Fifive family: Difference between revisions
Cleanup; -fourfives (addressed in sensamagic clan) |
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[[Comma list]]: 9765625/9565938 | [[Comma list]]: 9765625/9565938 | ||
{{Mapping|legend=1| 2 2 3 | 0 5 7 }} | |||
[[POTE | : mapping generators: ~78125/50421, ~27/25 | ||
[[Optimal tuning]] ([[POTE]]): ~78125/50421 = 1\2, ~27/25 = 140.624 | |||
{{Optimal ET sequence|legend=1| 8, 26, 34, 94, 128 }} | {{Optimal ET sequence|legend=1| 8, 26, 34, 94, 128 }} | ||
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{{See also| Jubilismic clan #Crepuscular }} | {{See also| Jubilismic clan #Crepuscular }} | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 50/49, 4375/4374 | [[Comma list]]: 50/49, 4375/4374 | ||
{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }} | |||
{{Multival|legend=1|10 14 14 -1 -6 -7}} | {{Multival|legend=1| 10 14 14 -1 -6 -7 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349 | ||
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | ||
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Comma list: 50/49, 99/98, 864/847 | Comma list: 50/49, 99/98, 864/847 | ||
Mapping: | Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }} | ||
POTE | Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587 | ||
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | ||
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Comma list: 50/49, 78/77, 99/98, 144/143 | Comma list: 50/49, 78/77, 99/98, 144/143 | ||
Mapping: | Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }} | ||
POTE | Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554 | ||
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | ||
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Comma list: 50/49, 78/77, 85/84, 99/98, 144/143 | Comma list: 50/49, 78/77, 85/84, 99/98, 144/143 | ||
Mapping: | Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }} | ||
POTE | Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405 | ||
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }} | ||
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== Fifives == | == Fifives == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 875/864, 83349/81920 | [[Comma list]]: 875/864, 83349/81920 | ||
{{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/25 = 139.909 | ||
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | ||
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Comma list: 100/99, 385/384, 3969/3872 | Comma list: 100/99, 385/384, 3969/3872 | ||
Mapping: | Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }} | ||
POTE | Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884 | ||
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | ||
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Comma list: 100/99, 105/104, 144/143, 1352/1331 | Comma list: 100/99, 105/104, 144/143, 1352/1331 | ||
Mapping: | Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }} | ||
POTE | Optimal tuning (POTE): ~55/39 = 1\2, ~12/11 = 139.867 | ||
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | ||
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Comma list: 100/99, 105/104, 144/143, 170/169, 221/220 | Comma list: 100/99, 105/104, 144/143, 170/169, 221/220 | ||
Mapping: | Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }} | ||
POTE | Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868 | ||
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }} | ||
Revision as of 14:30, 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]]
- mapping generators: ~78125/50421, ~27/25
Optimal tuning (POTE): ~78125/50421 = 1\2, ~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 ]]
Optimal tuning (POTE): ~7/5 = 1\2, ~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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~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]]
Optimal tuning (POTE): ~567/400 = 1\2, ~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]]
Optimal tuning (POTE): ~63/44 = 1\2, ~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]]
Optimal tuning (POTE): ~55/39 = 1\2, ~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]]
Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868
Optimal ET sequence: 8, 26, 34, 60
Badness: 0.029429