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Magic family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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[[Algebraic generator]]: Terzbirat, the positive root of 9''x''<sup>2</sup> - 8''x'' - 4 = (4 + 2√13)/9; approximately 380.3175 [[cent]]s.
[[Algebraic generator]]: Terzbirat, the positive root of 9''x''<sup>2</sup> - 8''x'' - 4 = (4 + 2√13)/9; approximately 380.3175 [[cent]]s.


{{Val list|legend=1| 19, 41, 60, 221c, 281c }}
{{Optimal ET sequence|legend=1| 19, 41, 60, 221c, 281c }}


[[Badness]]: 0.039163
[[Badness]]: 0.039163
Line 80: Line 80:
[[Algebraic generator]]: Tirzbirat or Septimage, the real root of 5''x''<sup>5</sup> + 4''x'' - 20, 380.7604 cents.
[[Algebraic generator]]: Tirzbirat or Septimage, the real root of 5''x''<sup>5</sup> + 4''x'' - 20, 380.7604 cents.


{{Val list|legend=1| 19, 41, 142cd, 183cd, 224cd }}
{{Optimal ET sequence|legend=1| 19, 41, 142cd, 183cd, 224cd }}


[[Badness]]: 0.018918
[[Badness]]: 0.018918
Line 104: Line 104:
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]


Optimal GPV sequence: {{Val list| 19, 22, 41, 104, 145c }}
{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145c }}


Badness: 0.020352
Badness: 0.020352
Line 122: Line 122:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]


Optimal GPV sequence: {{Val list| 19, 22f, 41, 265cdef }}
{{Optimal ET sequence|legend=1| 19, 22f, 41, 265cdef }}


Badness: 0.021509
Badness: 0.021509
Line 135: Line 135:
POTE generator: ~5/4 = 380.604
POTE generator: ~5/4 = 380.604


Optimal GPV sequence: {{Val list| 19, 22f, 41 }}
{{Optimal ET sequence|legend=1| 19, 22f, 41 }}


Badness: 0.020633
Badness: 0.020633
Line 150: Line 150:
POTE generator: ~5/4 = 380.416
POTE generator: ~5/4 = 380.416


Optimal GPV sequence: {{Val list| 19, 22f, 41 }}
{{Optimal ET sequence|legend=1| 19, 22f, 41 }}


==== Sorcery ====
==== Sorcery ====
Line 161: Line 161:
POTE generator: ~5/4 = 380.477
POTE generator: ~5/4 = 380.477


Optimal GPV sequence: {{Val list| 19, 22, 41f }}
{{Optimal ET sequence|legend=1| 19, 22, 41f }}


Badness: 0.025829
Badness: 0.025829
Line 174: Line 174:
POTE generator: ~5/4 = 380.729
POTE generator: ~5/4 = 380.729


Optimal GPV sequence: {{Val list| 19, 22, 41f }}
{{Optimal ET sequence|legend=1| 19, 22, 41f }}


Badness: 0.023768
Badness: 0.023768
Line 187: Line 187:
POTE generator: ~5/4 = 380.787
POTE generator: ~5/4 = 380.787


Optimal GPV sequence: {{Val list| 19f, 22, 41, 63, 104 }}
{{Optimal ET sequence|legend=1| 19f, 22, 41, 63, 104 }}


Badness: 0.025275
Badness: 0.025275
Line 200: Line 200:
POTE generator: ~5/4 = 380.827
POTE generator: ~5/4 = 380.827


Optimal GPV sequence: {{Val list| 19f, 22, 41, 63, 104g }}
{{Optimal ET sequence|legend=1| 19f, 22, 41, 63, 104g }}


Badness: 0.022032
Badness: 0.022032
Line 213: Line 213:
POTE generator: ~5/4 = 380.508
POTE generator: ~5/4 = 380.508


Optimal GPV sequence: {{Val list| 22, 60, 82 }}
{{Optimal ET sequence|legend=1| 22, 60, 82 }}


Badness: 0.055443
Badness: 0.055443
Line 226: Line 226:
POTE generator: ~5/4 = 380.508
POTE generator: ~5/4 = 380.508


Optimal GPV sequence: {{Val list| 22, 60, 82 }}
{{Optimal ET sequence|legend=1| 22, 60, 82 }}


Badness: 0.035654
Badness: 0.035654
Line 239: Line 239:
POTE generator: ~5/4 = 381.019
POTE generator: ~5/4 = 381.019


Optimal GPV sequence: {{Val list| 19e, 22, 41e, 63e }}
{{Optimal ET sequence|legend=1| 19e, 22, 41e, 63e }}


Badness: 0.027109
Badness: 0.027109
Line 252: Line 252:
POTE generator: ~5/4 = 380.520
POTE generator: ~5/4 = 380.520


Optimal GPV sequence: {{Val list| 19e, 22, 41ef }}
{{Optimal ET sequence|legend=1| 19e, 22, 41ef }}


Badness: 0.025522
Badness: 0.025522
Line 265: Line 265:
POTE generator: ~5/4 = 380.619
POTE generator: ~5/4 = 380.619


Optimal GPV sequence: {{Val list| 19eg, 22, 41efg }}
{{Optimal ET sequence|legend=1| 19eg, 22, 41efg }}


Badness: 0.020201
Badness: 0.020201
Line 278: Line 278:
POTE generator: ~5/4 = 380.483
POTE generator: ~5/4 = 380.483


Optimal GPV sequence: {{Val list| 19e, 22f, 41e }}
{{Optimal ET sequence|legend=1| 19e, 22f, 41e }}


Badness: 0.026089
Badness: 0.026089
Line 291: Line 291:
POTE generator: ~5/4 = 380.604
POTE generator: ~5/4 = 380.604


Optimal GPV sequence: {{Val list| 19eg, 22f, 41eg }}
{{Optimal ET sequence|legend=1| 19eg, 22f, 41eg }}


Badness: 0.020274
Badness: 0.020274
Line 304: Line 304:
POTE generator: ~5/4 = 379.642
POTE generator: ~5/4 = 379.642


Optimal GPV sequence: {{Val list| 3de, 19, 41ee, 60ee }}
{{Optimal ET sequence|legend=1| 3de, 19, 41ee, 60ee }}


Badness: 0.039282
Badness: 0.039282
Line 317: Line 317:
POTE generator: ~5/4 = 379.791
POTE generator: ~5/4 = 379.791


Optimal GPV sequence: {{Val list| 3def, 19, 41ee, 60ee }}
{{Optimal ET sequence|legend=1| 3def, 19, 41ee, 60ee }}


Badness: 0.031938
Badness: 0.031938
Line 330: Line 330:
POTE generator: ~5/4 = 379.116
POTE generator: ~5/4 = 379.116


Optimal GPV sequence: {{Val list| 3de, 19 }}
{{Optimal ET sequence|legend=1| 3de, 19 }}


Badness: 0.033317
Badness: 0.033317
Line 343: Line 343:
POTE generator: ~5/4 = 380.232
POTE generator: ~5/4 = 380.232


Optimal GPV sequence: {{Val list| 41, 60e, 101cd, 243cde }}
{{Optimal ET sequence|legend=1| 41, 60e, 101cd, 243cde }}


Badness: 0.030706
Badness: 0.030706
Line 356: Line 356:
POTE generator: ~5/4 = 380.189
POTE generator: ~5/4 = 380.189


Optimal GPV sequence: {{Val list| 41, 60e, 101cd }}
{{Optimal ET sequence|legend=1| 41, 60e, 101cd }}


Badness: 0.023547
Badness: 0.023547
Line 369: Line 369:
POTE generator: ~5/4 = 380.114
POTE generator: ~5/4 = 380.114


Optimal GPV sequence: {{Val list| 41, 60e, 101cd, 161cde }}
{{Optimal ET sequence|legend=1| 41, 60e, 101cd, 161cde }}


Badness: 0.020756
Badness: 0.020756
Line 382: Line 382:
POTE generator: ~5/4 = 380.233
POTE generator: ~5/4 = 380.233


Optimal GPV sequence: {{Val list| 22, 38d, 60e, 142cde }}
{{Optimal ET sequence|legend=1| 22, 38d, 60e, 142cde }}


Badness: 0.035864
Badness: 0.035864
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POTE generator: ~5/4 = 379.920
POTE generator: ~5/4 = 379.920


Optimal GPV sequence: {{Val list| 22f, 60e }}
{{Optimal ET sequence|legend=1| 22f, 60e }}


Badness: 0.034551
Badness: 0.034551
Line 408: Line 408:
POTE generator: ~14/11 = 409.910
POTE generator: ~14/11 = 409.910


Optimal GPV sequence: {{Val list| 38d, 41, 120cd, 161cd, 202cd }}
{{Optimal ET sequence|legend=1| 38d, 41, 120cd, 161cd, 202cd }}


Badness: 0.038519
Badness: 0.038519
Line 421: Line 421:
POTE generator: ~14/11 = 410.004
POTE generator: ~14/11 = 410.004


Optimal GPV sequence: {{Val list| 41, 79d, 120cd }}
{{Optimal ET sequence|legend=1| 41, 79d, 120cd }}


Badness: 0.030280
Badness: 0.030280
Line 447: Line 447:
* 9-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947
* 9-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947


{{Val list|legend=1| 16, 19, 73bcd, 92bcd }}
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcd }}


[[Badness]]: 0.056206
[[Badness]]: 0.056206
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* 11-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947


Optimal GPV sequence: {{Val list| 16, 19, 35, 54bd }}
{{Optimal ET sequence|legend=1| 16, 19, 35, 54bd }}


Badness: 0.048038
Badness: 0.048038
Line 478: Line 478:
POTE generator: ~5/4 = 377.653
POTE generator: ~5/4 = 377.653


Optimal GPV sequence: {{Val list| 16, 19, 35f, 54bdf }}
{{Optimal ET sequence|legend=1| 16, 19, 35f, 54bdf }}


Badness: 0.030386
Badness: 0.030386
Line 491: Line 491:
POTE generator: ~5/4 = 377.832
POTE generator: ~5/4 = 377.832


Optimal GPV sequence: {{Val list| 3, 10bd, 13bd, 16, 19e }}
{{Optimal ET sequence|legend=1| 3, 10bd, 13bd, 16, 19e }}


Badness: 0.046970
Badness: 0.046970
Line 504: Line 504:
POTE generator: ~5/4 = 377.838
POTE generator: ~5/4 = 377.838


Optimal GPV sequence: {{Val list| 3, 10bd, 13bd, 16, 19e }}
{{Optimal ET sequence|legend=1| 3, 10bd, 13bd, 16, 19e }}


Badness: 0.028732
Badness: 0.028732
Line 519: Line 519:
[[POTE generator]]: ~63/50 = 410.108
[[POTE generator]]: ~63/50 = 410.108


{{Val list|legend=1| 38, 41, 161c, 202c, 243c, 284c }}
{{Optimal ET sequence|legend=1| 38, 41, 161c, 202c, 243c, 284c }}


[[Badness]]: 0.107115
[[Badness]]: 0.107115
Line 534: Line 534:
[[POTE generator]]: ~147/100 = 673.290
[[POTE generator]]: ~147/100 = 673.290


{{Val list|legend=1| 16, 25, 41, 139c, 180c, 221c, 262c }}
{{Optimal ET sequence|legend=1| 16, 25, 41, 139c, 180c, 221c, 262c }}


[[Badness]]: 0.098334
[[Badness]]: 0.098334
Line 547: Line 547:
Mapping: [{{val| 1 10 4 0 13 }}, {{val| 0 -15 -3 5 -17 }}]
Mapping: [{{val| 1 10 4 0 13 }}, {{val| 0 -15 -3 5 -17 }}]


Optimal GPV sequence: {{Val list| 16, 25e, 41, 98c, 139c, 180c }}
{{Optimal ET sequence|legend=1| 16, 25e, 41, 98c, 139c, 180c }}


Badness: 0.045623
Badness: 0.045623
Line 560: Line 560:
POTE generator: ~22/15 = 673.359
POTE generator: ~22/15 = 673.359


Optimal GPV sequence: {{Val list| 16, 25e, 41, 98c, 139cf }}
{{Optimal ET sequence|legend=1| 16, 25e, 41, 98c, 139cf }}


Badness: 0.033081
Badness: 0.033081
Line 575: Line 575:
[[POTE generator]]: ~28/25 = 204.987
[[POTE generator]]: ~28/25 = 204.987


{{Val list|legend=1| 6, 35, 41, 158cd, 199cd, 240cd, 281cd }}
{{Optimal ET sequence|legend=1| 6, 35, 41, 158cd, 199cd, 240cd, 281cd }}


[[Badness]]: 0.127422
[[Badness]]: 0.127422
Line 588: Line 588:
POTE generator: ~28/25 = 204.956
POTE generator: ~28/25 = 204.956


Optimal GPV sequence: {{Val list| 6, 35, 41, 199cde, 240cde, 281cde }}
{{Optimal ET sequence|legend=1| 6, 35, 41, 199cde, 240cde, 281cde }}


Badness: 0.061572
Badness: 0.061572
Line 601: Line 601:
POTE generator: ~28/25 = 205.028
POTE generator: ~28/25 = 205.028


Optimal GPV sequence: {{Val list| 41, 117c, 158cd, 199cdef }}
{{Optimal ET sequence|legend=1| 41, 117c, 158cd, 199cdef }}


Badness: 0.044047
Badness: 0.044047
Line 616: Line 616:
[[POTE generator]]: ~5/4 = 379.7131
[[POTE generator]]: ~5/4 = 379.7131


{{Val list|legend=1| 25, 35, 60 }}
{{Optimal ET sequence|legend=1| 25, 35, 60 }}


[[Badness]]: 0.287190
[[Badness]]: 0.287190
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