Magic: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

* [[3L 7s]]: LssLssLsss where L = 7/6

* [[3L 10s]]: LsssLsssLssss where L = 9/8

==Interval chain==  

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.

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Magic&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&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;

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;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Interval chain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Interval chain&lt;/h2&gt;