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Magic

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**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.)

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

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.
* [[3L 4s]]: LsLsLss where L = 6/5
* [[3L 7s]]: LssLssLsss where L = 7/6
* [[3L 10s]]: LsssLsssLssss where L = 9/8
* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family#Magic-Telepathy|telepathy]] temperament). In 22edo they are identical.

==Interval chain== 
|| 0. || 380.352 || 760.704 || 1141.056 || 321.408 || 701.76 || 1082.112 || 262.464 || 642.816 || 1023.168 || 203.52 || 583.872 || 964.224 || 144.576 ||
|| 1/1 || 5/4 || 14/9 || 48/25~125/64 || 6/5 || 3/2 || 15/8 || 7/6 || (16/11) || 9/5 || 9/8 || 7/5 || 7/4 || (12/11) ||

The generator chain val for 13-limit magic is <0 5 1 12 -8 18|, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.

=[[Chords of magic]]= 

=Music=
[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]
[[magic16]]
[[http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3|A Piece in Paulsmagic]]
[[paulsmagic]]
[[@http://www.chrisvaisvil.com/|Chris Vaisvil]]

Original HTML content:

<html><head><title>Magic</title></head><body><strong>Magic</strong> 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 <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. 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 <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>, in which case it's identical to magic anyway.)<br />
<br />
EDOs that contain good magic scales include <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, and <a class="wiki_link" href="/41edo">41edo</a>.<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 />
<ul><li><a class="wiki_link" href="/3L%204s">3L 4s</a>: LsLsLss where L = 6/5</li><li><a class="wiki_link" href="/3L%207s">3L 7s</a>: LssLssLsss where L = 7/6</li><li><a class="wiki_link" href="/3L%2010s">3L 10s</a>: LsssLsssLssss where L = 9/8</li><li><a class="wiki_link" href="/3L%2013s">3L 13s</a>: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related <a class="wiki_link" href="/Magic%20family#Magic-Telepathy">telepathy</a> temperament). In 22edo they are identical.</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chain</h2>
 

<table class="wiki_table">
    <tr>
        <td>0.<br />
</td>
        <td>380.352<br />
</td>
        <td>760.704<br />
</td>
        <td>1141.056<br />
</td>
        <td>321.408<br />
</td>
        <td>701.76<br />
</td>
        <td>1082.112<br />
</td>
        <td>262.464<br />
</td>
        <td>642.816<br />
</td>
        <td>1023.168<br />
</td>
        <td>203.52<br />
</td>
        <td>583.872<br />
</td>
        <td>964.224<br />
</td>
        <td>144.576<br />
</td>
    </tr>
    <tr>
        <td>1/1<br />
</td>
        <td>5/4<br />
</td>
        <td>14/9<br />
</td>
        <td>48/25~125/64<br />
</td>
        <td>6/5<br />
</td>
        <td>3/2<br />
</td>
        <td>15/8<br />
</td>
        <td>7/6<br />
</td>
        <td>(16/11)<br />
</td>
        <td>9/5<br />
</td>
        <td>9/8<br />
</td>
        <td>7/5<br />
</td>
        <td>7/4<br />
</td>
        <td>(12/11)<br />
</td>
    </tr>
</table>

<br />
The generator chain val for 13-limit magic is &lt;0 5 1 12 -8 18|, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Chords of magic"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Chords%20of%20magic">Chords of magic</a></h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:4 -->Music</h1>
<a class="wiki_link_ext" href="http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3" rel="nofollow">Chromatic piece in magic 16</a><br />
<a class="wiki_link" href="/magic16">magic16</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3" rel="nofollow">A Piece in Paulsmagic</a><br />
<a class="wiki_link" href="/paulsmagic">paulsmagic</a><br />
<a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a></body></html>
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