Magic: Difference between revisions

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'''Magic''' is a [[linear temperament]] in which the ~380 cent [[generator]] represents [[5/4]], and five of those make a [[3/1]]. This implies that the [[magic comma]] [[3125/3072]] is [[tempering out|tempered out]], making it a member of the [[magic family]]. This article also assumes the default mapping for the prime 7, which tempers out [[225/224]] and makes two generators equivalent to [[14/9]]. [[7/4]] can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[muggles]], which may be better melodically for small [[mos scale]]s due to the smaller generator making the small step a bit larger, but there is little reason to use it unless you are using [[19edo]], in which case it is identical to magic anyway.)

Edos that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]].

Edos that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]], [[63edo]] and [[104edo]].

Magic has certain properties that commend it as a step up in complexity from traditional harmony:

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 '''Magic''' is a [[linear temperament]] in which the ~380 cent [[generator]] represents [[5/4]], and five of those make a [[3/1]]. This implies that the [[magic comma]] [[3125/3072]] is [[tempering out|tempered out]], making it a member of the [[magic family]]. This article also assumes the default mapping for the prime 7, which tempers out [[225/224]] and makes two generators equivalent to [[14/9]]. [[7/4]] can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[muggles]], which may be better melodically for small [[mos scale]]s due to the smaller generator making the small step a bit larger, but there is little reason to use it unless you are using [[19edo]], in which case it is identical to magic anyway.)
-Edos that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]].
+Edos that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]], [[63edo]] and [[104edo]].
 Magic has certain properties that commend it as a step up in complexity from traditional harmony: