Miscellaneous 7-limit temperaments: Difference between revisions

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 [[Badness]] (Sintel): 3.55
+== Mandos ==
+: ''For extensions, see [[Rastmic rank-3 clan #Mandos]].''
+Mandos tempers out the [[mandos comma]] in the 7-limit, equating the [[25/24|classical chromatic semitone]] with a stack of two septimal quartertones of [[36/35]], and splits the [[3/2|perfect fifth]] in two. A rank-2 temperament that does that is [[myna]], which introduces little extra [[damage]] over mandos. Its natural 11-limit extension tempers out [[243/242]] and [[176/175]], from the identity 31104/30625 = (176/175)<sup>2</sup>⋅(243/242).
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 31104/30625
+{{Mapping|legend=1| 1 1 0 6 | 0 2 0 5 | 0 0 1 -2 }}
+: Mapping generators: ~2, ~175/144, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.1782{{c}}, ~175/144 = 350.6514{{c}}, ~5/4 = 390.4750{{c}}
+: [[Error map]]: {{val| -0.822 -1.474 +2.518 +1.837 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/144 = 350.5166{{c}}, ~5/4 = 390.2032{{c}}
+: Error map: {{val| 0.000 -0.922 +3.889 +3.351 }}
+{{Optimal ET sequence|legend=1| 24, 27, 31, 58, 89, 154d, 181cd, 212cd, 270ccdd, 301ccd }}
+[[Badness]] (Sintel): 3.77
 == Decovulture ==