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autopatrolled, emailconfirmed
5,172 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 31: Line 31:
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]


{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }}


[[Badness]]: 0.007381
[[Badness]]: 0.007381
Line 72: Line 72:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/9 = 348.8296
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/9 = 348.8296


{{Val list|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}
{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 100e, 131bee }}


Scales: [[mohaha7]], [[mohaha10]]
Scales: [[mohaha7]], [[mohaha10]]
Line 91: Line 91:
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.8794
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.8794


Optimal GPV sequence: {{Val list| 7, 17c, 24, 31, 55 }}
{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 55 }}


Scales: [[mohaha7]], [[mohaha10]]
Scales: [[mohaha7]], [[mohaha10]]
Line 126: Line 126:
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.


{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}
{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }}


[[Badness]]: 0.013707
[[Badness]]: 0.013707
Line 155: Line 155:
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 GPV sequence: {{Val list| 12, 19e, 31, 105, 136b, 167be, 198be }}
{{Optimal ET sequence|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}


Badness: 0.017027
Badness: 0.017027
Line 175: Line 175:
: Eigenmonzo basis (unchanged-interval basis): 2.11/9
: Eigenmonzo basis (unchanged-interval basis): 2.11/9


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


Badness: 0.018048
Badness: 0.018048
Line 188: Line 188:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6486


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


Badness: 0.019037
Badness: 0.019037
Line 201: Line 201:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.5551


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


Badness: 0.017846
Badness: 0.017846
Line 214: Line 214:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0360


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


Badness: 0.019433
Badness: 0.019433
Line 227: Line 227:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2161


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


Badness: 0.017437
Badness: 0.017437
Line 240: Line 240:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9080


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


Badness: 0.019982
Badness: 0.019982
Line 253: Line 253:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9308


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


Badness: 0.018047
Badness: 0.018047
Line 275: Line 275:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]


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


Badness: 0.025899
Badness: 0.025899
Line 288: Line 288:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.2996


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


Badness: 0.020889
Badness: 0.020889
Line 301: Line 301:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.3271


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


Badness: 0.017611
Badness: 0.017611
Line 318: Line 318:
: Eigenmonzo basis (unchanged-interval basis): 2.13/9
: Eigenmonzo basis (unchanged-interval basis): 2.13/9


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


Badness: 0.026421
Badness: 0.026421
Line 331: Line 331:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5076


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


Badness: 0.027706
Badness: 0.027706
Line 344: Line 344:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.4848


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


Badness: 0.025315
Badness: 0.025315
Line 357: Line 357:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.6098


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


Badness: 0.027518
Badness: 0.027518
Line 370: Line 370:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.7012


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


Badness: 0.023613
Badness: 0.023613
Line 383: Line 383:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5384


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


Badness: 0.023881
Badness: 0.023881
Line 396: Line 396:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.5550


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


Badness: 0.020540
Badness: 0.020540
Line 411: Line 411:
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6109
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6109


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


Badness: 0.031433
Badness: 0.031433
Line 424: Line 424:
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 948.6173


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


Badness: 0.023380
Badness: 0.023380
Line 437: Line 437:
Optimal tuning (CTE): ~2 = 1\1, ~19/11 = 948.6088
Optimal tuning (CTE): ~2 = 1\1, ~19/11 = 948.6088


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


Badness: 0.018952
Badness: 0.018952
Line 452: Line 452:
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 697.1678
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 697.1678


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


Badness: 0.040668
Badness: 0.040668
Line 465: Line 465:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1740


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


Badness: 0.031491
Badness: 0.031491
Line 478: Line 478:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 697.1871


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


Badness: 0.024206
Badness: 0.024206
Line 507: Line 507:
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 GPV sequence: {{Val list| 12e, 19, 31, 81 }}
{{Optimal ET sequence|legend=1| 12e, 19, 31, 81 }}


Badness: 0.021543
Badness: 0.021543
Line 533: Line 533:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]


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


Badness: 0.020883
Badness: 0.020883
Line 546: Line 546:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3508


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


Badness: 0.019953
Badness: 0.019953
Line 559: Line 559:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3471


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


Badness: 0.017791
Badness: 0.017791
Line 572: Line 572:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4388


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


Badness: 0.022870
Badness: 0.022870
Line 585: Line 585:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4838


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


Badness: 0.020488
Badness: 0.020488
Line 602: Line 602:
: Eigenmonzo basis (unchanged-interval basis): 2.11
: Eigenmonzo basis (unchanged-interval basis): 2.11


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


Badness: 0.027666
Badness: 0.027666
Line 615: Line 615:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4069


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


Badness: 0.026836
Badness: 0.026836
Line 628: Line 628:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4731


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


Badness: 0.023540
Badness: 0.023540
Line 641: Line 641:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.6614


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


Badness: 0.026094
Badness: 0.026094
Line 654: Line 654:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 697.0160


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


Badness: 0.023104
Badness: 0.023104
Line 672: Line 672:
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]


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


Badness: 0.021423
Badness: 0.021423
Line 685: Line 685:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0983


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


Badness: 0.021182
Badness: 0.021182
Line 698: Line 698:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2161


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


Badness: 0.022980
Badness: 0.022980
Line 711: Line 711:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2774


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


Badness: 0.020293
Badness: 0.020293
Line 724: Line 724:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4501


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


Badness: 0.020171
Badness: 0.020171
Line 737: Line 737:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.121
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.121


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


Badness: 0.018045
Badness: 0.018045
Line 750: Line 750:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7897


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


Badness: 0.024763
Badness: 0.024763
Line 763: Line 763:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0114


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


Badness: 0.025535
Badness: 0.025535
Line 776: Line 776:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.1196


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


Badness: 0.022302
Badness: 0.022302
Line 789: Line 789:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0585
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.0585


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


Badness: 0.020139
Badness: 0.020139
Line 802: Line 802:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.9824
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.9824


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


Badness: 0.018168
Badness: 0.018168
Line 815: Line 815:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7980
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7980


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


Badness: 0.017069
Badness: 0.017069
Line 828: Line 828:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6746
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6746


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


Badness: 0.016129
Badness: 0.016129
Line 841: Line 841:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7239
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7239


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


Badness: 0.015356
Badness: 0.015356
Line 854: Line 854:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7160
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.7160


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


Badness: 0.013906
Badness: 0.013906
Line 867: Line 867:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6849
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6849


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


Badness: 0.013818
Badness: 0.013818
Line 880: Line 880:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.4125


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


Badness: 0.022099
Badness: 0.022099
Line 893: Line 893:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.9500


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


Badness: 0.019904
Badness: 0.019904
Line 906: Line 906:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 695.6202


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


Badness: 0.024243
Badness: 0.024243
Line 919: Line 919:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2789


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


Badness: 0.021400
Badness: 0.021400
Line 932: Line 932:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.8486


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


Badness: 0.018996
Badness: 0.018996
Line 945: Line 945:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.7022


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


Badness: 0.031539
Badness: 0.031539
Line 958: Line 958:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.2408


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


Badness: 0.026288
Badness: 0.026288
Line 973: Line 973:
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5324
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5324


Optimal GPV sequence: {{Val list| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
{{Optimal ET sequence|legend=1| 7d, 24d, 31, 100de, 131bdee, 162bdee }}


Badness: 0.025516
Badness: 0.025516
Line 986: Line 986:
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5444
Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 348.5444


Optimal GPV sequence: {{Val list| 7d, 24d, 31 }}
{{Optimal ET sequence|legend=1| 7d, 24d, 31 }}


Badness: 0.028071
Badness: 0.028071
Line 1,003: Line 1,003:
Optimal tuning (CTE): ~63/44 = 1\2, ~3/2 = 696.5199
Optimal tuning (CTE): ~63/44 = 1\2, ~3/2 = 696.5199


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


Badness: 0.038122
Badness: 0.038122
Line 1,016: Line 1,016:
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410
Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 696.3410


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


Badness: 0.028817
Badness: 0.028817
Line 1,029: Line 1,029:
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 696.3526


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


Badness: 0.022666
Badness: 0.022666
Line 1,042: Line 1,042:
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3837
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 696.3837


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


Badness: 0.017785
Badness: 0.017785
Line 1,055: Line 1,055:
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7074


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


Badness: 0.050729
Badness: 0.050729
Line 1,068: Line 1,068:
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7121


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


Badness: 0.035445
Badness: 0.035445
Line 1,081: Line 1,081:
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.7047


Optimal GPV sequence: {{Val list|7dg, 36dg, 43, 50, 93 }}
{{Optimal ET sequence|legend=1|7dg, 36dg, 43, 50, 93 }}


Badness: 0.025221
Badness: 0.025221
Line 1,115: Line 1,115:
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.


{{Val list|legend=1| 7, 19, 26, 45 }}
{{Optimal ET sequence|legend=1| 7, 19, 26, 45 }}


[[Badness]]: 0.038553
[[Badness]]: 0.038553
Line 1,135: Line 1,135:
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]


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


Badness: 0.033839
Badness: 0.033839
Line 1,155: Line 1,155:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]


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


Badness: 0.022260
Badness: 0.022260
Line 1,170: Line 1,170:
POTE generator: ~11/9 = 346.922
POTE generator: ~11/9 = 346.922


Optimal GPV sequence: {{Val list| 7, 31dd, 38d, 45e, 83bcddee }}
{{Optimal ET sequence|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}


Badness: 0.058785
Badness: 0.058785
Line 1,183: Line 1,183:
POTE generator: ~11/9 = 346.910
POTE generator: ~11/9 = 346.910


Optimal GPV sequence: {{Val list| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
{{Optimal ET sequence|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}


Badness: 0.034316
Badness: 0.034316
Line 1,206: Line 1,206:
* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [700.000, 715.587]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [700.000, 715.587]


{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}


[[Badness]]: 0.020690
[[Badness]]: 0.020690
Line 1,224: Line 1,224:
POTE generator: ~3/2 = 703.254
POTE generator: ~3/2 = 703.254


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


Badness: 0.024180
Badness: 0.024180
Line 1,242: Line 1,242:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = 705.882
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = 705.882


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


Badness: 0.024108
Badness: 0.024108
Line 1,255: Line 1,255:
POTE generator: ~3/2 = 704.905
POTE generator: ~3/2 = 704.905


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


Badness: 0.027295
Badness: 0.027295
Line 1,268: Line 1,268:
POTE generator: ~3/2 = 698.776
POTE generator: ~3/2 = 698.776


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


Badness: 0.021978
Badness: 0.021978
Line 1,281: Line 1,281:
POTE generator: ~3/2 = 695.762
POTE generator: ~3/2 = 695.762


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


Badness: 0.027039
Badness: 0.027039
Line 1,294: Line 1,294:
POTE generator: ~3/2 = 696.115
POTE generator: ~3/2 = 696.115


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


Badness: 0.024539
Badness: 0.024539
Line 1,307: Line 1,307:
POTE generator: ~3/2 = 696.217
POTE generator: ~3/2 = 696.217


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


Badness: 0.020398
Badness: 0.020398
Line 1,320: Line 1,320:
POTE generator: ~3/2 = 698.544
POTE generator: ~3/2 = 698.544


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


Badness: 0.018289
Badness: 0.018289
Line 1,333: Line 1,333:
POTE generator: ~3/2 = 705.004
POTE generator: ~3/2 = 705.004


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


Badness: 0.036562
Badness: 0.036562
Line 1,346: Line 1,346:
POTE generator: ~3/2 = 705.496
POTE generator: ~3/2 = 705.496


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


Badness: 0.027435
Badness: 0.027435
Line 1,359: Line 1,359:
POTE generator: ~3/2 = 698.491
POTE generator: ~3/2 = 698.491


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


Badness: 0.026141
Badness: 0.026141
Line 1,372: Line 1,372:
POTE generator: ~3/2 = 696.743
POTE generator: ~3/2 = 696.743


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


Badness: 0.023300
Badness: 0.023300
Line 1,385: Line 1,385:
POTE generator: ~3/2 = 696.978
POTE generator: ~3/2 = 696.978


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


Badness: 0.024535
Badness: 0.024535
Line 1,398: Line 1,398:
POTE generator: ~3/2 = 697.068
POTE generator: ~3/2 = 697.068


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


Badness: 0.021098
Badness: 0.021098
Line 1,418: Line 1,418:
POTE generator: ~11/9 = 350.934
POTE generator: ~11/9 = 350.934


Optimal GPV sequence: {{Val list| 7, 17c, 24d, 41cd }}
{{Optimal ET sequence|legend=1| 7, 17c, 24d, 41cd }}


Badness: 0.040240
Badness: 0.040240
Line 1,433: Line 1,433:
POTE generator: ~11/9 = 350.816
POTE generator: ~11/9 = 350.816


Optimal GPV sequence: {{Val list| 7, 17c, 24d, 41cd }}
{{Optimal ET sequence|legend=1| 7, 17c, 24d, 41cd }}


Badness: 0.027214
Badness: 0.027214
Line 1,450: Line 1,450:
[[POTE generator]]: ~3/2 = 700.140
[[POTE generator]]: ~3/2 = 700.140


{{Val list|legend=1| 5, 7d, 12d }}
{{Optimal ET sequence|legend=1| 5, 7d, 12d }}


[[Badness]]: 0.024848
[[Badness]]: 0.024848
Line 1,463: Line 1,463:
POTE generator: ~3/2 = 696.615
POTE generator: ~3/2 = 696.615


Optimal GPV sequence: {{Val list| 5, 7d, 12de }}
{{Optimal ET sequence|legend=1| 5, 7d, 12de }}


Badness: 0.025167
Badness: 0.025167
Line 1,476: Line 1,476:
[[POTE generator]]: ~3/2 = 704.889
[[POTE generator]]: ~3/2 = 704.889


{{Val list|legend=1| 5d, 12d, 17c, 29c }}
{{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }}


[[Badness]]: 0.134204
[[Badness]]: 0.134204
Line 1,489: Line 1,489:
POTE generator: ~3/2 = 705.096
POTE generator: ~3/2 = 705.096


Optimal GPV sequence: {{Val list| 5de, 12de, 17c, 29c }}
{{Optimal ET sequence|legend=1| 5de, 12de, 17c, 29c }}


Badness: 0.063262
Badness: 0.063262
Line 1,502: Line 1,502:
POTE generator: ~3/2 = 705.094
POTE generator: ~3/2 = 705.094


Optimal GPV sequence: {{Val list| 5de, 12de, 17c, 29c }}
{{Optimal ET sequence|legend=1| 5de, 12de, 17c, 29c }}


Badness: 0.040324
Badness: 0.040324
Line 1,529: Line 1,529:
* 7- and 9-odd-limit diamond monotone and tradeoff: ~7/6 = [240.000, 257.143]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~7/6 = [240.000, 257.143]


{{Val list|legend=1| 5, 14c, 19 }}
{{Optimal ET sequence|legend=1| 5, 14c, 19 }}


[[Badness]]: 0.026747
[[Badness]]: 0.026747
Line 1,549: Line 1,549:
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [252.632, 257.143]
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [252.632, 257.143]


Optimal GPV sequence: {{Val list| 14c, 19, 33cd, 52cd }}
{{Optimal ET sequence|legend=1| 14c, 19, 33cd, 52cd }}


Badness: 0.028947
Badness: 0.028947
Line 1,569: Line 1,569:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = 252.632
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = 252.632


Optimal GPV sequence: {{Val list| 14cf, 19, 33cdff, 52cdff }}
{{Optimal ET sequence|legend=1| 14cf, 19, 33cdff, 52cdff }}


Badness: 0.022503
Badness: 0.022503
Line 1,584: Line 1,584:
POTE generator: ~8/7 = 254.042
POTE generator: ~8/7 = 254.042


Optimal GPV sequence: {{Val list| 14c, 19e, 33cdee }}
{{Optimal ET sequence|legend=1| 14c, 19e, 33cdee }}


Badness: 0.028510
Badness: 0.028510
Line 1,599: Line 1,599:
POTE generator: ~8/7 = 251.079
POTE generator: ~8/7 = 251.079


Optimal GPV sequence: {{Val list| 19e, 24, 43de }}
{{Optimal ET sequence|legend=1| 19e, 24, 43de }}


Badness: 0.039647
Badness: 0.039647
Line 1,614: Line 1,614:
POTE generator: ~8/7 = 251.165
POTE generator: ~8/7 = 251.165


Optimal GPV sequence: {{Val list| 19e, 24, 43de }}
{{Optimal ET sequence|legend=1| 19e, 24, 43de }}


Badness: 0.025676
Badness: 0.025676
Line 1,629: Line 1,629:
POTE generator: ~8/7 = 251.173
POTE generator: ~8/7 = 251.173


Optimal GPV sequence: {{Val list| 5, 14ce, 19, 24, 43d }}
{{Optimal ET sequence|legend=1| 5, 14ce, 19, 24, 43d }}


Badness: 0.035673
Badness: 0.035673
Line 1,644: Line 1,644:
POTE generator: ~8/7 = 251.198
POTE generator: ~8/7 = 251.198


Optimal GPV sequence: {{Val list| 5, 14cef, 19, 24, 43d }}
{{Optimal ET sequence|legend=1| 5, 14cef, 19, 24, 43d }}


Badness: 0.026703
Badness: 0.026703
Line 1,679: Line 1,679:
[[Algebraic generator]]: Mohabis, real root of 3''x''<sup>3</sup> - 3''x''<sup>2</sup> - 1, 348.6067 cents. Corresponding recurrence converges quickly.
[[Algebraic generator]]: Mohabis, real root of 3''x''<sup>3</sup> - 3''x''<sup>2</sup> - 1, 348.6067 cents. Corresponding recurrence converges quickly.


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


[[Badness]]: 0.055714
[[Badness]]: 0.055714
Line 1,706: Line 1,706:
* 11-odd-limit diamond monotone and tradeoff: ~11/9 = [348.387, 350.000]
* 11-odd-limit diamond monotone and tradeoff: ~11/9 = [348.387, 350.000]


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


Badness: 0.026064
Badness: 0.026064
Line 1,723: Line 1,723:
POTE generator: ~11/9 = 348.558
POTE generator: ~11/9 = 348.558


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


Badness: 0.023388
Badness: 0.023388
Line 1,740: Line 1,740:
POTE generator: ~11/9 = 348.736
POTE generator: ~11/9 = 348.736


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


Badness: 0.020576
Badness: 0.020576
Line 1,757: Line 1,757:
POTE generator: ~11/9 = 348.810
POTE generator: ~11/9 = 348.810


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


Badness: 0.017302
Badness: 0.017302
Line 1,774: Line 1,774:
[[POTE generator]]: ~25/21 = 350.586
[[POTE generator]]: ~25/21 = 350.586


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


[[Badness]]: 0.077734
[[Badness]]: 0.077734
Line 1,791: Line 1,791:
POTE generator: ~11/9 = 350.565
POTE generator: ~11/9 = 350.565


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


Badness: 0.036207
Badness: 0.036207
Line 1,808: Line 1,808:
POTE generator: ~11/9 = 350.745
POTE generator: ~11/9 = 350.745


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


Badness: 0.028738
Badness: 0.028738
Line 1,838: Line 1,838:
: [[Eigenmonzo]]s (unchanged-intervals): 2, 5
: [[Eigenmonzo]]s (unchanged-intervals): 2, 5


{{Val list|legend=1| 5, 26, 31 }}
{{Optimal ET sequence|legend=1| 5, 26, 31 }}


[[Badness]]: 0.037146
[[Badness]]: 0.037146
Line 1,853: Line 1,853:
POTE generator: ~8/7 = 232.031
POTE generator: ~8/7 = 232.031


Optimal GPV sequence: {{Val list| 5, 26, 31, 88, 150be, 181bee }}
{{Optimal ET sequence|legend=1| 5, 26, 31, 88, 150be, 181bee }}


Badness: 0.025642
Badness: 0.025642
Line 1,868: Line 1,868:
POTE generator: ~8/7 = 231.811
POTE generator: ~8/7 = 231.811


Optimal GPV sequence: {{Val list| 5, 26, 31, 57, 88 }}
{{Optimal ET sequence|legend=1| 5, 26, 31, 57, 88 }}


Badness: 0.023954
Badness: 0.023954
Line 1,886: Line 1,886:
POTE generator: ~8/7 = 231.317
POTE generator: ~8/7 = 231.317


Optimal GPV sequence: {{Val list| 5e, 26, 57e, 83bce }}
{{Optimal ET sequence|legend=1| 5e, 26, 57e, 83bce }}


Badness: 0.055706
Badness: 0.055706
Line 1,901: Line 1,901:
POTE generator: ~8/7 = 231.293
POTE generator: ~8/7 = 231.293


Optimal GPV sequence: {{Val list| 5e, 26, 57e, 83bce }}
{{Optimal ET sequence|legend=1| 5e, 26, 57e, 83bce }}


Badness: 0.034124
Badness: 0.034124
Line 1,916: Line 1,916:
POTE generator: ~8/7 = 232.419
POTE generator: ~8/7 = 232.419


Optimal GPV sequence: {{Val list| 31, 129, 160be, 191bce, 222bce, 253bcee }}
{{Optimal ET sequence|legend=1| 31, 129, 160be, 191bce, 222bce, 253bcee }}


Badness: 0.031334
Badness: 0.031334
Line 1,931: Line 1,931:
POTE generator: ~8/7 = 232.640
POTE generator: ~8/7 = 232.640


Optimal GPV sequence: {{Val list| 31, 36, 67, 98 }}
{{Optimal ET sequence|legend=1| 31, 36, 67, 98 }}


Badness: 0.036857
Badness: 0.036857
Line 1,959: Line 1,959:
[[Algebraic generator]]: Radix, the real root of ''x''<sup>5</sup> - 2''x''<sup>4</sup> + 2''x''<sup>3</sup> - 2''x''<sup>2</sup> + 2''x'' - 2, also a root of ''x''<sup>6</sup> - ''x''<sup>5</sup> - 2. The recurrence converges.
[[Algebraic generator]]: Radix, the real root of ''x''<sup>5</sup> - 2''x''<sup>4</sup> + 2''x''<sup>3</sup> - 2''x''<sup>2</sup> + 2''x'' - 2, also a root of ''x''<sup>6</sup> - ''x''<sup>5</sup> - 2. The recurrence converges.


{{Val list|legend=1| 17c, 19, 55, 74d }}
{{Optimal ET sequence|legend=1| 17c, 19, 55, 74d }}


[[Badness]]: 0.046706
[[Badness]]: 0.046706
Line 1,972: Line 1,972:
POTE generator: ~10/7 = 633.073
POTE generator: ~10/7 = 633.073


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


Badness: 0.040721
Badness: 0.040721
Line 1,987: Line 1,987:
POTE generator: ~10/7 = 633.042
POTE generator: ~10/7 = 633.042


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


Badness: 0.027304
Badness: 0.027304
Line 2,000: Line 2,000:
POTE generator: ~10/7 = 633.061
POTE generator: ~10/7 = 633.061


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


Badness: 0.041592
Badness: 0.041592
Line 2,013: Line 2,013:
POTE generator: ~10/7 = 632.991
POTE generator: ~10/7 = 632.991


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


Badness: 0.026922
Badness: 0.026922
Line 2,026: Line 2,026:
POTE generator: ~10/7 = 631.370
POTE generator: ~10/7 = 631.370


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


Badness: 0.054829
Badness: 0.054829
Line 2,039: Line 2,039:
POTE generator: ~10/7 = 631.221
POTE generator: ~10/7 = 631.221


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


Badness: 0.036144
Badness: 0.036144
Line 2,056: Line 2,056:
[[Optimal tuning]] ([[CTE]]): ~56/45 = 1\3, ~3/2 = 695.827
[[Optimal tuning]] ([[CTE]]): ~56/45 = 1\3, ~3/2 = 695.827


{{Val list|legend=1| 12, 33cd, 45, 57 }}
{{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }}


[[Badness]]: 0.0692
[[Badness]]: 0.0692
Line 2,084: Line 2,084:
[[Algebraic generator]]: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.
[[Algebraic generator]]: Sceptre2, the positive root of 9''x''<sup>2</sup> + ''x'' - 16, or (sqrt (577) - 1)/18, which is 425.9311 cents.


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


[[Badness]]: 0.045993
[[Badness]]: 0.045993
Line 2,099: Line 2,099:
POTE generator: ~9/7 = 425.957
POTE generator: ~9/7 = 425.957


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


Badness: 0.021636
Badness: 0.021636
Line 2,112: Line 2,112:
POTE generator: ~9/7 = 425.550
POTE generator: ~9/7 = 425.550


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


Badness: 0.025514
Badness: 0.025514
Line 2,125: Line 2,125:
POTE generator: ~9/7 = 425.7516
POTE generator: ~9/7 = 425.7516


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


Badness: 0.026877
Badness: 0.026877
Line 2,138: Line 2,138:
POTE generator: ~9/7 = 426.276
POTE generator: ~9/7 = 426.276


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


Badness: 0.024522
Badness: 0.024522
Line 2,151: Line 2,151:
POTE generator: ~9/7 = 426.187
POTE generator: ~9/7 = 426.187


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


Badness: 0.022573
Badness: 0.022573
Line 2,164: Line 2,164:
POTE generator: ~9/7 = 426.225
POTE generator: ~9/7 = 426.225


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


Badness: 0.018839
Badness: 0.018839
Line 2,177: Line 2,177:
POTE generator: ~9/7 = 425.993
POTE generator: ~9/7 = 425.993


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


Badness: 0.056826
Badness: 0.056826
Line 2,196: Line 2,196:
[[POTE generator]]: ~54/49 = 139.343
[[POTE generator]]: ~54/49 = 139.343


{{Val list|legend=1| 17c, 26, 43, 69, 112bd }}
{{Optimal ET sequence|legend=1| 17c, 26, 43, 69, 112bd }}


[[Badness]]: 0.108656
[[Badness]]: 0.108656
Line 2,211: Line 2,211:
POTE generator: ~12/11 = 139.428
POTE generator: ~12/11 = 139.428


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


Badness: 0.047914
Badness: 0.047914
Line 2,226: Line 2,226:
POTE generator: ~12/11 = 139.387
POTE generator: ~12/11 = 139.387


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


Badness: 0.029285
Badness: 0.029285
Line 2,241: Line 2,241:
POTE generator: ~12/11 = 139.362
POTE generator: ~12/11 = 139.362


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


Badness: 0.020878
Badness: 0.020878
Line 2,256: Line 2,256:
POTE generator: ~12/11 = 139.313
POTE generator: ~12/11 = 139.313


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


Badness: 0.018229
Badness: 0.018229
Line 2,273: Line 2,273:
[[POTE generator]]: ~7/5 = 580.766
[[POTE generator]]: ~7/5 = 580.766


{{Val list|legend=1| 2cd, 29cd, 31 }}
{{Optimal ET sequence|legend=1| 2cd, 29cd, 31 }}


[[Badness]]: 0.082239
[[Badness]]: 0.082239
Line 2,286: Line 2,286:
POTE generator: ~7/5 = 580.647
POTE generator: ~7/5 = 580.647


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


Badness: 0.042869
Badness: 0.042869
Line 2,314: Line 2,314:
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [685.714, 700.000]
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [685.714, 700.000]


{{Val list|legend=1| 12, 26, 38, 102bcd, 140bccd, 178bbccdd }}
{{Optimal ET sequence|legend=1| 12, 26, 38, 102bcd, 140bccd, 178bbccdd }}


[[Badness]]: 0.031130
[[Badness]]: 0.031130
Line 2,337: Line 2,337:
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [685.714, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [685.714, 700.000]


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


Badness: 0.023124
Badness: 0.023124
Line 2,357: Line 2,357:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = 692.308
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = 692.308


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


Badness: 0.021565
Badness: 0.021565
Line 2,370: Line 2,370:
POTE generator: ~3/2 = 692.487
POTE generator: ~3/2 = 692.487


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


Badness: 0.018358
Badness: 0.018358
Line 2,383: Line 2,383:
POTE generator: ~3/2 = 692.299
POTE generator: ~3/2 = 692.299


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


Badness: 0.015118
Badness: 0.015118
Line 2,398: Line 2,398:
POTE generator: ~3/2 = 694.121
POTE generator: ~3/2 = 694.121


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


Badness: 0.026542
Badness: 0.026542
Line 2,413: Line 2,413:
POTE generator: ~3/2 = 690.548
POTE generator: ~3/2 = 690.548


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


Badness: 0.038577
Badness: 0.038577
Line 2,428: Line 2,428:
POTE generator: ~3/2 = 699.001
POTE generator: ~3/2 = 699.001


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


Badness: 0.043062
Badness: 0.043062
Line 2,447: Line 2,447:
POTE generator: ~11/8 = 552.5303
POTE generator: ~11/8 = 552.5303


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


Badness: 0.070689
Badness: 0.070689
Line 2,460: Line 2,460:
POTE generator: ~11/8 = 552.5324
POTE generator: ~11/8 = 552.5324


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


Badness: 0.040047
Badness: 0.040047
Line 2,473: Line 2,473:
POTE generator: ~11/8 = 552.6558
POTE generator: ~11/8 = 552.6558


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


Badness: 0.029499
Badness: 0.029499
Line 2,486: Line 2,486:
POTE generator: ~11/8 = 552.6382
POTE generator: ~11/8 = 552.6382


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


Badness: 0.023133
Badness: 0.023133
Line 2,505: Line 2,505:
[[POTE generator]]: ~48/35 = 552.2206
[[POTE generator]]: ~48/35 = 552.2206


{{Val list|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}


[[Badness]]: 0.116104
[[Badness]]: 0.116104
Line 2,518: Line 2,518:
POTE generator: ~11/8 = 552.0929
POTE generator: ~11/8 = 552.0929


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


Badness: 0.052099
Badness: 0.052099
Line 2,531: Line 2,531:
POTE generator: ~11/8 = 552.1498
POTE generator: ~11/8 = 552.1498


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


Badness: 0.031039
Badness: 0.031039
Line 2,544: Line 2,544:
POTE generator: ~11/8 = 552.1579
POTE generator: ~11/8 = 552.1579


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


Badness: 0.021260
Badness: 0.021260
Line 2,557: Line 2,557:
POTE generator: ~11/8 = 552.1196
POTE generator: ~11/8 = 552.1196


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


Badness: 0.016548
Badness: 0.016548
Line 2,574: Line 2,574:
[[POTE generator]]: ~7/6 = 275.794
[[POTE generator]]: ~7/6 = 275.794


{{Val list|legend=1| 26, 48c, 74, 174bd, 248bbd }}
{{Optimal ET sequence|legend=1| 26, 48c, 74, 174bd, 248bbd }}


[[Badness]]: 0.258825
[[Badness]]: 0.258825
Line 2,589: Line 2,589:
POTE generator: ~7/6 = 275.762
POTE generator: ~7/6 = 275.762


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


Badness: 0.101499
Badness: 0.101499
Line 2,604: Line 2,604:
POTE generator: ~7/6 = 275.774
POTE generator: ~7/6 = 275.774


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


Badness: 0.053482
Badness: 0.053482
Line 2,623: Line 2,623:
[[POTE generator]]: ~3/2 = 695.720
[[POTE generator]]: ~3/2 = 695.720


{{Val list|legend=1| 5, 45, 50 }}
{{Optimal ET sequence|legend=1| 5, 45, 50 }}


[[Badness]]: 0.102256
[[Badness]]: 0.102256
Line 2,638: Line 2,638:
POTE generator: ~3/2 = 696.536
POTE generator: ~3/2 = 696.536


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


Badness: 0.070378
Badness: 0.070378
Line 2,653: Line 2,653:
POTE generator: ~3/2 = 696.162
POTE generator: ~3/2 = 696.162


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


Badness: 0.048829
Badness: 0.048829
Line 2,670: Line 2,670:
[[POTE generator]]: ~8/7 = 238.396
[[POTE generator]]: ~8/7 = 238.396


{{Val list|legend=1| 19, 38, 57, 76, 95bc }}
{{Optimal ET sequence|legend=1| 19, 38, 57, 76, 95bc }}


[[Badness]]: 0.077023
[[Badness]]: 0.077023
Line 2,685: Line 2,685:
POTE generator: ~8/7 = 233.486
POTE generator: ~8/7 = 233.486


Optimal GPV sequence: {{Val list| 19, 38, 57, 76 }}
{{Optimal ET sequence|legend=1| 19, 38, 57, 76 }}


Badness: 0.066829
Badness: 0.066829
Line 2,700: Line 2,700:
POTE generator: ~8/7 = 234.890
POTE generator: ~8/7 = 234.890


Optimal GPV sequence: {{Val list| 19, 38, 57, 76 }}
{{Optimal ET sequence|legend=1| 19, 38, 57, 76 }}


Badness: 0.045844
Badness: 0.045844
Line 2,715: Line 2,715:
[[POTE generator]]: ~11/8 = 538.047
[[POTE generator]]: ~11/8 = 538.047


{{Val list|legend=1| 19, 38d }}
{{Optimal ET sequence|legend=1| 19, 38d }}


[[Badness]]: 0.036387
[[Badness]]: 0.036387
Line 2,730: Line 2,730:
POTE generator: ~11/8 = 537.061
POTE generator: ~11/8 = 537.061


Optimal GPV sequence: {{Val list| 19, 38df }}
{{Optimal ET sequence|legend=1| 19, 38df }}


Badness: 0.022933
Badness: 0.022933
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