Canou family: Difference between revisions

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 Badness: 3.511 × 10<sup>-3</sup>
+== Canta ==
+By adding [[896/891]], the pentacircle comma, [[33/32]] is equated with 28/27, so the scale is filled with this 33/32~28/27 mixture. This may be described as 75e & 80 & 99e, and 80edo makes the optimal.
+Commas: 896/891, 472392/471625
+Map: [<1 0 0 -1 6|, <0 1 2 2 -2|, <0 0 4 -3 -3|]
+POTE generators: ~3/2 = 703.7418, ~64/55 = 254.6133
+EDOs: {{EDOs|75e, 80, 99e, 179e}}
+Badness: 4.523 × 10<sup>-3</sup>
+=== 13-limit ===
+This adds [[351/350]], the ratwolfsma, to the comma list. Since 351/350 = (81/70)/(15/13). The 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale. Again 80edo makes the optimal.
+Commas: 351/350, 832/825, 13013/12960
+Map: [<1 0 0 -1 6 0|, <0 1 2 2 -2 3|, <0 0 4 -3 -3 5|]
+POTE generators: ~3/2 = 703.8423, ~15/13 = 254.3605
+EDOs: {{EDOs|75ef, 80, 99e, 104c, 179e, 184c, 203ce}}
+Badness: 3.470 × 10<sup>-3</sup>
+=== Gentcanta ===
+This adds [[352/351]], the minthma, as well as [[364/363]], the gentle comma, to the comma list. It is a natural extension of canta, as 896/891 factors neatly into (352/351)×(364/363). Again 80edo makes the optimal.
+Commas: 352/351, 364/363, 472392/471625
+Map: [<1 0 0 -1 6 11|, <0 1 2 2 -2 -5|, <0 0 4 -3 -3 -3|]
+POTE generators: ~3/2 = 703.8695, ~64/55 = 254.6321
+EDOs: {{EDOs|75e, 80, 99ef, 179ef}}
+Badness: 4.781 × 10<sup>-3</sup>
 [[Category:Theory]]