Magic: Difference between revisions
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Magic has certain properties that commend it as a step up in complexity from traditional harmony: | Magic has certain properties that commend it as a step up in complexity from traditional harmony: | ||
* It is the simplest mapping capable of tuning every [[9-odd-limit]] interval better than in [[12edo]]. | * It is the simplest mapping capable of tuning every [[9-odd-limit]] interval better than in [[12edo]]. | ||
* It is only slightly more complex than [[septimal meantone]] (both work well with a 19-note gamut). | |||
* 5-limit intervals are generally simpler than 7-limit intervals. | * 5-limit intervals are generally simpler than 7-limit intervals. | ||
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| 3 | | 3 | ||
| 1141.4 | | 1141.4 | ||
| 27/14 | | 27/14, 35/18, 48/25 | ||
|- | |- | ||
| 4 | | 4 | ||
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| 8 | | 8 | ||
| 643.7 | | 643.7 | ||
| (13/9, '''16/11''') | | 35/24, (13/9, '''16/11''') | ||
|- | |- | ||
| 9 | | 9 | ||
| Line 99: | Line 100: | ||
| 13 | | 13 | ||
| 145.9 | | 145.9 | ||
| (12/11, 13/12) | | 35/32, (12/11, 13/12) | ||
|} | |} | ||
<nowiki/>* In 7-limit CWE tuning | <nowiki/>* In 7-limit CWE tuning | ||
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{{See also| Magic Tetrachords }} | {{See also| Magic Tetrachords }} | ||
Because the generator is so close to 1/3 of an octave, and the interval left over is accordingly so small, all small magic mos scales consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following scales, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]]. | Because the generator is so close to 1/3 of an octave, and the interval left over is accordingly so small, all small magic mos scales consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following scales, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]], as well as [[33/32]] and [[27/26]] in tridecimal magic. | ||
* [[3L 4s]]: LsLsLss, where L represents 6/5; | * [[3L 4s]]: LsLsLss, where L represents 6/5; | ||
* [[3L 7s]]: LssLssLsss, where L represents 7/6; | * [[3L 7s]]: LssLssLsss, where L represents 7/6; | ||