 3 12 11 16 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/7 = 632.991
Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 632.991


{{Optimal ET sequence|legend=1| 17c, 19e, 36e }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 19e, 36e }}


Badness: 0.026922
Badness: 0.026922
Line 1,880: Line 1,878:
Comma list: 45/44, 81/80, 343/330
Comma list: 45/44, 81/80, 343/330


Mapping: [{{val| 1 0 -4 -3 -6 }}, {{val| 0 3 12 11 18 }}]
Mapping: {{mapping| 1 0 -4 -3 -6 | 0 3 12 11 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/7 = 631.370
Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 631.370


{{Optimal ET sequence|legend=1| 17cee, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 17cee, 19 }}


Badness: 0.054829
Badness: 0.054829
Line 1,893: Line 1,891:
Comma list: 45/44, 81/80, 91/88, 147/143
Comma list: 45/44, 81/80, 91/88, 147/143


Mapping: [{{val| 1 0 -4 -3 -6 0 }}, {{val| 0 3 12 11 18 7 }}]
Mapping: {{mapping| 1 0 -4 -3 -6 0 | 0 3 12 11 18 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~10/7 = 631.221
Optimal tuning (POTE): ~2 = 1200.000, ~10/7 = 631.221


{{Optimal ET sequence|legend=1| 17cee, 19 }}
Optimal ET sequence: {{Optimal ET sequence| 17cee, 19 }}


Badness: 0.036144
Badness: 0.036144
Line 1,910: Line 1,908:
{{Mapping|legend=1| 1 2 4 1 | 0 -3 -12 13 }}
{{Mapping|legend=1| 1 2 4 1 | 0 -3 -12 13 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~35/32 = 167.279
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~35/32 = 167.279


{{Optimal ET sequence|legend=1| 7, 36, 43, 79c }}
{{Optimal ET sequence|legend=1| 7, 36, 43, 79c }}
Line 1,923: Line 1,921:
Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 13 -11 }}
Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 13 -11 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.407
Optimal tuning (CTE): ~2 = 1200.000, ~11/10 = 167.407


Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Line 1,936: Line 1,934:
Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}
Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 13 -11 5 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.427
Optimal tuning (CTE): ~2 = 1200.000, ~11/10 = 167.427


Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
Line 1,949: Line 1,947:
[[Comma list]]: 81/80, 3125/3087
[[Comma list]]: 81/80, 3125/3087


[[Mapping]]: [{{val| 3 0 -12 -20 }}, {{val| 0 1 4 6 }}]
{{Mapping|legend=1| 3 0 -12 -20 | 0 1 4 6 }}


: mapping generators: ~56/45, ~3
: mapping generators: ~56/45, ~3


[[Optimal tuning]] ([[CTE]]): ~56/45 = 1\3, ~3/2 = 695.827
[[Optimal tuning]] ([[CTE]]): ~56/45 = 400.000, ~3/2 = 695.827


{{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }}
{{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }}
Line 1,968: Line 1,966:
[[Comma list]]: 81/80, 2401/2400
[[Comma list]]: 81/80, 2401/2400


[[Mapping]]: [{{val| 1 3 8 6 }}, {{val| 0 -4 -16 -9 }}]
{{Mapping|legend=1| 1 3 8 6 | 0 -4 -16 -9 }}


: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~9/7
Line 1,974: Line 1,972:
{{Multival|legend=1| 4 16 9 16 3 -24 }}
{{Multival|legend=1| 4 16 9 16 3 -24 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.942
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 425.942


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,994: Line 1,992:
Comma list: 81/80, 99/98, 121/120
Comma list: 81/80, 99/98, 121/120


Mapping: [{{val| 1 3 8 6 7 }}, {{val| 0 -4 -16 -9 -10 }}]
Mapping: {{mapping| 1 3 8 6 7 | 0 -4 -16 -9 -10 }}


{{Multival|legend=1| 4 16 9 10 16 3 2 -24 -32 -3 }}
{{Multival|legend=1| 4 16 9 10 16 3 2 -24 -32 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.957
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.957


{{Optimal ET sequence|legend=1| 14c, 17c, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 17c, 31 }}


Badness: 0.021636
Badness: 0.021636
Line 2,009: Line 2,007:
Comma list: 66/65, 81/80, 99/98, 121/120
Comma list: 66/65, 81/80, 99/98, 121/120


Mapping: [{{val| 1 3 8 6 7 3 }}, {{val| 0 -4 -16 -9 -10 2 }}]
Mapping: {{mapping| 1 3 8 6 7 3 | 0 -4 -16 -9 -10 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.550


{{Optimal ET sequence|legend=1| 14c, 17c, 31, 79cf }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 17c, 31, 79cf }}


Badness: 0.025514
Badness: 0.025514
Line 2,022: Line 2,020:
Comma list: 78/77, 81/80, 91/90, 99/98
Comma list: 78/77, 81/80, 91/90, 99/98


Mapping: [{{val| 1 3 8 6 7 9 }}, {{val| 0 -4 -16 -9 -10 -15 }}]
Mapping: {{mapping| 1 3 8 6 7 9 | 0 -4 -16 -9 -10 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.7516
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.7516


{{Optimal ET sequence|legend=1| 14cf, 17c, 31f }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 17c, 31f }}


Badness: 0.026877
Badness: 0.026877
Line 2,035: Line 2,033:
Comma list: 81/80, 99/98, 105/104, 121/120
Comma list: 81/80, 99/98, 105/104, 121/120


Mapping: [{{val| 1 3 8 6 7 14 }}, {{val| 0 -4 -16 -9 -10 -29 }}]
Mapping: {{mapping| 1 3 8 6 7 14 | 0 -4 -16 -9 -10 -29 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 426.276
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 426.276


{{Optimal ET sequence|legend=1| 14cf, 31, 45ef, 76e }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 45ef, 76e }}


Badness: 0.024522
Badness: 0.024522
Line 2,048: Line 2,046:
Comma list: 81/80, 99/98, 105/104, 120/119, 121/119
Comma list: 81/80, 99/98, 105/104, 120/119, 121/119


Mapping: [{{val| 1 3 8 6 7 14 8 }}, {{val| 0 -4 -16 -9 -10 -29 -11 }}]
Mapping: {{mapping| 1 3 8 6 7 14 8 | 0 -4 -16 -9 -10 -29 -11 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 426.187
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 426.187


{{Optimal ET sequence|legend=1| 14cf, 31, 76e }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 76e }}


Badness: 0.022573
Badness: 0.022573
Line 2,061: Line 2,059:
Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119
Comma list: 77/76, 81/80, 99/98, 105/104, 120/119, 121/119


Mapping: [{{val| 1 3 8 6 7 14 8 11 }}, {{val| 0 -4 -16 -9 -10 -29 -11 -19 }}]
Mapping: {{mapping| 1 3 8 6 7 14 8 11 | 0 -4 -16 -9 -10 -29 -11 -19 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 426.225
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 426.225


{{Optimal ET sequence|legend=1| 14cf, 31, 76e }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 31, 76e }}


Badness: 0.018839
Badness: 0.018839
Line 2,074: Line 2,072:
Comma list: 81/80, 385/384, 1375/1372
Comma list: 81/80, 385/384, 1375/1372


Mapping: [{{val| 1 3 8 6 -4 }}, {{val| 0 -4 -16 -9 21 }}]
Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}


{{Multival|legend=1| 4 16 9 -21 16 3 -47 -24 -104 -90 }}
{{Multival|legend=1| 4 16 9 -21 16 3 -47 -24 -104 -90 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.993
Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 425.993


{{Optimal ET sequence|legend=1| 14ce, 17ce, 31, 107b, 138b, 169be, 200be }}
Optimal ET sequence: {{Optimal ET sequence| 14ce, 17ce, 31, 107b, 138b, 169be, 200be }}


Badness: 0.056826
Badness: 0.056826
Line 2,091: Line 2,089:
[[Comma list]]: 81/80, 17280/16807
[[Comma list]]: 81/80, 17280/16807


[[Mapping]]: [{{val| 1 1 0 2 }}, {{val| 0 5 20 7 }}]
{{Mapping|legend=1| 1 1 0 2 | 0 5 20 7 }}


: mapping generators: ~2, ~54/49
: mapping generators: ~2, ~54/49
Line 2,097: Line 2,095:
{{Multival|legend=1| 5 20 7 20 -3 -40 }}
{{Multival|legend=1| 5 20 7 20 -3 -40 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/49 = 139.343
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~54/49 = 139.343


{{Optimal ET sequence|legend=1| 17c, 26, 43, 69, 112bd }}
{{Optimal ET sequence|legend=1| 17c, 26, 43, 69, 112bd }}
Line 2,108: Line 2,106:
Comma list: 81/80, 99/98, 864/847
Comma list: 81/80, 99/98, 864/847


Mapping: [{{val| 1 1 0 2 3 }}, {{val| 0 5 20 7 4 }}]
Mapping: {{mapping| 1 1 0 2 3 | 0 5 20 7 4 }}


{{Multival|legend=1| 5 20 7 4 20 -3 -11 -40 -60 -13 }}
Wedgie: {{multival| 5 20 7 4 20 -3 -11 -40 -60 -13 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 139.428
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.428


{{Optimal ET sequence|legend=1| 17c, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 26, 43, 69 }}


Badness: 0.047914
Badness: 0.047914
Line 2,123: Line 2,121:
Comma list: 78/77, 81/80, 99/98, 144/143
Comma list: 78/77, 81/80, 99/98, 144/143


Mapping: [{{val| 1 1 0 2 3 3 }}, {{val| 0 5 20 7 4 6 }}]
Mapping: {{mapping| 1 1 0 2 3 3 | 0 5 20 7 4 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 139.387
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.387


{{Optimal ET sequence|legend=1| 17c, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 26, 43, 69 }}


Badness: 0.029285
Badness: 0.029285
Line 2,136: Line 2,134:
Comma list: 78/77, 81/80, 99/98, 144/143, 189/187
Comma list: 78/77, 81/80, 99/98, 144/143, 189/187


Mapping: [{{val| 1 1 0 2 3 3 2 }}, {{val| 0 5 20 7 4 6 18 }}]
Mapping: {{mapping| 1 1 0 2 3 3 2 | 0 5 20 7 4 6 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 139.362
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.362


{{Optimal ET sequence|legend=1| 17cg, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17cg, 26, 43, 69 }}


Badness: 0.020878
Badness: 0.020878
Line 2,149: Line 2,147:
Comma list: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143
Comma list: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143


Mapping: [{{val| 1 1 0 2 3 3 2 1 }}, {{val| 0 5 20 7 4 6 18 28 }}]
Mapping: {{mapping| 1 1 0 2 3 3 2 1 | 0 5 20 7 4 6 18 28 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 139.313
Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 139.313


{{Optimal ET sequence|legend=1| 17cgh, 26, 43, 69 }}
Optimal ET sequence: {{Optimal ET sequence| 17cgh, 26, 43, 69 }}


Badness: 0.018229
Badness: 0.018229
Line 2,164: Line 2,162:
[[Comma list]]: 81/80, 16875/16807
[[Comma list]]: 81/80, 16875/16807


[[Mapping]]: [{{val| 1 4 12 12 }}, {{val| 0 -5 -20 -19 }}]
{{Mapping|legend=1| 1 4 12 12 | 0 -5 -20 -19 }}


{{Multival|legend=1| 5 20 19 20 16 -12 }}
{{Multival|legend=1| 5 20 19 20 16 -12 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 580.766
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 580.766


{{Optimal ET sequence|legend=1| 2cd, 29cd, 31 }}
{{Optimal ET sequence|legend=1| 2cd, 29cd, 31 }}
Line 2,179: Line 2,177:
Comma list: 81/80, 99/98, 2541/2500
Comma list: 81/80, 99/98, 2541/2500


Mapping: [{{val| 1 4 12 12 17 }}, {{val| 0 -5 -20 -19 -28 }}]
Mapping: {{mapping| 1 4 12 12 17 | 0 -5 -20 -19 -28 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.647
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.647


{{Optimal ET sequence|legend=1| 2cde, 29cde, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 2cde, 29cde, 31 }}


Badness: 0.042869
Badness: 0.042869
Line 2,196: Line 2,194:
[[Comma list]]: 50/49, 81/80
[[Comma list]]: 50/49, 81/80


[[Mapping]]: [{{val| 2 0 -8 -7 }}, {{val| 0 1 4 4 }}]
{{Mapping|legend=1| 2 0 -8 -7 | 0 1 4 4 }}


: mapping generators: ~7/5, ~3
: mapping generators: ~7/5, ~3
Line 2,202: Line 2,200:
{{Multival|legend=1| 2 8 8 8 7 -4 }}
{{Multival|legend=1| 2 8 8 8 7 -4 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 694.375
[[Optimal tuning]] ([[POTE]]): ~7/5 = 600.000, ~3/2 = 694.375


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 2,221: Line 2,219:
Comma list: 45/44, 50/49, 81/80
Comma list: 45/44, 50/49, 81/80


Mapping: [{{val| 2 0 -8 -7 -12 }}, {{val| 0 1 4 4 6 }}]
Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}


{{Multival|legend=1| 2 8 8 12 8 7 12 -4 0 6 }}
{{Multival|legend=1| 2 8 8 12 8 7 12 -4 0 6 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 692.840
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.840


Tuning ranges:  
Tuning ranges:  
Line 2,231: Line 2,229:
* 11-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]


{{Optimal ET sequence|legend=1| 12, 14c, 26, 90bce, 116bcce }}
Optimal ET sequence: {{Optimal ET sequence| 12, 14c, 26, 90bce, 116bcce }}


Badness: 0.023124
Badness: 0.023124
Line 2,240: Line 2,238:
Comma list: 45/44, 50/49, 78/77, 81/80
Comma list: 45/44, 50/49, 78/77, 81/80


Mapping: [{{val| 2 0 -8 -7 -12 -21 }}, {{val| 0 1 4 4 6 9 }}]
Mapping: {{mapping| 2 0 -8 -7 -12 -21 | 0 1 4 4 6 9 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 692.673
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.673


Tuning ranges:  
Tuning ranges:  
Line 2,248: Line 2,246:
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]


{{Optimal ET sequence|legend=1| 12f, 14cf, 26, 38e }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26, 38e }}


Badness: 0.021565
Badness: 0.021565
Line 2,257: Line 2,255:
Comma list: 45/44, 50/49, 78/77, 81/80, 85/84
Comma list: 45/44, 50/49, 78/77, 81/80, 85/84


Mapping: [{{val| 2 0 -8 -7 -12 -21 5 }}, {{val| 0 1 4 4 6 9 1 }}]
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 | 0 1 4 4 6 9 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 692.487
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.487


{{Optimal ET sequence|legend=1| 12f, 14cf, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}


Badness: 0.018358
Badness: 0.018358
Line 2,270: Line 2,268:
Comma list: 45/44, 50/49, 57/56, 78/77, 81/80, 85/84
Comma list: 45/44, 50/49, 57/56, 78/77, 81/80, 85/84


Mapping: [{{val| 2 0 -8 -7 -12 -21 5 -1 }}, {{val| 0 1 4 4 6 9 1 3 }}]
Mapping: {{mapping| 2 0 -8 -7 -12 -21 5 -1 | 0 1 4 4 6 9 1 3 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 692.299
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 692.299


{{Optimal ET sequence|legend=1| 12f, 14cf, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14cf, 26 }}


Badness: 0.015118
Badness: 0.015118
Line 2,283: Line 2,281:
Comma list: 27/26, 40/39, 45/44, 50/49
Comma list: 27/26, 40/39, 45/44, 50/49


Mapping: [{{val| 2 0 -8 -7 -12 -2 }}, {{val| 0 1 4 4 6 3 }}]
Mapping: {{mapping| 2 0 -8 -7 -12 -2 | 0 1 4 4 6 3 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 694.121
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 694.121


{{Optimal ET sequence|legend=1| 12f, 14c, 26f, 38eff }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 14c, 26f, 38eff }}


Badness: 0.026542
Badness: 0.026542
Line 2,296: Line 2,294:
Comma list: 33/32, 50/49, 55/54
Comma list: 33/32, 50/49, 55/54


Mapping: [{{val| 2 0 -8 -7 10 }}, {{val| 0 1 4 4 -1 }}]
Mapping: {{mapping| 2 0 -8 -7 10 | 0 1 4 4 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 690.548
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 690.548


{{Optimal ET sequence|legend=1| 12e, 14c, 26e, 40cee }}
Optimal ET sequence: {{Optimal ET sequence| 12e, 14c, 26e, 40cee }}


Badness: 0.038577
Badness: 0.038577
Line 2,309: Line 2,307:
Comma list: 50/49, 56/55, 81/77
Comma list: 50/49, 56/55, 81/77


Mapping: [{{val| 2 0 -8 -7 7 }}, {{val| 0 1 4 4 0 }}]
Mapping: {{mapping| 2 0 -8 -7 7 | 0 1 4 4 0 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 699.001
Optimal tuning (POTE): ~7/5 = 600.000, ~3/2 = 699.001


{{Optimal ET sequence|legend=1| 2cd, 10cd, 12 }}
Optimal ET sequence: {{Optimal ET sequence| 2cd, 10cd, 12 }}


Badness: 0.043062
Badness: 0.043062
Line 2,326: Line 2,324:
Comma list: 50/49, 81/80, 864/847
Comma list: 50/49, 81/80, 864/847


Mapping: [{{val| 2 1 -4 -3 8 }}, {{val| 0 2 8 8 -1 }}]
Mapping: {{mapping| 2 1 -4 -3 8 | 0 2 8 8 -1 }}


: mapping generators: ~7/5, ~16/11
: mapping generators: ~7/5, ~16/11


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 552.5303
Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.5303


{{Optimal ET sequence|legend=1| 24d, 26, 50d }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26, 50d }}


Badness: 0.070689
Badness: 0.070689
Line 2,341: Line 2,339:
Comma list: 50/49, 78/77, 81/80, 144/143
Comma list: 50/49, 78/77, 81/80, 144/143


Mapping: [{{val| 2 1 -4 -3 8 2 }}, {{val| 0 2 8 8 -1 5 }}]
Mapping: {{mapping| 2 1 -4 -3 8 2 | 0 2 8 8 -1 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 552.5324
Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.5324


{{Optimal ET sequence|legend=1| 24d, 26, 50d }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26, 50d }}


Badness: 0.040047
Badness: 0.040047
Line 2,354: Line 2,352:
Comma list: 50/49, 78/77, 81/80, 85/84, 144/143
Comma list: 50/49, 78/77, 81/80, 85/84, 144/143


Mapping: [{{val| 2 1 -4 -3 8 2 6 }}, {{val| 0 2 8 8 -1 5 2 }}]
Mapping: {{mapping| 2 1 -4 -3 8 2 6 | 0 2 8 8 -1 5 2 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 552.6558
Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.6558


{{Optimal ET sequence|legend=1| 24d, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26 }}


Badness: 0.029499
Badness: 0.029499
Line 2,367: Line 2,365:
Comma list: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143
Comma list: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143


Mapping: [{{val| 2 1 -4 -3 8 2 6 2 }}, {{val| 0 2 8 8 -1 5 2 6 }}]
Mapping: {{mapping| 2 1 -4 -3 8 2 6 2 | 0 2 8 8 -1 5 2 6 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 552.6382
Optimal tuning (POTE): ~7/5 = 600.000, ~11/8 = 552.6382


{{Optimal ET sequence|legend=1| 24d, 26 }}
Optimal ET sequence: {{Optimal ET sequence| 24d, 26 }}


Badness: 0.023133
Badness: 0.023133
Line 2,382: Line 2,380:
[[Comma list]]: 81/80, 300125/294912
[[Comma list]]: 81/80, 300125/294912


[[Mapping]]: [{{val| 2 1 -4 11 }}, {{val| 0 2 8 -5 }}]
{{Mapping|legend=1| 2 1 -4 11 | 0 2 8 -5 }}


: mapping generators: ~735/512, ~35/24
: mapping generators: ~735/512, ~35/24
Line 2,388: Line 2,386:
{{Multival|legend=1| 4 16 -10 16 -27 -68 }}
{{Multival|legend=1| 4 16 -10 16 -27 -68 }}


[[Optimal tuning]] ([[POTE]]): ~735/512 = 1\2, ~48/35 = 552.2206
[[Optimal tuning]] ([[POTE]]): ~735/512 = 600.000, ~48/35 = 552.2206


{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
Line 2,399: Line 2,397:
Comma list: 81/80, 245/242, 385/384
Comma list: 81/80, 245/242, 385/384


Mapping: [{{val| 2 1 -4 11 8 }}, {{val| 0 2 8 -5 -1 }}]
Mapping: {{mapping| 2 1 -4 11 8 | 0 2 8 -5 -1 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~11/8 = 552.0929
Optimal tuning (POTE): ~99/70 = 600.000, ~11/8 = 552.0929


{{Optimal ET sequence|legend=1| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}


Badness: 0.052099
Badness: 0.052099
Line 2,412: Line 2,410:
Comma list: 81/80, 105/104, 144/143, 245/242
Comma list: 81/80, 105/104, 144/143, 245/242


Mapping: [{{val| 2 1 -4 11 8 2 }}, {{val| 0 2 8 -5 -1 5 }}]
Mapping: {{mapping| 2 1 -4 11 8 2 | 0 2 8 -5 -1 5 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~11/8 = 552.1498
Optimal tuning (POTE): ~99/70 = 600.000, ~11/8 = 552.1498


{{Optimal ET sequence|legend=1| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}


Badness: 0.031039
Badness: 0.031039
Line 2,425: Line 2,423:
Comma list: 81/80, 105/104, 144/143, 245/242, 273/272
Comma list: 81/80, 105/104, 144/143, 245/242, 273/272


Mapping: [{{val| 2 1 -4 11 8 2 6 }}, {{val| 0 2 8 -5 -1 5 2 }}]
Mapping: {{mapping| 2 1 -4 11 8 2 6 | 0 2 8 -5 -1 5 2 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~11/8 = 552.1579
Optimal tuning (POTE): ~17/12 = 600.000, ~11/8 = 552.1579


{{Optimal ET sequence|legend=1| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}


Badness: 0.021260
Badness: 0.021260
Line 2,438: Line 2,436:
Comma list: 81/80, 105/104, 133/132, 144/143, 171/170, 210/209
Comma list: 81/80, 105/104, 133/132, 144/143, 171/170, 210/209


Mapping: [{{val| 2 1 -4 11 8 2 6 2 }}, {{val| 0 2 8 -5 -1 5 2 6 }}]
Mapping: {{mapping| 2 1 -4 11 8 2 6 2 | 0 2 8 -5 -1 5 2 6 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~11/8 = 552.1196
Optimal tuning (POTE): ~17/12 = 600.000, ~11/8 = 552.1196


{{Optimal ET sequence|legend=1| 24, 26, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 24, 26, 50 }}


Badness: 0.016548
Badness: 0.016548
Line 2,451: Line 2,449:
[[Comma list]]: 81/80, 5898240/5764801
[[Comma list]]: 81/80, 5898240/5764801


[[Mapping]]: [{{val| 2 5 12 7 }}, {{val| 0 -4 -16 -3 }}]
{{Mapping|legend=1| 2 5 12 7 | 0 -4 -16 -3 }}


Mapping generators: ~2401/1728, ~7/6
: mapping generators: ~2401/1728, ~7/6


{{Multival|legend=1| 8 32 6 32 -13 -76 }}
{{Multival|legend=1| 8 32 6 32 -13 -76 }}


[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 1\2, ~7/6 = 275.794
[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000, ~7/6 = 275.794


{{Optimal ET sequence|legend=1| 26, 48c, 74, 174bd, 248bbd }}
{{Optimal ET sequence|legend=1| 26, 48c, 74, 174bd, 248bbd }}
Line 2,468: Line 2,466:
Comma list: 81/80, 99/98, 73728/73205
Comma list: 81/80, 99/98, 73728/73205


Mapping: [{{val| 2 5 12 7 6 }}, {{val| 0 -4 -16 -3 2 }}]
Mapping: {{mapping| 2 5 12 7 6 | 0 -4 -16 -3 2 }}


Optimal tuning (POTE): ~363/256 = 1\2, ~7/6 = 275.762
Optimal tuning (POTE): ~363/256 = 600.000, ~7/6 = 275.762


{{Optimal ET sequence|legend=1| 26, 48c, 74, 248bbd, 322bbdd }}
Optimal ET sequence: {{Optimal ET sequence| 26, 48c, 74, 248bbd, 322bbdd }}


Badness: 0.101499
Badness: 0.101499
Line 2,481: Line 2,479:
Comma list: 81/80, 99/98, 144/143, 2200/2197
Comma list: 81/80, 99/98, 144/143, 2200/2197


Mapping: [{{val| 2 5 12 7 6 12 }}, {{val| 0 -4 -16 -3 2 -10 }}]
Mapping: {{mapping| 2 5 12 7 6 12 | 0 -4 -16 -3 2 -10 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 275.774
Optimal tuning (POTE): ~55/39 = 600.000, ~7/6 = 275.774


{{Optimal ET sequence|legend=1| 26, 48c, 74, 174bd, 248bbd, 322bbdd }}
Optimal ET sequence: {{Optimal ET sequence| 26, 48c, 74, 174bd, 248bbd, 322bbdd }}


Badness: 0.053482
Badness: 0.053482
Line 2,496: Line 2,494:
[[Comma list]]: 81/80, 16807/16384
[[Comma list]]: 81/80, 16807/16384


[[Mapping]]: [{{val| 5 0 -20 14 }}, {{val| 0 1 4 0 }}]
{{Mapping|legend=1| 5 0 -20 14 | 0 1 4 0 }}


: mapping generators: ~8/7, ~3
: mapping generators: ~8/7, ~3
Line 2,502: Line 2,500:
{{Multival|legend=1| 5 20 0 20 -14 -56 }}
{{Multival|legend=1| 5 20 0 20 -14 -56 }}


[[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~3/2 = 695.720
[[Optimal tuning]] ([[POTE]]): ~8/7 = 240.000, ~3/2 = 695.720


{{Optimal ET sequence|legend=1| 5, 45, 50 }}
{{Optimal ET sequence|legend=1| 5, 45, 50 }}
Line 2,513: Line 2,511:
Comma list: 81/80, 385/384, 2401/2376
Comma list: 81/80, 385/384, 2401/2376


Mapping: [{{val| 5 0 -20 14 41 }}, {{val| 0 1 4 0 -3 }}]
Mapping: {{mapping| 5 0 -20 14 41 | 0 1 4 0 -3 }}


Optimal tuning (POTE): ~8/7 = 1\5, ~3/2 = 696.536
Optimal tuning (POTE): ~8/7 = 240.000, ~3/2 = 696.536


{{Optimal ET sequence|legend=1| 5, 45, 50, 155bdd, 205bddd }}
Optimal ET sequence: {{Optimal ET sequence| 5, 45, 50, 155bdd, 205bddd }}


Badness: 0.070378
Badness: 0.070378
Line 2,526: Line 2,524:
Comma list: 81/80, 105/104, 144/143, 2401/2376
Comma list: 81/80, 105/104, 144/143, 2401/2376


Mapping: [{{val| 5 0 -20 14 41 -21 }}, {{val| 0 1 4 0 -3 5 }}]
Mapping: {{mapping| 5 0 -20 14 41 -21 | 0 1 4 0 -3 5 }}


Optimal tuning (POTE): ~8/7 = 1\5, ~3/2 = 696.162
Optimal tuning (POTE): ~8/7 = 240.000, ~3/2 = 696.162


{{Optimal ET sequence|legend=1| 5, 45f, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 5, 45f, 50 }}


Badness: 0.048829
Badness: 0.048829
Line 2,540: Line 2,538:
[[Comma list]]: 81/80, 96/95
[[Comma list]]: 81/80, 96/95


[[Gencom]]: [2 4/3; 81/80 96/95]
{{Mapping|legend=2| 1 2 4 3 | 0 -1 -4 3 }}


[[Gencom|Gencom mapping]]: [{{val|1 2 4 0 0 0 0 3}}, {{val|0 -1 -4 0 0 0 0 3}}]
{{Mapping|legend=3| 1 2 4 0 0 0 0 3 | 0 -1 -4 0 0 0 0 3 }}


[[Mapping|Sval mapping]]: [{{val|1 2 4 3}}, {{val|0 -1 -4 3}}]
: [[gencom]]: [2 4/3; 81/80 96/95]


[[Tp tuning|POL2 generator]]: ~3/2 = 697.867
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 697.867


{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }}
Line 2,561: Line 2,559:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2/1 = 1\1, ~3/2 = 694.6998
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~3/2 = 694.700


{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }}
{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }}
Line 2,576: Line 2,574:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


Optimal tuning (CTE): ~2/1 = 1\1, ~3/2 = 693.9513
Optimal tuning (CTE): ~2/1 = 1\1, ~3/2 = 693.951


Optimal ET sequence: {{Optimal ET sequence| 7, 12, 19, 26, 45f }}
Optimal ET sequence: {{Optimal ET sequence| 7, 12, 19, 26, 45f }}
Line 2,591: Line 2,589:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 696.0387
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~3/2 = 696.0387


{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }}
{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }}
Line 2,606: Line 2,604:
: sval mapping generators: ~2, ~3
: sval mapping generators: ~2, ~3


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 689.6993
Optimal tuning (CTE): ~2 = 1200.000, ~3/2 = 689.6993


Optimal ET sequence: {{Optimal ET sequence| 7, 19eff, 26eff, 33ceeff, 40ceeff }}
Optimal ET sequence: {{Optimal ET sequence| 7, 19eff, 26eff, 33ceeff, 40ceeff }}
Retrieved from "https://en.xen.wiki/w/Meantone_family"