Hemimean clan: Difference between revisions

@@ Line 922: / Line 922: @@
 == Isra ==
-Isra results from taking every other generator of [[septimal meantone]]. It is named after the Isrāʾ (''iss-RAH'') night journey in the Qur'an, because it's similar to [[luna]].
+Isra results from taking every other generator of [[septimal meantone]]. It is named after the Isrāʾ (''iss-RAH'') night journey in the Qur'an, because it is similar to [[luna]].
-Subgroup: 2.9.5.7
+[[Subgroup]]: 2.9.5.7
-Comma list: 81/80, 126/125
+[[Comma list]]: 81/80, 126/125
-Mapping: [{{val| 1 3 2 2 }}, {{val| 0 1 2 5 }}]
+{{Mapping|legend=2| 1 0 -4 -13 | 0 1 2 5 }}
-Mapping generators: ~2, ~9/8
+: sval mapping generators: ~2, ~9
-POTE generator: ~9/8 = 192.9898
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.9898
 {{Optimal ET sequence|legend=1| 6, 19, 25, 31, 56b, 87b }}
 === Tutone ===
-{{See also| Chromatic pairs #Tutone }}
+Tutone is every other step of [[Meantone vs meanpop|undecimal meantone]].
+[[Subgroup]]: 2.9.5.7.11
+[[Comma list]]: 81/80, 99/98, 126/125
+{{Mapping|legend=2| 1 0 -4 -13 -25 | 0 1 2 5 9 }}
+{{Mapping|legend=3| 1 3/2 2 2 2 | 0 1/2 2 5 9 }}
+: [[gencom]]: [2 9/8; 81/80 99/98 126/125]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 193.937
+{{Optimal ET sequence|legend=1| 6, 19e, 25, 31, 68b, 99b }}
+[[Badness]]: 0.00536
 === Deutone ===