Sengic family: Difference between revisions

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 == Sengic ==
+Sengic is naturally a 2.3.5.7.13 subgroup temperament due to the identity 686/675 = (91/90)(196/195) and 91/90 = (169/168)(196/195). This identifies the last generator as 13/12~14/13~15/14.
 [[Subgroup]]: 2.3.5.7
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 : mapping generators: ~2, ~3, ~15/14
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.154, ~15/14 = 129.824
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 703.7873, ~15/14 = 129.6451
-{{Optimal ET sequence|legend=1| 9, 10, 17c, 19, 27, 46 }}
+{{Optimal ET sequence|legend=1| 8d, 9, 10, 17c, 19, 27, 46 }}
 [[Badness]]: 0.320 × 10<sup>-3</sup>
 [[Projection pair]]s: ~5 = 3375/686, ~7 = 675/98 to 2.3.7/5
+=== 2.3.5.7.13 subgroup ===
+Subgroup: 2.3.5.7.13
+Comma list: 91/90, 169/168
+Sval mapping: {{mapping| 1 0 2 1 2 | 0 1 0 1 1 | 0 0 3 2 1 }}
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 704.5918, ~14/13 = 129.7585
+{{Optimal ET sequence|legend=1| 8d, 9, 10, 17c, 19, 27, 46, 111df, 121df }}
+Badness: 0.320 × 10<sup>-3</sup>
 == Demeter ==