113edo: Difference between revisions

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== Theory ==

113edo is [[consistency|distinctly consistent]] in the [[13-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] the [[amity comma]] and the [[ampersand comma]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and 1071875/1062882 in the [[7-limit]]; [[243/242]], [[385/384]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[325/324]], [[364/363]], [[729/728]], and 1625/1617 in the [[13-limit]]. It notably [[support]]s the 5-limit [[amity]] temperament, 7-limit [[amicable]] temperament, 7- and 11-limit [[miracle]] temperament, and 13-limit [[manna]] temperament.

113edo might be notable as a no-fives system, where it is consistent in the [[29-odd-limit]] and serves as a nearly optimal tuning for [[slendric]], in particular a 2.3.7.13.17.29 extension of slendric harmonies known as [[euslendric]].

=== Prime harmonics ===

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 == Theory ==
 edo is [[consistency|distinctly consistent]] in the [[13-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] the [[amity comma]] and the [[ampersand comma]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and 1071875/1062882 in the [[7-limit]]; [[243/242]], [[385/384]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[325/324]], [[364/363]], [[729/728]], and 1625/1617 in the [[13-limit]]. It notably [[support]]s the 5-limit [[amity]] temperament, 7-limit [[amicable]] temperament, 7- and 11-limit [[miracle]] temperament, and 13-limit [[manna]] temperament.
+edo might be notable as a no-fives system, where it is consistent in the [[29-odd-limit]] and serves as a nearly optimal tuning for [[slendric]], in particular a 2.3.7.13.17.29 extension of slendric harmonies known as [[euslendric]].
 === Prime harmonics ===