Gammic family: Difference between revisions

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 [[Badness]] (Sintel): 0.404
+==== 2.3.5.7.17.31 subgroup ====
+Since neptune splits the interval of [[5/3]] into two, we can accurately map each part to [[40/31]]~[[31/24]] by tempering out [[961/960]] (S31). This is especially natural, as combined with tempering out 1225/1224 (S35) and 24576/24565 (S16/S17), we can map (17/16)<sup>2</sup> (6 gammic generators) to [[35/31]]. This also gives us its complement with respect to [[5/4]], the interval of 5 gammic generators representing a quarter of a perfect fifth, as [[31/28]].
+[[Subgroup]]: 2.3.5.7.17.31
+[[Comma list]]: 868/867, 961/960, 1225/1224, 2401/2400
+{{Mapping|legend=1| 1 21 13 13 7 20 | 0 -40 -22 -21 -6 -31 }}
+: mapping generators: ~2, ~7/5
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, 7/5 = 582.451
+{{Optimal ET sequence|legend=1| 35, 68, 103, 171, 752k, 923k, 1094k, 1265kk }}
+[[Badness]] (Sintel): 0.393
 === 11-limit ===