75edo: Difference between revisions

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== Theory ==

In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it ~~tenpers~~ [[225/224]] and [[1728/1715]]. In the 11-limit, 75e [[val]] {{val| 75 119 174 211 '''260''' }} scores lower in [[TE error|error]], and tempers [[100/99]] and [[243/242]], whereas the [[patent val]] {{val| 75 119 174 211 '''259''' }} tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.

In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tempers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e [[val]] {{val| 75 119 174 211 '''260''' }} scores lower in [[TE error|error]], and tempers [[100/99]] and [[243/242]], whereas the [[patent val]] {{val| 75 119 174 211 '''259''' }} tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.

It provides the [[optimal patent val]] for the [[fog]] temperament in the 7-limit and the [[Temperament merging|31 & 44 temperament]] in the 19-limit.

@@ Line 9: / Line 9: @@
 == Theory ==
-In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tenpers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e [[val]] {{val| 75 119 174 211 '''260''' }} scores lower in [[TE error|error]], and tempers [[100/99]] and [[243/242]], whereas the [[patent val]] {{val| 75 119 174 211 '''259''' }} tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.
+In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tempers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e [[val]] {{val| 75 119 174 211 '''260''' }} scores lower in [[TE error|error]], and tempers [[100/99]] and [[243/242]], whereas the [[patent val]] {{val| 75 119 174 211 '''259''' }} tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.
 It provides the [[optimal patent val]] for the [[fog]] temperament in the 7-limit and the [[Temperament merging|31 & 44 temperament]] in the 19-limit.