Magic: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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<h4>Original Wikitext content:</h4>

**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 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 [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)

Magic has certain properties that commend it as a step up in complexity from traditional harmony:

It fails to be a panacea because:

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.

//[[http://x31eq.com/music/dingsheng.mp3|Golden Age]] disco involving magic comma pumps.//

//[[http://x31eq.com/music/dingshi.mp3|Extravagant Food]] a single magic comma pump in under 60 seconds in 60-equal.//

<h4>Original HTML content:</h4>

&lt;strong&gt;Magic&lt;/strong&gt; 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 &lt;a class="wiki_link" href="/magic%20comma"&gt;magic comma&lt;/a&gt; 3125/3072 is tempered out, making it a member of the &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/Magic%20family#Muggles"&gt;muggles&lt;/a&gt;, but there's basically no reason to use it unless you're using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, in which case it's identical to magic anyway.)&lt;br /&gt;

&lt;br /&gt;

&lt;br /&gt;

Magic has certain properties that commend it as a step up in complexity from traditional harmony:&lt;br /&gt;

It fails to be a panacea because:&lt;br /&gt;

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.&lt;br /&gt;

&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/3L%204s"&gt;3L 4s&lt;/a&gt;: LsLsLss where L = 6/5&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/3L%207s"&gt;3L 7s&lt;/a&gt;: LssLssLsss where L = 7/6&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/3L%2010s"&gt;3L 10s&lt;/a&gt;: LsssLsssLssss where L = 9/8&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/3L%2013s"&gt;3L 13s&lt;/a&gt;: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related &lt;a class="wiki_link" href="/Magic%20family#Magic-Telepathy"&gt;telepathy&lt;/a&gt; temperament). In 22edo they are identical.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;