Luna family: Difference between revisions

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@@ Line 71: / Line 71: @@
 [[Comma list]]: 48828125/48771072, 67108864/66976875
-{{Mapping|legend=1| 1 4 2 -5 | 0 -30 4 97 }}
+{{Mapping|legend=1| 1 -26 6 92 | 0 30 -4 -97 }}
-: mapping generators: ~2, ~200/189
+: mapping generators: ~2, ~189/100
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~200/189 = 96.591{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9023{{c}}, ~189/100 = 1103.3197{{c}} (~200/189 = 96.5827{{c}})
+: [[error map]]: {{val| -0.098 +0.175 -0.178 +0.180 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4097{{c}} (~200/189 = 96.5903{{c}})
+: error map: {{val| 0.000 +0.336 +0.047 +0.432 }}
 {{Optimal ET sequence|legend=1| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }}
-[[Badness]] (Smith): 0.179304
+[[Badness]] (Sintel): 4.54
 === 11-limit ===
@@ Line 85: / Line 89: @@
 Comma list: 5632/5625, 14641/14580, 131072/130977
-Mapping: {{mapping| 1 4 2 -5 7 | 0 -30 4 97 -44 }}
+Mapping: {{mapping| 1 -26 6 92 -37 | 0 30 -4 -97 44 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 96.587{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0004{{c}}, ~189/100 = 1103.4136{{c}} (~200/189 = 96.5868{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4133{{c}} (~200/189 = 96.5867{{c}})
 {{Optimal ET sequence|legend=0| 87, 236, 323, 410 }}
-Badness (Smith): 0.100077
+Badness (Sintel): 3.31
 === 13-limit ===
@@ Line 98: / Line 104: @@
 Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580
-Mapping: {{mapping| 1 4 2 -5 7 7 | 0 -30 4 97 -44 -41 }}
+Mapping: {{mapping| 1 -26 6 92 -37 -34 | 0 30 -4 -97 44 41 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~143/135 = 96.586{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0257{{c}}, ~189/100 = 1103.4377{{c}} (~143/135 = 96.5880{{c}})
+* CWE: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4133{{c}} (~143/135 = 96.5869{{c}})
 {{Optimal ET sequence|legend=0| 87, 236, 323, 410 }}
-Badness (Smith): 0.046151
+Badness (Sintel): 1.91
 == Semiluna ==
@@ Line 111: / Line 119: @@
 [[Comma list]]: 4802000/4782969, 95703125/95551488
-{{Mapping|legend=1| 2 8 4 23 | 0 -15 2 -54 }}
+{{Mapping|legend=1| 2 -7 6 -31 | 0 15 -2 54 }}
-: mapping generators: ~10125/7168, ~2187/1960
+: mapping generators: ~10125/7168, ~4375/3456
-[[Optimal tuning]] ([[POTE]]): ~99/70 = 600.0000{{c}}, ~2187/1960 = 193.1725{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~10125/7168 = 600.0000{{c}}, ~4375/3456 = 406.8061{{c}} (~2187/1960 = 193.1624{{c}})
+: [[error map]]: {{val| -0.063 +0.358 -0.115 -0.318 }}
+* [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~4375/3456 = 406.8263{{c}} (~2187/1960 = 193.1737{{c}})
+: error map: {{val| 0.000 +0.440 +0.034 -0.203 }}
 {{Optimal ET sequence|legend=1| 56d, 118, 292, 410 }}
-[[Badness]] (Smith): 0.192167
+[[Badness]] (Sintel): 4.86
 === 11-limit ===
@@ Line 125: / Line 137: @@
 Comma list: 5632/5625, 9801/9800, 14641/14580
-Mapping: {{mapping| 2 8 4 23 14 | 0 -15 2 -54 -22 }}
+Mapping: {{mapping| 2 -7 6 -31 -8 | 0 15 -2 54 22 }}
-Optimal tuning (POTE): ~99/70 = 600.0000{{c}}, ~121/108 = 193.1732{{c}}
+Optimal tunings:
+* WE: ~99/70 = 600.0093{{c}}, ~486/385 = 406.8331{{c}} (~121/108 = 193.1762{{c}})
+* CWE: ~99/70 = 600.0000{{c}}, ~486/385 = 406.8272{{c}} (~121/108 = 193.1728{{c}})
 {{Optimal ET sequence|legend=0| 56d, 118, 292, 410 }}
-Badness (Smith): 0.067783
+Badness (Sintel): 2.24
 [[Category:Temperament families]]
 [[Category:Luna family| ]] <!-- main article -->
 [[Category:Rank 2]]