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 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 [[Magic family #Muggles|muggles]], but there is ~~basically no~~ reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)

'''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 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 [[Magic family #Muggles|muggles]], which may be better melodically for small MOSes due to the smaller generator making the small step a bit larger, but there is little reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)

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

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 {{Wikipedia| Magic temperament }}
-'''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 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 [[Magic family #Muggles|muggles]], but there is basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)
+'''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 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 [[Magic family #Muggles|muggles]], which may be better melodically for small MOSes due to the smaller generator making the small step a bit larger, but there is little reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)
 EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]].