Magic: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:x31eq|x31eq]] and made on <tt>2014-08-31 06:50:17 UTC</tt>.

: This revision was by author [[User:x31eq|x31eq]] and made on <tt>2014-08-31 07:04:23 UTC</tt>.

: The original revision id was <tt>~~520238678~~</tt>.

: The original revision id was <tt>520239044</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]].

Magic has certain properties required for an accurate step up in complexity from traditional harmony:

* Every non-trivial 9-limit interval is better tuned than in [[12edo]].

* It is the simplest mapping with the above property.

* It is only slightly higher in complexity then meantone (both work well with a 19 note gamut).

* 5-limit intervals are simpler than other 7-limit intervals.

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>.

Magic has certain properties required for an accurate step up in complexity from traditional harmony:

* Every non-trivial 9-limit interval is better tuned than in <a class="wiki_link" href="/12edo">12edo</a>.

* It is the simplest mapping with the above property.

* It is only slightly higher in complexity then meantone (both work well with a 19 note gamut).

* 5-limit intervals are simpler than other 7-limit intervals.

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.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 06:50:17 UTC</tt>.<br>
+: This revision was by author [[User:x31eq|x31eq]] and made on <tt>2014-08-31 07:04:23 UTC</tt>.<br>
-: The original revision id was <tt>520238678</tt>.<br>
+: The original revision id was <tt>520239044</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>
@@ Line 10: / Line 10: @@
 EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]].
+Magic has certain properties required for an accurate step up in complexity from traditional harmony:
+  * Every non-trivial 9-limit interval is better tuned than in [[12edo]].
+  * It is the simplest mapping with the above property.
+  * It is only slightly higher in complexity then meantone (both work well with a 19 note gamut).
+  * 5-limit intervals are simpler than other 7-limit intervals.
 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.
@@ Line 69: / Line 75: @@
 &lt;br /&gt;
 EDOs that contain good magic scales include &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60edo&lt;/a&gt; and &lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+Magic has certain properties required for an accurate step up in complexity from traditional harmony:&lt;br /&gt;
+  * Every non-trivial 9-limit interval is better tuned than in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;.&lt;br /&gt;
+  * It is the simplest mapping with the above property.&lt;br /&gt;
+  * It is only slightly higher in complexity then meantone (both work well with a 19 note gamut).&lt;br /&gt;
+  * 5-limit intervals are simpler than other 7-limit intervals.&lt;br /&gt;
 &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;