Greenwoodmic temperaments: Difference between revisions

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@@ Line 13: / Line 13: @@
 == Secund ==
+Secund tempers out the greendwoodma, the [[avicennma]], and the [[orwellisma]]. It may be described as the {{nowrap| 9 & 26 }} temperament, with a [[ploidacot]] signature of pentacot. It divides the [[3/2|perfect fifth]] into five [[~]][[16/15]] generators, two for [[7/6]] and three for [[9/7]].
 [[Subgroup]]: 2.3.5.7
@@ Line 18: / Line 20: @@
 {{Mapping|legend=1| 1 1 3 2 | 0 5 -6 7 }}
 : mapping generators: ~2, ~16/15
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~16/15 = 138.454
+* [[WE]]: ~2 = 1203.6786{{c}}, ~16/15 = 138.3805{{c}}
-: [[error map]]: {{val| 0.000 -9.684 -17.038 +0.353 }}
+: [[error map]]: {{val| +3.679 -6.374 -5.561 +7.195 }}
-* [[POTE]]: ~2 = 1200.000, ~16/15 = 137.958
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 138.0648{{c}}
-: error map: {{val| 0.000 -12.167 -14.059 -3.123 }}
+: error map: {{val| 0.000 -11.631 -14.702 -2.372 }}
 {{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
-[[Badness]] (Smith): 0.089840
+[[Badness]] (Sintel): 2.27
 === 11-limit ===
@@ Line 39: / Line 40: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~12/11 = 138.420
+* WE: ~2 = 1202.9415{{c}}, ~12/11 = 138.2377{{c}}
-* POTE: ~2 = 1200.000, ~12/11 = 137.900
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.9970{{c}}
 {{Optimal ET sequence|legend=0| 9, 17, 26, 61bc }}
-Badness (Smith): 0.042562
+Badness (Sintel): 1.41
 ==== 13-limit ====
@@ Line 54: / Line 55: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~12/11 = 137.455
+* WE: ~2 = 1202.4465{{c}}, ~12/11 = 137.2165{{c}}
-* POTE: ~2 = 1200.000, ~12/11 = 136.937
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.0309{{c}}
 {{Optimal ET sequence|legend=0| 9, 35 }}
-Badness (Smith): 0.049684
+Badness (Sintel): 2.05
 ==== Secundly ====
@@ Line 69: / Line 70: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~13/12 = 138.583
+* WE: ~2 = 1203.0195{{c}}, ~13/12 = 138.2642{{c}}
-* POTE: ~2 = 1200.000, ~13/12 = 137.917
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 138.0317{{c}}
 {{Optimal ET sequence|legend=0| 9, 17, 26, 61bcf }}
-Badness (Smith): 0.026212
+Badness (Sintel): 1.08
 == Semishallowtone ==
@@ Line 84: / Line 85: @@
 {{Mapping|legend=1| 2 0 36 15 | 0 1 -10 -3 }}
 : mapping generators: ~189/128, ~3
 [[Optimal tuning]]s:
-* [[CTE]]: ~189/128 = 600.000, ~3/2 = 681.532 (~64/63 = 81.532)
+* [[WE]]: ~189/128 = 603.1653{{c}}, ~3/2 = 686.6365{{c}} (~64/63 = 83.4712{{c}})
-: [[error map]]: {{val| 0.000 -20.423 -1.629 -13.421 }}
+: [[error map]]: {{val| +6.331 -8.988 -2.034 -0.248 }}
-* [[CWE]]: ~189/128 = 600.000, ~3/2 = 682.650 (~64/63 = 82.650)
+* [[CWE]]: ~189/128 = 600.0000{{c}}, ~3/2 = 682.6498{{c}} (~64/63 = 82.6498{{c}})
 : error map: {{val| 0.000 -19.305 -12.811 -16.775 }}
 {{Optimal ET sequence|legend=1| 14c, 44bd, 58bcd }}
-[[Badness]]:
+[[Badness]] (Sintel): 8.42
-* Smith: 0.333
-* Dirichlet: 8.420
 === 11-limit ===
@@ Line 107: / Line 105: @@
 Optimal tunings:
-* CTE: ~189/128 = 600.000, ~3/2 = 681.438 (~64/63 = 81.438)
+* WE: ~189/128 = 603.0536{{c}}, ~3/2 = 686.6175{{c}} (~64/63 = 83.5640{{c}})
-* CWE: ~189/128 = 600.000, ~3/2 = 682.724 (~64/63 = 82.724)
+* CWE: ~189/128 = 600.0000{{c}}, ~3/2 = 682.7238{{c}} (~64/63 = 82.7238{{c}})
 {{Optimal ET sequence|legend=0| 14c, 44bd, 58bcde, 72bbccddee }}
-Badness:
+Badness (Sintel): 4.15
-* Smith: 0.125
-* Dirichlet: 4.148
 === 13-limit ===
@@ Line 124: / Line 120: @@
 Optimal tunings:
-* CTE: ~91/64 = 600.000, ~3/2 = 681.406 (~64/63 = 81.406)
+* WE: ~91/64 = 601.8872{{c}}, ~3/2 = 684.4774{{c}} (~64/63 = 82.5902{{c}})
-* CWE: ~91/64 = 600.000, ~3/2 = 682.168 (~64/63 = 82.168)
+* CWE: ~91/64 = 600.0000{{c}}, ~3/2 = 682.1676{{c}} (~64/63 = 82.1676{{c}})
 {{Optimal ET sequence|legend=0| 14c, 30b }}
-Badness:
+Badness (Sintel): 4.38
-* Smith: 0.106
-* Dirichlet: 4.377
 [[Category:Temperament collections]]
 [[Category:Greenwoodmic temperaments| ]] <!-- main article -->
-[[Category:Greenwoodmic| ]] <!-- key article -->
 [[Category:Rank 2]]