Schismic–countercommatic equivalence continuum: Difference between revisions

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@@ Line 137: / Line 137: @@
 Examples of temperaments with fractional values of ''n'':
-* [[Marvel temperaments #Septimin|Septimin]] ({{nowrap|''n'' {{=}} −11/2}})
+* [[Septimin]] ({{nowrap|''n'' {{=}} −11/2}})
 * [[Shibboleth]] ({{nowrap|''n'' {{=}} −9/2}})
-* [[Mirkwai clan #Pluto|Pluto]] ({{nowrap|''n'' {{=}} −7/2}})
+* [[Pluto]] ({{nowrap|''n'' {{=}} −7/2}})
 * 3737 & 5585 ({{nowrap|''n'' {{=}} 31/3 {{=}} 10.{{overline|3}}}})
 * 1277 & 2513 ({{nowrap|''n'' {{=}} 21/2}})
-== Hemififths (5-limit) ==
+== Kwai (5-limit) ==
-: ''For extensions, see [[Breedsmic temperaments #Hemififths]].''
+: ''For extensions, see [[Hemifamity temperaments #Kwai]].''
 [[Subgroup]]: 2.3.5
-[[Comma list]]: 858993459200/847288609443
+[[Comma list]]: {{monzo| 50 -33 1 }}
-{{Mapping|legend=1| 1 1 -5 | 0 2 25 }}
+{{Mapping|legend=1| 1 0 -50 | 0 1 33 }}
+: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~655360/531441 = 351.476{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.792{{c}}, ~3/2 = 702.5077{{c}}
+: [[error map]]: {{val| -0.208 +0.345 -0.023 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.6243{{c}}
+: error map: {{val| 0.000 +0.669 +0.288 }}
-{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338, 915b, 1253bc }}
+{{Optimal ET sequence|legend=1| 41, 111, 152, 2017bbc, 2169bbc }}
-[[Badness]] (Smith): 0.372848
+[[Badness]] (Sintel): 14.9
-== Kwai (5-limit) ==
+== Cotoneum (5-limit) ==
-: ''For extensions, see [[Hemifamity temperaments #Kwai]].''
+: ''For extensions, see [[Garischismic clan #Cotoneum]].''
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 50 -33 1 }} = 5629499534213120/5559060566555523
+[[Comma list]]: {{monzo| 80 -49 -1 }}
-{{Mapping|legend=1| 1 0 -50 | 0 1 33 }}
+{{Mapping|legend=1| 1 0 80 | 0 1 -49 }}
+: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.630{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8849{{c}}, ~3/2 = 702.2471{{c}}
+: [[error map]]: {{val| -0.115 +0.177 +0.008 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.3162{{c}}
+: error map: {{val| 0.000 +0.361 +0.190 }}
-{{Optimal ET sequence|legend=1| 41, 111, 152 }}
+{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b, 3759bbc }}
-[[Badness]] (Smith): 0.636715
+[[Badness]] (Sintel): 29.1
-== Cotoneum (5-limit) ==
+== Hemififths (5-limit) ==
-: ''For extensions, see [[Garischismic clan #Cotoneum]].''
+: ''For extensions, see [[Breedsmic temperaments #Hemififths]].''
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 80 -49 -1 }}
+[[Comma list]]: 858993459200/847288609443
-{{Mapping|legend=1| 1 0 80 | 0 1 -49 }}
+{{Mapping|legend=1| 1 1 -5 | 0 2 25 }}
+: mapping generators: ~2, ~655360/531441
-[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.315{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7047{{c}}, ~655360/531441 = 351.3898{{c}}
+: [[error map]]: {{val| -0.295 +0.529 -0.091 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~655360/531441 = 351.4654{{c}}
+: error map: {{val| 0.000 +0.976 +0.322 }}
-{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b }}
+{{Optimal ET sequence|legend=1| 17c, 41, 58, 99, 239, 338, 915b, 1253bc }}
-[[Badness]] (Smith): 1.240078
+[[Badness]] (Sintel): 8.75
 == Newt (5-limit) ==
@@ Line 196: / Line 211: @@
 {{Mapping|legend=1| 1 1 19 | 0 2 -57 }}
+: mapping generators: ~2, ~{{monzo| 47 -28 -1 }}
-[[Optimal tuning]] ([[POTE]]): ~{{monzo| 47 -28 -1 }} = 351.114{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9120{{c}}, ~{{monzo| 47 -28 -1 }} = 351.0878{{c}}
+: [[error map]]: {{val| -0.088 +0.133 +0.010 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 47 -28 -1 }} = 351.1146{{c}}
+: error map: {{val| 0.000 +0.274 +0.152 }}
 {{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}
-[[Badness]] (Smith): 1.528465
+[[Badness]] (Sintel): 35.9
 [[Category:41edo]]
 [[Category:Equivalence continua]]