11-limit: Difference between revisions

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Relative to their size, [[edo]]s which do (relatively) well in supporting 11-limit intervals are: [[12edo]], [[15edo]], [[22edo]], [[31edo]], [[41edo]], [[46edo]], [[58edo]], [[72edo]], [[118edo]], [[130edo]] and [[152edo]].

=Music=

[[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm|Study #3]] [[http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3|play]] by [[Dave Hill]]

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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;11-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;11-limit&lt;/em&gt; consists of all &lt;a class="wiki_link" href="/JustIntonation"&gt;justly tuned&lt;/a&gt; intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are &lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;, &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;, &lt;a class="wiki_link" href="/27_22"&gt;27/22&lt;/a&gt; and &lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt;. The 11 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 11. Reduced to an octave, these are the ratios 1/1, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, 11/9, 5/4, 14/11, 9/7, 4/3, 11/8, 7/5, 10/7, 16/11, 3/2, 14/9, 11/7, 8/5, 18/11, 5/3, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 2/1.&lt;br /&gt;

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Relative to their size, &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;s which do (relatively) well in supporting 11-limit intervals are: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt; and &lt;a class="wiki_link" href="/152edo"&gt;152edo&lt;/a&gt;.&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;

&lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow"&gt;Study #3&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Dave%20Hill"&gt;Dave Hill&lt;/a&gt;&lt;br /&gt;