Factor 9 grid: Difference between revisions

@@ Line 54: / Line 54: @@
 === Factor 9 grid (495 & 666) ===
-Subgroup: 2.3.5.7.11.13.17.19.23
+[[Subgroup]]: 2.3.5.7.11.13.17.19.23
-Comma list: 442/441, 715/714, 2300/2299, 3060/3059, 3179/3174, 9025/9009, 57375/57344
+[[Comma list]]: 442/441, 715/714, 2300/2299, 3060/3059, 3179/3174, 9025/9009, 57375/57344
-POTE Generator: 63.0631c (~28/27)
+[[Mapping]] [[generators]]: ~250/231, ~336/323
+[[Optimal tuning]] ([[CTE]]): ~336/323 = 70.270
 Vals: 171f, 495, 666.
-This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its reduced generator interval is the smallest interval in the Factor 9 Grid system. So in the end, 666edo does ironically represent the Factor 9 grid well. The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit:
+This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its period minus reduced generator interval also maps to the smallest interval in the Factor 9 Grid system, [[28/27]]. So in the end, 666edo does ironically represent the Factor 9 grid well. The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit:
 === Real Factor 9 grid (4973 & 6691) ===