No-twos subgroup temperaments: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 274: / Line 274: @@
 Badness (Dirichlet): 1.723
+== Procyon ==
+This tempers out the [[Don Page comma]] between [[7/5]] and [[9/7]], allowing an accurate representation of the 5:7:9 chord, similar to the 3:5:7 in Sirius.
+[[Subgroup]]: 3.5.7
+[[Comma list]]: 823543/820125
+{{Mapping|legend=2|1 2 2|0 -7 -3}}
+: sval mapping generators: ~3, ~17/9
+[[Optimal tuning]] ([[CTE]]): ~3 = 1\1edt, ~49/45 = 145.333
+[[Support]]ing [[ET]]s: b13, b157, b144, b170, b131, b183, b118, b14, b105, b12c, b196, b92, b27, b79
+Badness (Dirichlet): 0.200
+=== Erigone ===
+Erigone splits the (tritave-augmented) generator of [[No-twos subgroup temperaments#Procyon|procyon]] into three, allowing for an accurate representation of 11/9 at -19 generators and 13/9 at -13 generators.
+[[Subgroup]]: 3.5.7.11.13
+[[Comma list]]: 1575/1573, 4459/4455, 847/845
+{{Mapping|legend=2|1 9 5 9 7|0 -21 -9 -19 -13}}
+: sval mapping generators: ~3, ~49/33
+[[Optimal tuning]] ([[CWE]]): ~3 = 1\1edt, ~49/33 = 682.443
+[[Optimal ET sequence]]: [[25edt|b25ce]], [[39edt|b39]], [[92edt|b92]], [[131edt|b131]], [[170edt|b170]], [[301edt|b301]], [[471edt|b471]]
+Badness (Dirichlet): 0.214
 == Sirius ==
@@ Line 348: / Line 383: @@
 Badness (Dirichlet): 0.841
-== Procyon ==
-This tempers out the [[Don Page comma]] between [[7/5]] and [[9/7]], allowing an accurate representation of the 5:7:9 chord, similar to the 3:5:7 in Sirius.
-[[Subgroup]]: 3.5.7
-[[Comma list]]: 823543/820125
-{{Mapping|legend=2|1 2 2|0 -7 -3}}
-: sval mapping generators: ~3, ~17/9
-[[Optimal tuning]] ([[CTE]]): ~3 = 1\1edt, ~49/45 = 145.333
-[[Support]]ing [[ET]]s: b13, b157, b144, b170, b131, b183, b118, b14, b105, b12c, b196, b92, b27, b79
-Badness (Dirichlet): 0.200
-=== Erigone ===
-Erigone splits the (tritave-augmented) generator of [[No-twos subgroup temperaments#Procyon|procyon]] into three, allowing for an accurate representation of 11/9 at -19 generators and 13/9 at -13 generators.
-[[Subgroup]]: 3.5.7.11.13
-[[Comma list]]: 1575/1573, 4459/4455, 847/845
-{{Mapping|legend=2|1 9 5 9 7|0 -21 -9 -19 -13}}
-: sval mapping generators: ~3, ~49/33
-[[Optimal tuning]] ([[CWE]]): ~3 = 1\1edt, ~49/33 = 682.443
-[[Optimal ET sequence]]: [[25edt|b25ce]], [[39edt|b39]], [[92edt|b92]], [[131edt|b131]], [[170edt|b170]], [[301edt|b301]], [[471edt|b471]]
-Badness (Dirichlet): 0.214
 = 3.5.11 subgroup temperaments =