Fifive 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]]: ~27/25 = 140.624
[[POTE generator]]: ~27/25 = 140.624


{{Val list|legend=1| 8, 26, 34, 94, 128 }}
{{Optimal ET sequence|legend=1| 8, 26, 34, 94, 128 }}


[[Badness]]: 0.205812
[[Badness]]: 0.205812
Line 27: Line 27:
[[POTE generator]]: ~27/25 = 140.349
[[POTE generator]]: ~27/25 = 140.349


{{Val list|legend=1| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


[[Badness]]: 0.086669
[[Badness]]: 0.086669
Line 40: Line 40:
POTE generator: ~12/11 = 140.587
POTE generator: ~12/11 = 140.587


Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


Badness: 0.040758
Badness: 0.040758
Line 53: Line 53:
POTE generator: ~12/11 = 140.554
POTE generator: ~12/11 = 140.554


Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


Badness: 0.024368
Badness: 0.024368
Line 66: Line 66:
POTE generator: ~12/11 = 140.405
POTE generator: ~12/11 = 140.405


Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


Badness: 0.018567
Badness: 0.018567
Line 79: Line 79:
[[POTE generator]]: ~27/25 = 139.909
[[POTE generator]]: ~27/25 = 139.909


{{Val list|legend=1| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}


[[Badness]]: 0.130589
[[Badness]]: 0.130589
Line 92: Line 92:
POTE generator: ~12/11 = 139.884
POTE generator: ~12/11 = 139.884


Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}


Badness: 0.080306
Badness: 0.080306
Line 105: Line 105:
POTE generator: ~12/11 = 139.867
POTE generator: ~12/11 = 139.867


Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}


Badness: 0.044253
Badness: 0.044253
Line 118: Line 118:
POTE generator: ~12/11 = 139.868
POTE generator: ~12/11 = 139.868


Optimal GPV sequence: {{Val list| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}


Badness: 0.029429
Badness: 0.029429
Line 131: Line 131:
[[POTE generator]]: ~27/25 = 140.754
[[POTE generator]]: ~27/25 = 140.754


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


[[Badness]]: 0.114143
[[Badness]]: 0.114143
Line 144: Line 144:
POTE generator: ~27/25 = 140.771
POTE generator: ~27/25 = 140.771


Optimal GPV sequence: {{Val list| 8de, 60, 68, 128, 196 }}
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }}


Badness: 0.120165
Badness: 0.120165
Line 157: Line 157:
POTE generator: ~13/12 = 140.760
POTE generator: ~13/12 = 140.760


Optimal GPV sequence: {{Val list| 8de, 60, 68, 128, 196f }}
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }}


Badness: 0.067365
Badness: 0.067365
Line 170: Line 170:
POTE generator: ~27/25 = 140.630
POTE generator: ~27/25 = 140.630


Optimal GPV sequence: {{Val list| 8d, 60e, 68, 128e }}
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}


Badness: 0.057268
Badness: 0.057268
Line 183: Line 183:
POTE generator: ~13/12 = 140.728
POTE generator: ~13/12 = 140.728


Optimal GPV sequence: {{Val list| 8d, 60e, 68, 128e }}
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}


Badness: 0.036128
Badness: 0.036128
Line 196: Line 196:
POTE generator: ~13/12 = 140.718
POTE generator: ~13/12 = 140.718


Optimal GPV sequence: {{Val list| 8d, 60e, 68, 128e }}
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}


Badness: 0.024796
Badness: 0.024796

Revision as of 16:06, 7 May 2023

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

Optimal ET sequence: 8, 26, 34, 94, 128

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

Optimal ET sequence: 8d, 26, 34d, 60d

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 ET sequence: 8d, 26, 34d, 60d

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 ET sequence: 8d, 26, 34d, 60d

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 ET sequence: 8d, 26, 34d, 60d

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

Optimal ET sequence: 8, 26, 34, 60

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 ET sequence: 8, 26, 34, 60

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 ET sequence: 8, 26, 34, 60

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 ET sequence: 8, 26, 34, 60

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

Optimal ET sequence: 8d, 60, 68, 128

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 ET sequence: 8de, 60, 68, 128, 196

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 ET sequence: 8de, 60, 68, 128, 196f

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

POTE generator: ~13/12 = 140.728

Optimal ET sequence: 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: [⟨4 4 6 7 11 12 14], ⟨0 5 7 9 6 6 5]]

POTE generator: ~13/12 = 140.718

Optimal ET sequence: 8d, 60e, 68, 128e

Badness: 0.024796

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