Magic: Difference between revisions

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{{Infobox regtemp

| Title = Magic

| Subgroups = 2.3.5, 2.3.5.7

| Comma basis = 3125/3072 (2.3.5); <br>225/224, 245/243 (2.3.5.7)

| Generator = 5/4

| Mapping = 1; 5 1 12

| Pergen = (P8, P5/5)

| Color name = Guti

| Edo join 1 = 19 | Edo join 2 = 22

| Optimization method = CTE

| Generator tuning = 380.7

| MOS scales = [[3L 4s]], [[3L 7s]], ... [[3L 16s]], [[19L 3s]]

| Odd limit 1 = 5 | Mistuning 1 = 5.9 | Complexity 1 = 13

| Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 41

}}

'''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.)

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 {{Wikipedia| Magic temperament }}
+{{Infobox regtemp
+| Title = Magic
+| Subgroups = 2.3.5, 2.3.5.7
+| Comma basis = 3125/3072 (2.3.5); <br>225/224, 245/243 (2.3.5.7)
+| Generator = 5/4
+| Mapping = 1; 5 1 12
+| Pergen = (P8, P5/5)
+| Color name = Guti
+| Edo join 1 = 19 | Edo join 2 = 22
+| Optimization method = CTE
+| Generator tuning = 380.7
+| MOS scales = [[3L 4s]], [[3L 7s]], ... [[3L 16s]], [[19L 3s]]
+| Odd limit 1 = 5 | Mistuning 1 = 5.9 | Complexity 1 = 13
+| Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 41
+}}
 '''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.)