Fifive family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
Cleanup; -fourfives (addressed in sensamagic clan) |
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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 }} | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 121: | Line 126: | ||
Badness: 0.029429 | Badness: 0.029429 | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Fifive family| ]] <!-- main article --> | |||
[[Category:Fifive| ]] <!-- key article --> | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
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:
- Fourfives (+245/243) → Sensamagic clan
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 sequence: 8, 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 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