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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:iamcamtaylor|iamcamtaylor]] and made on <tt>2017-03-14 21:27:15 UTC</tt>.<br>
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| : The original revision id was <tt>608844543</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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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">112EDO has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which is identical to the perfect fifth of [[xenharmonic/56edo|56edo]], a great inverse gentle fifth where +5 fifths gives a near-just 27:28 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of [[xenharmonic/7edo|7edo]]) and +9 fifths gives a close approximation to 17:21.
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| One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[xenharmonic/17edo|17edo]], but sharing a similar structure.
| | == Theory == |
| | 112edo has two great [[3/2|perfect fifth]]s, the lower of which approximates [[quarter-comma meantone]] (just a tad lower), and the upper of which—the [[patent fifth]]—is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27]] while −8 fifths gives a near-just [[39/32]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17]]. |
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| =Music in 112EDO=
| | One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure. |
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| [[https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv|Circulating 2.3.7.11.13 Floaty Piano Improv]] by Cam Taylor</pre></div>
| | === Odd harmonics === |
| <h4>Original HTML content:</h4>
| | {{Harmonics in equal|112|intervals=odd}} |
| <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"><html><head><title>112edo</title></head><body>112EDO has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which is identical to the perfect fifth of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/56edo">56edo</a>, a great inverse gentle fifth where +5 fifths gives a near-just 27:28 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a>) and +9 fifths gives a close approximation to 17:21.<br />
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| | === Subsets and supersets === |
| One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>, but sharing a similar structure.<br />
| | Since 112 factors into {{factorization|112}}, 112edo has subset edos {{EDOs| 2, 4, 7, 8, 14, 16, 28, and 56 }}. [[224edo]], which doubles it, is a strong 13-limit system. |
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Music in 112EDO"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music in 112EDO</h1>
| | == Intervals == |
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| | {{Interval table}} |
| <a class="wiki_link_ext" href="https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv" rel="nofollow">Circulating 2.3.7.11.13 Floaty Piano Improv</a> by Cam Taylor</body></html></pre></div>
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| | == Music == |
| | ; [[Cam Taylor]] |
| | * [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv''] |
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| | == See also == |
| | [[Skip fretting system 112 9 11]] |
| | [[Category:Listen]] |