Magic: Difference between revisions
Move scale analysis to the proper section |
→Scales: 13-limit interpretations |
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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 [[meantone]] (both work well with a 19-note gamut). | * 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. | ||
| Line 60: | Line 60: | ||
| 3 | | 3 | ||
| 1141.4 | | 1141.4 | ||
| 27/14 | | 27/14, 35/18, 48/25 | ||
|- | |- | ||
| 4 | | 4 | ||
| Line 80: | Line 80: | ||
| 8 | | 8 | ||
| 643.7 | | 643.7 | ||
| (13/9, '''16/11''') | | 35/24, (13/9, '''16/11''') | ||
|- | |- | ||
| 9 | | 9 | ||
| Line 100: | 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; | ||
* [[3L 10s]]: LsssLsssLssss, where L represents 9/8; | * [[3L 10s]]: LsssLsssLssss, where L represents 9/8; | ||
* [[3L 13s]]: LssssLssssLsssss, where L | * [[3L 13s]]: LssssLssssLsssss, where L represents [[12/11]]~[[13/12]] in tridecimal magic. | ||
=== Scala files === | === Scala files === | ||
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! Comments | ! Comments | ||
|- | |- | ||
|[[16edo|5\16]] | | [[16edo|5\16]] | ||
| | | | ||
|375.000 | | 375.000 | ||
| | | Flatter tunings may be analysed as [[submerged]] | ||
|- | |- | ||
| | | | ||
|[[25/24]] | | [[25/24]] | ||
|376.443 | | 376.443 | ||
|1/3-comma | | 1/3-comma | ||
|- | |- | ||
| | | | ||
|[[125/72]] | | [[125/72]] | ||
|377.853 | | 377.853 | ||
|2/7-comma | | 2/7-comma | ||
|- | |- | ||
| | | | ||
| Line 298: | Line 298: | ||
| | | | ||
|- | |- | ||
| | | | ||
|[[45/32]] | | [[45/32]] | ||
|380.929 | | 380.929 | ||
| | | 2/11-comma | ||
|- | |- | ||
| [[63edo|20\63]] | | [[63edo|20\63]] | ||
| | | | ||
| Line 325: | Line 324: | ||
|- | |- | ||
| | | | ||
|[[75/64]] | | [[75/64]] | ||
|382.083 | | 382.083 | ||
|1/7-comma | | 1/7-comma | ||
|- | |- | ||
| | | | ||
| Line 334: | Line 333: | ||
| | | | ||
|- | |- | ||
|[[25edo|8\25]] | | [[25edo|8\25]] | ||
| | | | ||
|384.000 | | 384.000 | ||
| | | Sharper tunings may be analysed as [[anthoine]] | ||
|- | |- | ||
| | | | ||
| [[5/4]] | | [[5/4]] | ||
| 386.314 | | 386.314 | ||
| Untempered | | Untempered | ||
|} | |} | ||
<nowiki/> * Besides the octave | <nowiki/> * Besides the octave | ||