112edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

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

~~: This revision was by author~~ [[~~User:PiotrGrochowski~~|~~PiotrGrochowski~~]] and ~~made on <tt>2016~~-09-~~15 03:27:15 UTC<~~/~~tt>~~.~~<br>~~

~~: The original revision id was <tt>592121694</tt>~~.~~<br>~~

== Theory ==

~~: The revision comment was: <tt></tt><br>~~

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]].

~~The revision contents are below~~, ~~presented both in the original Wikispaces Wikitext format~~, and ~~in HTML exactly as Wikispaces rendered~~ it.~~<br>~~

~~<h4>Original Wikitext content:</h4>~~

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.

~~<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">Approximates 1/4 comma meantone</pre></div>~~

~~<h4>Original HTML content:</h4>~~

=== Odd harmonics ===

~~<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>Approximates 1/4 comma meantone</body></html></pre></div>

=== Subsets and supersets ===

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.

== Intervals ==

== Music ==

; [[Cam Taylor]]

* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']

== See also ==

[[Skip fretting system 112 9 11]]

[[Category:Listen]]

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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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-15 03:27:15 UTC</tt>.<br>
-: The original revision id was <tt>592121694</tt>.<br>
+== Theory ==
-: The revision comment was: <tt></tt><br>
+edo 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]].
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
+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.
-<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">Approximates 1/4 comma meantone</pre></div>
-<h4>Original HTML content:</h4>
+=== Odd harmonics ===
-<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;112edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Approximates 1/4 comma meantone&lt;/body&gt;&lt;/html&gt;</pre></div>
+{{Harmonics in equal|112|intervals=odd}}
+=== Subsets and supersets ===
+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.
+== Intervals ==
+{{Interval table}}
+== Music ==
+; [[Cam Taylor]]
+* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']
+== See also ==
+[[Skip fretting system 112 9 11]]
+[[Category:Listen]]