27/20: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 13:20:12 UTC</tt>.<br>

: The original revision id was <tt>300949748</tt>.<br>

<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">In [[5-limit]] [[Just Intonation]], 27/20 is an interval measuring about 519.6¢. It differs from the [[4_3|4/3]] perfect fourth by [[81_80|81/80]] (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3_2|3/2]] perfect fifths, or as the interval between [[10_9|10/9]] and [[4_3|4/3]]. In [[12edo]] and [[meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls," as compared to simpler intervals within the 5-limit such as [[5_4|5/4]] and [[9_8|9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.

<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;27_20&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 27/20 is an interval measuring about 519.6¢. It differs from the &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt; perfect fourth by &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt; (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifths, or as the interval between &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; and &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;. In &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a &amp;quot;wolf&amp;quot; interval, implying that it &amp;quot;howls,&amp;quot; as compared to simpler intervals within the 5-limit such as &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; and &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.&lt;br /&gt;