Unicorn family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 10: Line 10:
[[POTE generator]]: ~250/243 = 62.458
[[POTE generator]]: ~250/243 = 62.458


{{Val list|legend=1| 19, 58, 77, 96, 173, 269 }}
{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}


[[Badness]]: 0.150487
[[Badness]]: 0.150487
Line 25: Line 25:
[[POTE generator]]: ~28/27 = 62.278
[[POTE generator]]: ~28/27 = 62.278


{{Val list|legend=1| 19, 39d, 58, 77, 135c }}
{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c }}


[[Badness]]: 0.040913
[[Badness]]: 0.040913
Line 38: Line 38:
POTE generator: ~28/27 = 62.101
POTE generator: ~28/27 = 62.101


Optimal GPV sequence: {{Val list| 19, 39d, 58 }}
{{Optimal ET sequence|legend=1| 19, 39d, 58 }}


Badness: 0.039156
Badness: 0.039156
Line 51: Line 51:
POTE generator: ~28/27 = 62.119
POTE generator: ~28/27 = 62.119


Optimal GPV sequence: {{Val list| 19, 39df, 58 }}
{{Optimal ET sequence|legend=1| 19, 39df, 58 }}


Badness: 0.023667
Badness: 0.023667
Line 64: Line 64:
POTE generator: ~28/27 = 62.431
POTE generator: ~28/27 = 62.431


Optimal GPV sequence: {{Val list| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=1| 19, 58e, 77, 96d, 173d }}


Badness: 0.065940
Badness: 0.065940
Line 77: Line 77:
POTE generator: ~28/27 = 62.434
POTE generator: ~28/27 = 62.434


Optimal GPV sequence: {{Val list| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=1| 19, 58e, 77, 96d, 173d }}


Badness: 0.036155
Badness: 0.036155
Line 90: Line 90:
POTE generator: ~28/27 = 62.196
POTE generator: ~28/27 = 62.196


Optimal GPV sequence: {{Val list| 58, 77, 135c, 193c, 328cc }}
{{Optimal ET sequence|legend=1| 58, 77, 135c, 193c, 328cc }}


Badness: 0.041426
Badness: 0.041426
Line 103: Line 103:
POTE generator: ~28/27 = 62.197
POTE generator: ~28/27 = 62.197


Optimal GPV sequence: {{Val list| 58, 77, 135c, 193cf, 328ccff }}
{{Optimal ET sequence|legend=1| 58, 77, 135c, 193cf, 328ccff }}


Badness: 0.022842
Badness: 0.022842
Line 116: Line 116:
POTE generator: ~28/27 = 62.292
POTE generator: ~28/27 = 62.292


Optimal GPV sequence: {{Val list| 58, 96d, 154, 212ce, 366cce }}
{{Optimal ET sequence|legend=1| 58, 96d, 154, 212ce, 366cce }}


Badness: 0.052757
Badness: 0.052757
Line 129: Line 129:
POTE generator: ~28/27 = 62.301
POTE generator: ~28/27 = 62.301


Optimal GPV sequence: {{Val list| 58, 96d, 154, 366ccef }}
{{Optimal ET sequence|legend=1| 58, 96d, 154, 366ccef }}


Badness: 0.028795
Badness: 0.028795
Line 144: Line 144:
[[POTE generator]]: ~21/20 = 62.920
[[POTE generator]]: ~21/20 = 62.920


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


[[Badness]]: 0.081864
[[Badness]]: 0.081864
Line 157: Line 157:
POTE generator: ~21/20 = 62.874
POTE generator: ~21/20 = 62.874


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


Badness: 0.059319
Badness: 0.059319
Line 170: Line 170:
POTE generator: ~21/20 = 63.043
POTE generator: ~21/20 = 63.043


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


Badness: 0.039343
Badness: 0.039343

Revision as of 16:04, 7 May 2023

The unicorn family tempers out the unicorn comma, 1594323/1562500 = [-2 13 -8⟩.

Unicorn

Subgroup: 2.3.5

Comma list: 1594323/1562500

Mapping: [⟨1 2 3], ⟨0 -8 -13]]

POTE generator: ~250/243 = 62.458

Optimal ET sequence: 19, 58, 77, 96, 173, 269

Badness: 0.150487

Septimal unicorn

Subgroup: 2.3.5.7

Comma list: 126/125, 10976/10935

Mapping: [⟨1 2 3 4], ⟨0 -8 -13 -23]]

Wedgie: ⟨⟨ 8 13 23 2 14 17 ]]

POTE generator: ~28/27 = 62.278

Optimal ET sequence: 19, 39d, 58, 77, 135c

Badness: 0.040913

Alicorn

Subgroup: 2.3.5.7.11

Comma list: 126/125, 540/539, 896/891

Mapping: [⟨1 2 3 4 3], ⟨0 -8 -13 -23 9]]

POTE generator: ~28/27 = 62.101

Optimal ET sequence: 19, 39d, 58

Badness: 0.039156

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 144/143, 196/195, 676/675

Mapping: [⟨1 2 3 4 3 5], ⟨0 -8 -13 -23 9 -25]]

POTE generator: ~28/27 = 62.119

Optimal ET sequence: 19, 39df, 58

Badness: 0.023667

Camahueto

Subgroup: 2.3.5.7.11

Comma list: 126/125, 385/384, 10976/10935

Mapping: [⟨1 2 3 4 2], ⟨0 -8 -13 -23 28]]

POTE generator: ~28/27 = 62.431

Optimal ET sequence: 19, 58e, 77, 96d, 173d

Badness: 0.065940

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 385/384, 676/675

Mapping: [⟨1 2 3 4 2 5], ⟨0 -8 -13 -23 28 -25]]

POTE generator: ~28/27 = 62.434

Optimal ET sequence: 19, 58e, 77, 96d, 173d

Badness: 0.036155

Qilin

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 10976/10935

Mapping: [⟨1 2 3 4 6], ⟨0 -8 -13 -23 -49]]

POTE generator: ~28/27 = 62.196

Optimal ET sequence: 58, 77, 135c, 193c, 328cc

Badness: 0.041426

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 196/195, 2200/2197

Mapping: [⟨1 2 3 4 6 5], ⟨0 -8 -13 -23 -49 -25]]

POTE generator: ~28/27 = 62.197

Optimal ET sequence: 58, 77, 135c, 193cf, 328ccff

Badness: 0.022842

Monocerus

Subgroup: 2.3.5.7.11

Comma list: 126/125, 243/242, 5488/5445

Mapping: [⟨2 4 6 8 9], ⟨0 -8 -13 -23 -20]]

POTE generator: ~28/27 = 62.292

Optimal ET sequence: 58, 96d, 154, 212ce, 366cce

Badness: 0.052757

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 364/363, 676/675

Mapping: [⟨2 4 6 8 9 10], ⟨0 -8 -13 -23 -20 -25]]

POTE generator: ~28/27 = 62.301

Optimal ET sequence: 58, 96d, 154, 366ccef

Badness: 0.028795

Rhinoceros

Subgroup: 2.3.5.7

Comma list: 49/48, 4375/4374

Mapping: [⟨1 2 3 3], ⟨0 -8 -13 -4]]

Wedgie: ⟨⟨ 8 13 4 2 -16 -27 ]]

POTE generator: ~21/20 = 62.920

Optimal ET sequence: 1c, 19

Badness: 0.081864

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -8 -13 -4 -10]]

POTE generator: ~21/20 = 62.874

Optimal ET sequence: 1ce, 19

Badness: 0.059319

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 78/77, 100/99, 126/121

Mapping: [⟨1 2 3 3 4 4], ⟨0 -8 -13 -4 -10 -6]]

POTE generator: ~21/20 = 63.043

Optimal ET sequence: 1ce, 19

Badness: 0.039343

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