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Semicomma family: Difference between revisions

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5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 17: Line 17:
* 5-odd-limit diamond monotone and tradeoff: ~75/64 = [271.229, 271.708]
* 5-odd-limit diamond monotone and tradeoff: ~75/64 = [271.229, 271.708]


{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
{{Optimal ET sequence|legend=1| 22, 31, 53, 190, 243, 296, 645c }}


[[Badness]]: 0.040807
[[Badness]]: 0.040807
Line 64: Line 64:
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.


{{Val list|legend=1| 9, 22, 31, 53, 84, 137, 221d, 358d }}
{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137, 221d, 358d }}


[[Badness]]: 0.020735
[[Badness]]: 0.020735
Line 87: Line 87:
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.727]
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.727]


Optimal GPV sequence: {{Val list| 9, 22, 31, 53, 84e }}
{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84e }}


Badness: 0.015231
Badness: 0.015231
Line 105: Line 105:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 271.698]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 271.698]


Optimal GPV sequence: {{Val list| 22, 31, 53, 84e, 137e }}
{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 137e }}


Badness: 0.019718
Badness: 0.019718
Line 118: Line 118:
POTE generator: ~7/6 = 271.301
POTE generator: ~7/6 = 271.301


Optimal GPV sequence: {{Val list| 9, 22, 31f }}
{{Optimal ET sequence|legend=1| 9, 22, 31f }}


Badness: 0.023086
Badness: 0.023086
Line 136: Line 136:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.727]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 272.727]


Optimal GPV sequence: {{Val list| 22f, 31 }}
{{Optimal ET sequence|legend=1| 22f, 31 }}


Badness: 0.019931
Badness: 0.019931
Line 154: Line 154:
* 13- and 15-odd-limit diamond monotone and tradeoff: ~13/12 = [135.484, 136.364]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~13/12 = [135.484, 136.364]


Optimal GPV sequence: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
{{Optimal ET sequence|legend=1| 9, 35bd, 44, 53, 62, 115ef, 168eef }}


Badness: 0.027120
Badness: 0.027120
Line 172: Line 172:
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 271.698]
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [270.968, 271.698]


Optimal GPV sequence: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}
{{Optimal ET sequence|legend=1| 31, 84, 115, 376b, 491bd, 606bde }}


Badness: 0.031438
Badness: 0.031438
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POTE generator: ~55/36 = 735.752
POTE generator: ~55/36 = 735.752


Optimal GPV sequence: {{Val list| 31, 106, 137, 442bd }}
{{Optimal ET sequence|legend=1| 31, 106, 137, 442bd }}


Badness: 0.038377
Badness: 0.038377
Line 202: Line 202:
[[POTE generator]]: ~75/64 = 271.607
[[POTE generator]]: ~75/64 = 271.607


{{Val list|legend=1| 53, 137d, 190, 243 }}
{{Optimal ET sequence|legend=1| 53, 137d, 190, 243 }}


[[Badness]]: 0.088355
[[Badness]]: 0.088355
Line 219: Line 219:
[[POTE generator]]: ~448/375 = 309.472
[[POTE generator]]: ~448/375 = 309.472


{{Val list|legend=1| 31, 97, 128, 159, 190 }}
{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}


[[Badness]]: 0.080575
[[Badness]]: 0.080575
Line 232: Line 232:
POTE generator: ~448/375 = 309.471
POTE generator: ~448/375 = 309.471


Optimal GPV sequence: {{Val list| 31, 97, 128, 159, 190 }}
{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}


Badness: 0.029807
Badness: 0.029807
Line 249: Line 249:
[[POTE generator]]: ~8/7 = 232.094
[[POTE generator]]: ~8/7 = 232.094


{{Val list|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }}
{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }}


[[Badness]]: 0.075754
[[Badness]]: 0.075754
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POTE generator: ~8/7 = 232.083
POTE generator: ~8/7 = 232.083


Optimal GPV sequence: {{Val list| 31, 119, 150, 181, 212, 455ee, 667cdee }}
{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 455ee, 667cdee }}


Badness: 0.036493
Badness: 0.036493
Line 279: Line 279:
[[POTE generator]]: ~2625/2048 = 425.673
[[POTE generator]]: ~2625/2048 = 425.673


{{Val list|legend=1| 31, 172, 203, 234, 265, 296 }}
{{Optimal ET sequence|legend=1| 31, 172, 203, 234, 265, 296 }}


[[Badness]]: 0.143488
[[Badness]]: 0.143488
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POTE generator: ~2625/2048 = 425.679
POTE generator: ~2625/2048 = 425.679


Optimal GPV sequence: {{Val list| 31, 172e, 203e, 234, 265, 296, 919bc, 1215bcc, 1511bcc }}
{{Optimal ET sequence|legend=1| 31, 172e, 203e, 234, 265, 296, 919bc, 1215bcc, 1511bcc }}


Badness: 0.052774
Badness: 0.052774
Line 309: Line 309:
[[POTE generator]]: ~405/392 = 54.324
[[POTE generator]]: ~405/392 = 54.324


{{Val list|legend=1| 22, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}
{{Optimal ET sequence|legend=1| 22, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}


[[Badness]]: 0.168897
[[Badness]]: 0.168897
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POTE generator: ~33/32 = 54.334
POTE generator: ~33/32 = 54.334


Optimal GPV sequence: {{Val list| 22, 221, 243, 265, 773ce, 1038ccee, 1303ccee }}
{{Optimal ET sequence|legend=1| 22, 221, 243, 265, 773ce, 1038ccee, 1303ccee }}


Badness: 0.097202
Badness: 0.097202
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POTE generator: ~405/392 = 54.316
POTE generator: ~405/392 = 54.316


Optimal GPV sequence: {{Val list| 22, 199d, 221e, 243e }}
{{Optimal ET sequence|legend=1| 22, 199d, 221e, 243e }}


Badness: 0.078657
Badness: 0.078657
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