Valinorsmic clan: Difference between revisions

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VisualWikitext

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 * ''[[Draco]]'' (+19683/19600) → [[Cataharry family #Draco|Cataharry family]]
-Considered below is manwe, besides the no-3 subgroup temperament. For the rank-4 valinorsmic temperament, see [[Rank-4 temperament #Valinorsmic (176/175)]].
+Considered below are manwe and augenic, besides the no-3 subgroup temperament. For the rank-4 valinorsmic temperament, see [[Rank-4 temperament #Valinorsmic (176/175)]].
 == Valinor ==
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 : sval mapping generators: ~2, ~5, ~7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 389.7641, ~7/4 = 972.1113
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.311¢, ~5/4 = 389.540¢, ~7/4 = 971.553¢
+* [[CWE]]: ~2 = 1200.000¢, ~5/4 = 389.393¢, ~7/4 = 971.520¢
 {{Optimal ET sequence|legend=1| 6, 15, 21, 22, 25, 28, 31, 37, 163c, 200cd, 237cd, 274cd }}
-[[Badness]]: 1.73 × 10<sup>-6</sup>
+[[Badness]] (Sintel): 0.079
 == Manwe ==
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 : mapping generators: ~2, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.360¢, ~3/2 = 702.695¢, ~5/4 = 389.312¢
+* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 702.592¢, ~5/4 = 389.376¢
 {{Optimal ET sequence|legend=1| 15, 31, 46, 77, 80, 111 }}
-[[Badness]]: 0.679 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.816
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 176/175, 1331/1323, 351/350
+Comma list: 176/175, 351/350, 1331/1323
+Mapping: {{mapping| 1 0 0 12 8 13 | 0 1 0 3 3 0 | 0 0 1 -6 -4 -4 }}
+Optimal tunings:
+* WE: ~2 = 1199.435¢, ~3/2 = 702.506¢, ~5/4 = 389.233¢
+* CWE: ~2 = 1200.000¢, ~3/2 = 702.703¢, ~5/4 = 389.430¢
+{{Optimal ET sequence|legend=0| 31, 46, 77, 80, 111 }}
+Badness (Sintel): 1.073
+== Augenic ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 56/55, 128/125
+{{Mapping|legend=1| 3 0 7 0 2 | 0 1 0 0 0 | 0 0 0 1 1 }}
+: mapping generators: ~5/4, ~3, ~7
-Mapping: {{mapping| 1 0 0 12 8 | 0 1 0 3 3 | 0 0 1 -6 -4 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~5/4 = 398.924¢, ~3/2 = 705.145¢, ~7/4 = 969.111¢
+* [[CWE]]: ~5/4 = 400.000¢, ~3/2 = 705.349¢, ~7/4 = 968.440¢
-{{Optimal ET sequence|legend=1| 31, 46, 77, 80, 111 }}
+{{Optimal ET sequence|legend=1| 6, 9, 12, 15, 24, 27e }}
-Badness: 1.147 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.735
 [[Category:Temperament clans]]