Quince clan: Difference between revisions
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[[Gencom]]: [2 14/13; 343/338 640/637] | [[Gencom]]: [2 14/13; 343/338 640/637] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4}}, {{val|0 0 -7 -2 -3}}] | [[Gencom|Gencom mapping]]: [{{val|1 0 3 3 0 4}}, {{val|0 0 -7 -2 0 -3}}] | ||
[[Mapping|Sval mapping]]: [{{val|1 3 3 4}}, {{val|0 -7 -2 -3}}] | [[Mapping|Sval mapping]]: [{{val|1 3 3 4}}, {{val|0 -7 -2 -3}}] | ||
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[[Gencom]]: [2 14/13; 170/169 224/221 640/637] | [[Gencom]]: [2 14/13; 170/169 224/221 640/637] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4}}, {{val|0 0 -7 -2 -3 1}}] | [[Gencom|Gencom mapping]]: [{{val|1 0 3 3 0 4 4}}, {{val|0 0 -7 -2 0 -3 1}}] | ||
[[Mapping|Sval mapping]]: [{{val|1 3 3 4 4}}, {{val|0 -7 -2 -3 1}}] | [[Mapping|Sval mapping]]: [{{val|1 3 3 4 4}}, {{val|0 -7 -2 -3 1}}] | ||
| Line 62: | Line 62: | ||
[[Gencom]]: [2 14/13; 170/169 343/338 640/637 16384/16055] | [[Gencom]]: [2 14/13; 170/169 343/338 640/637 16384/16055] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4 3}}, {{val|0 0 -7 -2 -3 1 13}}] | [[Gencom|Gencom mapping]]: [{{val|1 0 3 3 0 4 4 3}}, {{val|0 0 -7 -2 0 -3 1 13}}] | ||
[[Mapping|Sval mapping]]: [{{val|1 3 3 4 4 3}}, {{val|0 -7 -2 -3 1 13}}] | [[Mapping|Sval mapping]]: [{{val|1 3 3 4 4 3}}, {{val|0 -7 -2 -3 1 13}}] | ||
Revision as of 16:33, 27 November 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
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
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
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