36edo: Difference between revisions

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<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]

36edo, by definition, divides the 2:1 octave into 36 equal steps, each of which is exactly 33.333... cents.

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<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;36edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:15:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;a href="#As a harmonic temperament"&gt;As a harmonic temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Approximations"&gt;Approximations&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;

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36 is a highly composite number, factoring into 2x2x3x3. Since 36 is divisible by 12, it contains the overly-familiar &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; as a subset. It divides 12edo's 100-cent half step into three microtonal step of approximately 33 cents, which could be called &amp;quot;sixth tones.&amp;quot; 36edo also contains &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt; (&amp;quot;third tones&amp;quot;) and &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; (&amp;quot;two-thirds tones&amp;quot;) as subsets, not to mention the &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt; whole tone scale, &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt; full-diminished seventh chord, and the &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt; augmented triad, all of which are present in 12edo.&lt;br /&gt;