Quince clan: Difference between revisions

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-The '''quince clan''' tempers out quince, the no-threes comma {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
+{{Technical data page}}
-* [[Gamelismic clan #Miracle|miracle]] {225/224, 1029/1024}
+The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
-* [[Ragismic microtemperaments #Quincy|quincy]] {4375/4374, 823543/819200}
+* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
-* [[Varunismic temperaments #Octowerck|octowerck]] {321489/320000, 420175/419904}
+* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* [[31-comma temperaments #Birds|birds]] {3136/3125, 823543/819200}
+* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]
+* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]
+* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
+* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]
+* ''[[Countermiracle]]'' (+6144/6125) → [[Porwell temperaments #Countermiracle|Porwell temperaments]]
-[[Category:Regular temperament theory]]
+== Mercy ==
-[[Category:Temperament clan]]
+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]].
-[[Category:Quince]]
+[[Subgroup]]: 2.5.7
+[[Comma list]]: 823543/819200
+{{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}
+: mapping generators: ~2, ~343/320
+{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}
+: gencom: [2 343/320; 823543/819200]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 116.291
+{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
+==== 2.5.7.13 subgroup ====
+Subgroup: 2.5.7.13
+Comma list: 343/338, 640/637
+Sval mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}
+Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
+: gencom: [2 14/13; 343/338 640/637]
+Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094
+{{Optimal ET sequence|legend=1| 10, 21, 31}}
+==== 2.5.7.13.17 subgroup ====
+Subgroup: 2.5.7.13.17
+Comma list: 170/169, 224/221, 640/637
+Sval mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
+Gencom mapping: {{mapping| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
+: gencom: [2 14/13; 170/169 224/221 640/637]
+Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769
+{{Optimal ET sequence|legend=1| 10, 21, 31 }}
+==== 2.5.7.13.17.19 subgroup ====
+Subgroup: 2.5.7.13.17.19
+Comma list: 170/169, 343/338, 640/637, 16384/16055
+Sval mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
+Gencom mapping: {{mapping| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}
+: gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]
+Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716
+{{Optimal ET sequence|legend=1| 10, 21, 31, 52f }}
+[[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Quince clan| ]] <!-- main article -->
+[[Category:Quince| ]] <!-- key article -->
 [[Category:Rank 2]]