8th-octave temperaments: Difference between revisions

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 == Octatonic ==
-[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].
+[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the [[undecimal octatonic comma]], the difference between a stack of eight 12/11's and the octave.
 [[Subgroup]]: 2.3.11
-[[Comma list]]: {{monzo|15 8 0 0 -8}}
+[[Comma list]]: 214990848/214358881
-{{Mapping|legend=1|8 0 15|0 1 1}}
+{{Mapping|legend=2| 8 0 15 | 0 1 1 }}
+: mapping generators: ~12/11, ~3
-: Mapping generators: ~12/11, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~12/11 = 149.9917{{c}}, ~3/2 = 701.9324{{c}}
+: [[error map]]: {{val| -0.066 -0.089 +0.424 }}
+* [[CWE]]: ~12/11 = 150.0000{{c}}, ~3/2 = 701.9147{{c}}
+: error map: {{val| 0.000 -0.040 +0.597 }}
-[[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...
+{{Optimal ET sequence|legend=1| 8, 16, 24, 104, 128, 152, 176, 200, 1024e, 1224e, 1424e, 1624e }}
+[[Badness]] (Sintel): 0.515
 {{Navbox fractional-octave}}