Fifive family: Difference between revisions

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No edit summary
Line 56: Line 56:


Badness: 0.024368
Badness: 0.024368
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 78/77, 85/84, 99/98, 144/143
Mapping: [{{val|2 2 3 4 6 6 7}}, {{val|0 5 7 7 4 6 5}}]
POTE generator: ~12/11 = 140.405
Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
Badness: 0.018567


== Fifives ==
== Fifives ==
Line 68: Line 81:
{{Val list|legend=1| 8, 26, 34, 60 }}
{{Val list|legend=1| 8, 26, 34, 60 }}


Badness: 0.130589
[[Badness]]: 0.130589


=== 11-limit ===
=== 11-limit ===
Line 77: Line 90:
Mapping: [{{val|2 2 3 7 6}}, {{val|0 5 7 -6 4}}]
Mapping: [{{val|2 2 3 7 6}}, {{val|0 5 7 -6 4}}]


POTE generator: ~27/25 = 139.884
POTE generator: ~12/11 = 139.884


Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
Line 90: Line 103:
Mapping: [{{val|2 2 3 7 6 6}}, {{val|0 5 7 -6 4 6}}]
Mapping: [{{val|2 2 3 7 6 6}}, {{val|0 5 7 -6 4 6}}]


POTE generator: ~27/25 = 139.867
POTE generator: ~12/11 = 139.867


Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}


Badness: 0.044253
Badness: 0.044253
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 144/143, 170/169, 221/220
Mapping: [{{val|2 2 3 7 6 6 7}}, {{val|0 5 7 -6 4 6 5}}]
POTE generator: ~12/11 = 139.868
Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
Badness: 0.029429


== Fourfives ==
== Fourfives ==
Line 105: Line 131:
[[POTE generator]]: ~27/25 = 140.754
[[POTE generator]]: ~27/25 = 140.754


{{Val list| 8d, 60, 68, 128 }}
{{Val list|legend=1| 8d, 60, 68, 128 }}


[[Badness]]: 0.114143
[[Badness]]: 0.114143
Line 122: Line 148:
Badness: 0.120165
Badness: 0.120165


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 134: Line 160:


Badness: 0.067365
Badness: 0.067365
=== Quadrafives ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 1375/1372
Mapping: [{{val|4 4 6 7 11}}, {{val|0 5 7 9 6}}]
POTE generator: ~27/25 = 140.630
Optimal GPV sequence: {{Val list| 8d, 60e, 68, 128e }}
Badness: 0.057268
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 245/243, 275/273
Mapping: [{{val|4 4 6 7 11 12}}, {{val|0 5 7 9 6 6}}]
POTE generator: ~13/12 = 140.728
Optimal GPV sequence: {{Val list| 8d, 60e, 68, 128e }}
Badness: 0.036128
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243
Mapping: [{{val|4 4 6 7 11 12 14}}, {{val|0 5 7 9 6 6 5}}]
POTE generator: ~13/12 = 140.718
Optimal GPV sequence: {{Val list| 8d, 60e, 68, 128e }}
Badness: 0.024796


[[Category:Theory]]
[[Category:Theory]]

Revision as of 13:26, 18 May 2022

This tempers out the fifive comma, 9765625/9565938 = [-1 -14 10⟩.

Fifive

Subgroup: 2.3.5

Comma: 9765625/9565938

Mapping: [⟨2 2 3], ⟨0 5 7]]

POTE generator: ~27/25 = 140.624

Template:Val list

Badness: 0.205812

Crepuscular

See also: Jubilismic clan § Crepuscular

Subgroup: 2.3.5.7

Comma list: 50/49, 4375/4374

Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]

Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]

POTE generator: ~27/25 = 140.349

Template:Val list

Badness: 0.086669

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 864/847

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

POTE generator: ~12/11 = 140.587

Optimal GPV sequence: Template:Val list

Badness: 0.040758

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 78/77, 99/98, 144/143

Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]

POTE generator: ~12/11 = 140.554

Optimal GPV sequence: Template:Val list

Badness: 0.024368

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 50/49, 78/77, 85/84, 99/98, 144/143

Mapping: [⟨2 2 3 4 6 6 7], ⟨0 5 7 7 4 6 5]]

POTE generator: ~12/11 = 140.405

Optimal GPV sequence: Template:Val list

Badness: 0.018567

Fifives

Subgroup: 2.3.5.7

Comma list: 875/864, 83349/81920

Mapping: [⟨2 2 3 7], ⟨0 5 7 -6]]

POTE generator: ~27/25 = 139.909

Template:Val list

Badness: 0.130589

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 3969/3872

Mapping: [⟨2 2 3 7 6], ⟨0 5 7 -6 4]]

POTE generator: ~12/11 = 139.884

Optimal GPV sequence: Template:Val list

Badness: 0.080306

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 144/143, 1352/1331

Mapping: [⟨2 2 3 7 6 6], ⟨0 5 7 -6 4 6]]

POTE generator: ~12/11 = 139.867

Optimal GPV sequence: Template:Val list

Badness: 0.044253

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 100/99, 105/104, 144/143, 170/169, 221/220

Mapping: [⟨2 2 3 7 6 6 7], ⟨0 5 7 -6 4 6 5]]

POTE generator: ~12/11 = 139.868

Optimal GPV sequence: Template:Val list

Badness: 0.029429

Fourfives

Subgroup: 2.3.5.7

Comma list: 245/243, 235298/234375

Mapping: [⟨4 4 6 7], ⟨0 5 7 9]]

POTE generator: ~27/25 = 140.754

Template:Val list

Badness: 0.114143

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 235298/234375

Mapping: [⟨4 4 6 7 19], ⟨0 5 7 9 -11]]

POTE generator: ~27/25 = 140.771

Optimal GPV sequence: Template:Val list

Badness: 0.120165

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 385/384, 20000/19773

Mapping: [⟨4 4 6 7 19 12], ⟨0 5 7 9 -11 6]]

POTE generator: ~13/12 = 140.760

Optimal GPV sequence: Template:Val list

Badness: 0.067365

Quadrafives

Subgroup: 2.3.5.7.11

Comma list: 121/120, 245/243, 1375/1372

Mapping: [⟨4 4 6 7 11], ⟨0 5 7 9 6]]

POTE generator: ~27/25 = 140.630

Optimal GPV sequence: Template:Val list

Badness: 0.057268

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 196/195, 245/243, 275/273

Mapping: [⟨4 4 6 7 11 12], ⟨0 5 7 9 6 6]]

POTE generator: ~13/12 = 140.728

Optimal GPV sequence: Template:Val list

Badness: 0.036128

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 170/169, 196/195, 245/243

Mapping: [⟨4 4 6 7 11 12 14], ⟨0 5 7 9 6 6 5]]

POTE generator: ~13/12 = 140.718

Optimal GPV sequence: Template:Val list

Badness: 0.024796

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