Fifive family: Difference between revisions

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Cmloegcmluin (talk | contribs)
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Cleanup; -fourfives (addressed in sensamagic clan)
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This tempers out the fifive comma, 9765625/9565938 = {{monzo|-1 -14 10}}.
The '''fifive family''' tempers out the [[fifive comma]], 9765625/9565938 = {{monzo| -1 -14 10 }}.
 
Temperaments discussed elsewhere include:
* ''[[Fourfives]]'' (+245/243) → [[Sensamagic clan #Fourfives|Sensamagic clan]]
 
Considered below are crepuscular and fifives.  


== Fifive ==
== Fifive ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 9765625/9565938
[[Comma list]]: 9765625/9565938


[[Mapping]]: [{{val|2 2 3}}, {{val|0 5 7}}]
[[Mapping]]: [{{val|2 2 3}}, {{val|0 5 7}}]
Line 15: Line 20:


== Crepuscular ==
== Crepuscular ==
{{see also|Jubilismic clan #Crepuscular}}
{{See also| Jubilismic clan #Crepuscular }}


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 121: Line 126:


Badness: 0.029429
Badness: 0.029429
== Fourfives ==
Subgroup: 2.3.5.7
[[Comma list]]: 245/243, 235298/234375
[[Mapping]]: [{{val|4 4 6 7}}, {{val|0 5 7 9}}]
[[POTE generator]]: ~27/25 = 140.754
{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}
[[Badness]]: 0.114143
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 235298/234375
Mapping: [{{val|4 4 6 7 19}}, {{val|0 5 7 9 -11}}]
POTE generator: ~27/25 = 140.771
{{Optimal ET sequence|legend=1| 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: [{{val|4 4 6 7 19 12}}, {{val|0 5 7 9 -11 6}}]
POTE generator: ~13/12 = 140.760
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }}
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 ET sequence|legend=1| 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 ET sequence|legend=1| 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 ET sequence|legend=1| 8d, 60e, 68, 128e }}
Badness: 0.024796


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Fifive family| ]] <!-- main article -->
[[Category:Fifive| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Fifive]]

Revision as of 14:22, 22 August 2023

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

Temperaments discussed elsewhere include:

Considered below are crepuscular and fifives.

Fifive

Subgroup: 2.3.5

Comma list: 9765625/9565938

Mapping: [2 2 3], 0 5 7]]

POTE generator: ~27/25 = 140.624

Optimal ET sequence8, 26, 34, 94, 128

Badness: 0.205812

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 sequence8d, 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 sequence8d, 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 sequence8d, 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 sequence8d, 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 sequence8, 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 sequence8, 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 sequence8, 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 sequence8, 26, 34, 60

Badness: 0.029429