Quince clan: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
-[[#Essence|Essence]]
+{{Technical data page}}
+The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
+* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
+* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
+* ''[[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]]
-This tempers out quince, the no-threes comma |-15 0 -2 7&gt; = 823543/819200. Quince temperaments include miracle, quincy, octowerck and birds as well as the ones listed below.
+== 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]].
-=Essence=
+[[Subgroup]]: 2.5.7
-Essence is of interest because of the abundant supply of essentially tempered chords.
-Commas: 321489/320000, 823543/820125
+[[Comma list]]: 823543/819200
-POTE generator: ~243/196 = 372.597
+{{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}
-Map: [&lt;2 10 27 23|, &lt;0 -11 -36 -28|]
+: mapping generators: ~2, ~343/320
-Wedgie: &lt;&lt;22 72 56 63 27 -72||
+{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}
-EDOs: 58, 190, 248, 438d, 686d
+: gencom: [2 343/320; 823543/819200]
-Badness: 0.1736
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 116.291
-==11-limit==
+{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
-Commas: 441/440, 8019/8000, 456533/455625
-POTE generator: ~243/196 = 372.599
+==== 2.5.7.13 subgroup ====
+Subgroup: 2.5.7.13
-Map: [&lt;2 10 27 23 33|, &lt;0 -11 -36 -28 -42|]
+Comma list: 343/338, 640/637
-EDOs: 58, 190, 248, 438d
+Sval mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}
-Badness: 0.0464
+Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
-==13-limit==
+: gencom: [2 14/13; 343/338 640/637]
-Commas: 441/440, 729/728, 847/845, 1001/1000
-POTE generator: ~243/196 = 372.602
+Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094
-Map: [&lt;2 10 27 23 33 31|, &lt;0 -11 -36 -28 -42 -38|]
+{{Optimal ET sequence|legend=1| 10, 21, 31}}
-EDOs: 58, 190, 248, 438d
+==== 2.5.7.13.17 subgroup ====
+Subgroup: 2.5.7.13.17
-Badness: 0.0261
+Comma list: 170/169, 224/221, 640/637
-[[Category:Theory]]
+Sval mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
-[[Category:Temperament clan]]
+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]]