Magic: Difference between revisions
Wikispaces>x31eq **Imported revision 520239044 - Original comment: ** |
Wikispaces>x31eq **Imported revision 520240530 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:x31eq|x31eq]] and made on <tt>2014-08-31 07: | : This revision was by author [[User:x31eq|x31eq]] and made on <tt>2014-08-31 07:47:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>520240530</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]]. | EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]]. | ||
Magic has certain properties | Magic has certain properties that commend it as a step up in complexity from traditional harmony: | ||
* Every non-trivial 9-limit interval is better tuned than in [[12edo]]. | * Every non-trivial 9-limit interval is better tuned than in [[12edo]]. | ||
* It is the simplest mapping with the above property. | * It is the simplest mapping with the above property. | ||
* It is only slightly | * It is only slightly more complex than meantone (both work well with a 19 note gamut). | ||
* 5-limit intervals are simpler than other 7-limit intervals. | * 5-limit intervals are simpler than other 7-limit intervals. | ||
It fails to be a panacea because: | |||
* It has no proper MOS scales of between 3 and 16 notes. | |||
* It is more complex than meantone | |||
* The 3/2 approximation is 5 times as complex as the 5/4 approximation (the generator) so modulation by fifths is more constrained than you may be used to. | |||
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. | Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. | ||
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EDOs that contain good magic scales include <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/60edo">60edo</a> and <a class="wiki_link" href="/104edo">104edo</a>.<br /> | EDOs that contain good magic scales include <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/60edo">60edo</a> and <a class="wiki_link" href="/104edo">104edo</a>.<br /> | ||
<br /> | <br /> | ||
Magic has certain properties | Magic has certain properties that commend it as a step up in complexity from traditional harmony:<br /> | ||
* Every non-trivial 9-limit interval is better tuned than in <a class="wiki_link" href="/12edo">12edo</a>.<br /> | * Every non-trivial 9-limit interval is better tuned than in <a class="wiki_link" href="/12edo">12edo</a>.<br /> | ||
* It is the simplest mapping with the above property.<br /> | * It is the simplest mapping with the above property.<br /> | ||
* It is only slightly | * It is only slightly more complex than meantone (both work well with a 19 note gamut).<br /> | ||
* 5-limit intervals are simpler than other 7-limit intervals.<br /> | * 5-limit intervals are simpler than other 7-limit intervals.<br /> | ||
<br /> | |||
It fails to be a panacea because:<br /> | |||
* It has no proper MOS scales of between 3 and 16 notes.<br /> | |||
* It is more complex than meantone<br /> | |||
* The 3/2 approximation is 5 times as complex as the 5/4 approximation (the generator) so modulation by fifths is more constrained than you may be used to.<br /> | |||
<br /> | <br /> | ||
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br /> | Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br /> | ||