Quince clan: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]: ~343/320 = 116.291 | [[POTE generator]]: ~343/320 = 116.291 | ||
{{ | {{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }} | ||
====2.5.7.13==== | ====2.5.7.13==== | ||
Subgroup: 2.5.7.13 | Subgroup: 2.5.7.13 | ||
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[[Tp tuning|POL2 generator]]: ~14/13 = 116.094 | [[Tp tuning|POL2 generator]]: ~14/13 = 116.094 | ||
{{ | {{Optimal ET sequence|legend=1| 10, 21, 31}} | ||
====2.5.7.13.17==== | ====2.5.7.13.17==== | ||
Subgroup: 2.5.7.13.17 | Subgroup: 2.5.7.13.17 | ||
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[[Tp tuning|POL2 generator]]: ~14/13 = 115.769 | [[Tp tuning|POL2 generator]]: ~14/13 = 115.769 | ||
{{ | {{Optimal ET sequence|legend=1| 10, 21, 31}} | ||
====2.5.7.13.17.19==== | ====2.5.7.13.17.19==== | ||
Subgroup: 2.5.7.13.17.19 | Subgroup: 2.5.7.13.17.19 | ||
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[[Tp tuning|POL2 generator]]: ~14/13 = 115.716 | [[Tp tuning|POL2 generator]]: ~14/13 = 115.716 | ||
{{ | {{Optimal ET sequence|legend=1| 10, 21, 31, 52f}} | ||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Quince clan| ]] <!-- main article --> | [[Category:Quince clan| ]] <!-- main article --> | ||
Revision as of 18:21, 7 May 2023
The quince clan tempers out quince, the no-threes comma [-15 0 -2 7⟩ = 823543/819200. Quince temperaments include:
- Casablanca ({126/125, 589824/588245})
- Miracle ({225/224, 1029/1024})
- Quincy ({4375/4374, 823543/819200})
- Birds ({3136/3125, 823543/819200})
- Octowerck ({321489/320000, 420175/419904})
- Cotoneum ({10976/10935, 823543/819200})
- Countermiracle ({6144/6125, 50421/50000})
Mercy
Mercy is the no-3 version of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of 31edo. Two generators make an 8/7; five generators make a 7/5.
Subgroup: 2.5.7
Comma list: 823543/819200
Sval mapping: [⟨1 3 3], ⟨0 -7 -2]]
Mapping generators: ~2, ~343/320
Gencom mapping: [⟨1 0 3 3], ⟨0 0 -7 -2]] Gencom: [2 343/320; 823543/819200]
POTE generator: ~343/320 = 116.291
Optimal ET sequence: 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd
2.5.7.13
Subgroup: 2.5.7.13
Comma list: 343/338, 640/637
Gencom: [2 14/13; 343/338 640/637]
Gencom mapping: [⟨1 0 3 3 0 4], ⟨0 0 -7 -2 0 -3]]
Sval mapping: [⟨1 3 3 4], ⟨0 -7 -2 -3]]
POL2 generator: ~14/13 = 116.094
Optimal ET sequence: 10, 21, 31
2.5.7.13.17
Subgroup: 2.5.7.13.17
Comma list: 170/169, 224/221, 640/637
Gencom: [2 14/13; 170/169 224/221 640/637]
Gencom mapping: [⟨1 0 3 3 0 4 4], ⟨0 0 -7 -2 0 -3 1]]
Sval mapping: [⟨1 3 3 4 4], ⟨0 -7 -2 -3 1]]
POL2 generator: ~14/13 = 115.769
Optimal ET sequence: 10, 21, 31
2.5.7.13.17.19
Subgroup: 2.5.7.13.17.19
Comma list: 170/169, 343/338, 640/637, 16384/16055
Gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]
Gencom mapping: [⟨1 0 3 3 0 4 4 3], ⟨0 0 -7 -2 0 -3 1 13]]
Sval mapping: [⟨1 3 3 4 4 3], ⟨0 -7 -2 -3 1 13]]
POL2 generator: ~14/13 = 115.716
Optimal ET sequence: 10, 21, 31, 52f