Quince clan: Difference between revisions
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No-3 quince now has a name |
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== Mercy == | == Mercy == | ||
Mercy is the no-3 version of miracle. Two generators make an [[8/7]]; five generators make a [[7/5]]. | 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|31edo.]] Two generators make an [[8/7]]; five generators make a [[7/5]]. | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
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Gencom mapping: [{{val| 1 0 3 3 }}, {{val| 0 0 -7 -2 }}] | Gencom mapping: [{{val| 1 0 3 3 }}, {{val| 0 0 -7 -2 }}] | ||
[[Category:Rank 2]] | |||
[[Gencom]]: [2 343/320; 823543/819200] | [[Gencom]]: [2 343/320; 823543/819200] | ||
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[[Category:Temperament clan]] | [[Category:Temperament clan]] | ||
[[Category:Quince clan| ]] <!-- main article --> | [[Category:Quince clan| ]] <!-- main article --> | ||
Revision as of 18:32, 16 September 2021
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