Magic: Difference between revisions
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| Generator = 5/4 | | Generator = 5/4 | ||
| Mapping = 1; 5 1 12 | | Mapping = 1; 5 1 12 | ||
| Pergen = (P8, | | Pergen = (P8, P12/5) | ||
| Color name = | | Color name = Laquinyoti | ||
| Edo join 1 = 19 | Edo join 2 = 22 | | Edo join 1 = 19 | Edo join 2 = 22 | ||
| Optimization method = CTE | | Optimization method = CTE | ||
| Generator tuning = 380.7 | | Generator tuning = 380.7 | ||
| MOS scales = [[3L 4s]], [[3L 7s]], | | MOS scales = [[3L 4s]], [[3L 7s]], …, [[3L 16s]], [[19L 3s]] | ||
| Odd limit 1 = 5 | Mistuning 1 = 5.9 | Complexity 1 = 13 | | Odd limit 1 = 5 | Mistuning 1 = 5.9 | Complexity 1 = 13 | ||
| Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 41 | | Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 41 | ||
}} | }} | ||
{{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 [[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.) | '''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.) | ||