240edo: Difference between revisions

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== Theory ==

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

240edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705{{c}} sharp fifth inherited from [[80edo]].

Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempering out|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] 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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 {{Infobox ET}}
-{{EDO intro|240}}
+{{ED intro}}
 == Theory ==
-edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].
+edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705{{c}} sharp fifth inherited from [[80edo]].
 Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempering out|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] 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.