40ed10: Difference between revisions

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+== 40ed10 as a generator ==
+ED10 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[Subgroup temperaments|subgroup temperament]] which tempers out 4624/4617, 6144/6137, and 6885/6859, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintilischis'' temperament). This temperament is supported by {{Val list|12, 253, 265, 277, 289, 301}}, and [[313edo|313]] EDOs.
+Tempering out 400/399 (equating 20/19 and 21/20) leads ''[[Schismatic family #Quintilipyth|quintilipyth]]'' (12&amp;253), and tempering out 476/475 (equating 19/17 with 28/25) leads ''[[Schismatic family #Quintaschis|quintaschis]]'' (12&amp;289).
+; Quintilischis (12&amp;289)
+'''2.3.5.17.19 subgroup'''<br>
+Comma list: 4624/4617, 6144/6137, 6885/6859<br>
+Gencom: [2 18/17; 4624/4617 6144/6137 6885/6859]<br>
+Gencom mapping: [{{val|1 2 -1 5 4}}, {{val|0 -5 40 -11 3}}]<br>
+POTE generator: ~18/17 = 99.652<br>
+Vals: 12, 253, 265, 277, 289<br>
+RMS error: 0.1636 cents<br><br>
+; [[Schismatic family #Quintilipyth|Quintilipyth]] (12 &amp; 253)
+'''7-limit'''<br>
+Comma list: 32805/32768, 9765625/9680832<br>
+Mapping: [{{val|1 2 -1 -4}}, {{val|0 -5 40 82}}]<br>
+POTE generator: ~625/588 = 99.625<br>
+Vals: 12, 253, 265<br>
+Badness: 0.253966<br><br>
+'''11-limit'''<br>
+Comma list: 1375/1372, 4375/4356, 32805/32768<br>
+Mapping: [{{val|1 2 -1 -4 -7}}, {{val|0 -5 40 82 126}}]<br>
+POTE generator: ~35/33 = 99.616<br>
+Vals: 12, 253, 265, 518c, 783cc<br>
+Badness: 0.113044<br><br>
+'''13-limit'''<br>
+Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647<br>
+Mapping: [{{val|1 2 -1 -4 -7 -9}}, {{val|0 -5 40 82 126 153}}]<br>
+POTE generator: ~35/33 = 99.612<br>
+Vals: 12f, 253, 518c, 771cc<br>
+Badness: 0.069127<br><br>
+'''17-limit'''<br>
+Comma list: 375/374, 595/594, 833/832, 1375/1372, 8624/8619<br>
+Mapping: [{{val|1 2 -1 -4 -7 -9 5}}, {{val|0 -5 40 82 126 153 -11}}]<br>
+POTE generator: ~18/17 = 99.612<br>
+Vals: 12f, 253, 518c, 771cc<br>
+Badness: 0.045992<br><br>
+'''19-limit'''<br>
+Comma list: 375/374, 400/399, 495/494, 595/594, 1375/1372, 3978/3971<br>
+Mapping: [{{val|1 2 -1 -4 -7 -9 5 4}}, {{val|0 -5 40 82 126 153 -11 3}}]<br>
+POTE generator: ~18/17 = 99.615<br>
+Vals: 12f, 253, 265, 518ch<br>
+Badness: 0.038155<br><br>
+; [[Schismatic family #Quintaschis|Quintaschis]] (12 &amp; 289)
+'''7-limit'''<br>
+Comma list: 32805/32768, 49009212/48828125<br>
+Mapping: [{{val|1 2 -1 -5}}, {{val|0 -5 40 94}}]<br>
+POTE generator: ~200/189 = 99.664<br>
+Vals: 12, 277d, 289<br>
+Badness: 0.132890<br><br>
+'''11-limit'''<br>
+Comma list: 441/440, 32805/32768, 1953125/1951488<br>
+Mapping: [{{val|1 2 -1 -5 -8}}, {{val|0 -5 40 94 138}}]<br>
+POTE generator: ~35/33 = 99.653<br>
+Vals: 12, 277d, 289<br>
+Badness: 0.111477<br><br>
+'''13-limit'''<br>
+Comma list: 364/363, 441/440, 32805/32768, 109512/109375<br>
+Mapping: [{{val|1 2 -1 -5 -8 -11}}, {{val|0 -5 40 94 138 177}}]<br>
+POTE generator: ~35/33 = 99.658<br>
+Vals: 12f, 277df, 289<br>
+Badness: 0.074218<br><br>
+'''17-limit'''<br>
+Comma list: 364/363, 441/440, 595/594, 3757/3750, 32805/32768<br>
+Mapping: [{{val|1 2 -1 -5 -8 -11 5}}, {{val|0 -5 40 94 138 177 -11}}]<br>
+POTE generator: ~18/17 = 99.656<br>
+Vals: 12f, 277df, 289<br>
+Badness: 0.050571<br><br>
+'''19-limit'''<br>
+Comma list: 364/363, 441/440, 476/475, 595/594, 3757/3750, 6885/6859<br>
+Mapping: [{{val|1 2 -1 -5 -8 -11 5 4}}, {{val|0 -5 40 94 138 177 -11 3}}]<br>
+POTE generator: ~18/17 = 99.659<br>
+Vals: 12f, 277df, 289<br>
+Badness: 0.042120<br><br>
+; [[Schismatic family #Quintaschis|Quintahelenic]] (12 &amp; 301)
+'''11-limit'''<br>
+Comma list: 5632/5625, 8019/8000, 151263/151250<br>
+Mapping: [{{val|1 2 -1 -5 -9}}, {{val|0 -5 40 94 150}}]<br>
+POTE generator: ~200/189 = 99.671<br>
+Vals: 12, 289e, 301, 915, 1216ce<br>
+Badness: 0.082225<br><br>
+'''13-limit'''<br>
+Comma list: 847/845, 1716/1715, 5632/5625, 8019/8000<br>
+Mapping: [{{val|1 2 -1 -5 -9 -11}}, {{val|0 -5 40 94 150 177}}]<br>
+POTE generator: ~200/189 = 99.661<br>
+Vals: 12f, 289e, 301<br>
+Badness: 0.055570<br><br>
+'''17-limit'''<br>
+Comma list: 561/560, 833/832, 847/845, 1701/1700, 3757/3750<br>
+Mapping: [{{val|1 2 -1 -5 -9 -11 5}}, {{val|0 -5 40 94 150 177 -11}}]<br>
+POTE generator: ~18/17 = 99.665<br>
+Vals: 12f, 289e, 301<br>
+Badness: 0.040412<br><br>
+'''19-limit'''<br>
+Comma list: 476/475, 495/494, 561/560, 833/832, 847/845, 1701/1700<br>
+Mapping: [{{val|1 2 -1 -5 -9 -11 5 4}}, {{val|0 -5 40 94 150 177 -11 3}}]<br>
+POTE generator: ~18/17 = 99.668<br>
+Vals: 12f, 289e, 301<br>
+Badness: 0.036840<br><br>
+; [[Schismatic family #Quintaschis|Quintahelenoid]] (12 &amp; 301)
+'''13-limit'''<br>
+Comma list: 729/728, 1001/1000, 4096/4095, 86515/86436<br>
+Mapping: [{{val|1 2 -1 -5 -9 14}}, {{val|0 -5 40 94 150 -124}}]<br>
+POTE generator: ~200/189 = 99.672<br>
+Vals: 12, 301, 614, 915<br>
+Badness: 0.066108<br><br>
+'''17-limit'''<br>
+Comma list: 561/560, 729/728, 1001/1000, 4096/4095, 14161/14157<br>
+Mapping: [{{val|1 2 -1 -5 -9 14 5}}, {{val|0 -5 40 94 150 -124 -11}}]<br>
+POTE generator: ~18/17 = 99.671<br>
+Vals: 12, 301, 915gg, 1216cegg<br>
+Badness: 0.047908<br><br>
+'''19-limit'''<br>
+Comma list: 476/475, 561/560, 729/728, 1001/1000, 4096/4095, 6144/6137<br>
+Mapping: [{{val|1 2 -1 -5 -9 14 5 4}}, {{val|0 -5 40 94 150 -124 -11 3}}]<br>
+POTE generator: ~18/17 = 99.672<br>
+Vals: 12, 301, 614gh, 915gghh<br>
+Badness: 0.039542<br><br>
 [[Category:Equal-step tuning]]
 [[Category:Ed10]]