118edo: Difference between revisions

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== Theory ==

118edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. In addition, 118edo excellently ~~represents~~ the 22 Shruti scale.

118edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. In addition, 118edo excellently approximates the 22 Shruti scale.

In the 7-limit, it is particularly notable for tempering out the [[gamelisma]], 1029/1024, and is an excellent tuning for the rank three [[Gamelismic family|gamelan]] temperament, and for [[guiron]], the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo]] does better with that.

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 == Theory ==
-edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. In addition, 118edo excellently represents the 22 Shruti scale.
+edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. In addition, 118edo excellently approximates the 22 Shruti scale.
 In the 7-limit, it is particularly notable for tempering out the [[gamelisma]], 1029/1024, and is an excellent tuning for the rank three [[Gamelismic family|gamelan]] temperament, and for [[guiron]], the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo]] does better with that.