240edo: Difference between revisions

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==Theory==

240edo ~~is a [[dual-fifth system]]. Nonetheless, it~~ is [[consistent]] in the 5-limit and notably provides the [[optimal patent val]] for the [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. ~~Alternate~~ mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].

240edo is [[consistent]] in the 5-odd-limit and notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, its mapping for 3 is not well approximated, meaning it's a [[dual-fifth system]], with alternate mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].

Although no longer consistent to to the higher limits, 240edo's patent val tempers out the [[225/224]] in the 7-limit, supporting [[marvel]] and [[spectacle]] temperaments with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.

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 {{EDO intro|240}}
 ==Theory==
-edo is a [[dual-fifth system]]. Nonetheless, it is [[consistent]] in the 5-limit and notably provides the [[optimal patent val]] for the [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. Alternate mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].
+edo is [[consistent]] in the 5-odd-limit and notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, its mapping for 3 is not well approximated, meaning it's a [[dual-fifth system]], with alternate mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].
 Although no longer consistent to to the higher limits, 240edo's patent val tempers out the [[225/224]] in the 7-limit, supporting [[marvel]] and [[spectacle]] temperaments with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.