Canou family: Difference between revisions

@@ Line 22: / Line 22: @@
 Badness: 0.001122
+== Semicanou ==
+Semicanou adds 9801/9800, the kalisma, to the comma list, and may be described as 80 & 94 & 118. It splits the octave into two equal parts, each representing 99/70. Note that 99/70 = (81/70)×(11/9), this extension is more than natural.
+The other comma necessary to define it is 14641/14580], which is the difference between [[121/120]] and [[243/242]]. By flattening the 11th harmonic by one cent, it identifies [[20/11]] by three [[11/9]]'s stacked, so an octave can be divided into 11/9-11/9-11/9-11/10.
+Still 80edo can be used as a tuning. Other options include 94edo, 118edo, and [[104edo]] in 104c val.
+Commas: 9801/9800, 14641/14580
+Map: [<2 0 0 -2 1|, <0 1 2 2 2|, <0 0 4 -3 1|]
+POTE generators: ~3/2 = 702.3850, ~81/70 = 254.6168 or ~11/9 = 345.3832
+EDOs: {{EDOs|80, 94, 118, 198, 212, 292, 330e, 410}}
+Badness: 0.002197
+=== 13-limit ===
+This adds [[352/351]], the minthma, to the comma list. It is a natural extension to the 13-limit.
+Commas: 352/351, 9801/9800, 14641/14580
+Map: [<2 0 0 -2 1 11|, <0 1 2 2 2 -1|, <0 0 4 -3 1 1|]
+POTE generators: ~3/2 = 702.8788, ~81/70 = 254.6664 or ~11/9 = 345.3336
+EDOs: {{EDOs|80, 94, 118, 174d, 198}}
 [[Category:Temperament]]
 [[Category:Family]]
 [[Category:Canou]]