18/13: Difference between revisions

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**Imported revision 313095040 - Original comment: lemma in bold**
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = tridecimal augmented fourth, low tritone
: This revision was by author [[User:guest|guest]] and made on <tt>2012-03-21 04:29:31 UTC</tt>.<br>
| Color name = 3u4, thu 4th
: The original revision id was <tt>313095040</tt>.<br>
| Sound = jid_18_13_pluck_adu_dr220.mp3
: The revision comment was: <tt>lemma in bold</tt><br>
}}
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>
<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 [[13-limit]] [[Just Intonation]], **18/13** is a low tritone measuring about 563.4¢. It represents the interval between the 13th and 18th overtones of the [[overtone scales|harmonic series]]. The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13_8|13/8]] and [[9_8|9/8]] are both a little sharp. The inversion of 18/13 is [[13_9|13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.


Other just tritones include [[7_5|7/5]], [[10_7|10/7]], [[45_32|45/32]], [[64_45|64/45]], [[24_17|24/17]], [[17_12|17/12]], [[23_16|23/16]], [[32_23|32/23]], and, of course, infinitely many more intervals.
In [[13-limit]] [[just intonation]], '''18/13''', the '''tridecimal augmented fourth''' is a '''low [[tritone]]''' measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the [[overtone scales|harmonic series]].  


See: [[Gallery of Just Intervals]]</pre></div>
The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8]] and [[9/8]] are both a little sharp. The inversion of 18/13 is [[13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is [[169/162]], approximately 73.2¢.
<h4>Original HTML content:</h4>
 
<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;18_13&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, &lt;strong&gt;18/13&lt;/strong&gt; is a low tritone measuring about 563.4¢. It represents the interval between the 13th and 18th overtones of the &lt;a class="wiki_link" href="/overtone%20scales"&gt;harmonic series&lt;/a&gt;. The low tritone in &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt; approximates 18/13 quite well, while 17edo's approximations of &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; and &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; are both a little sharp. The inversion of 18/13 is &lt;a class="wiki_link" href="/13_9"&gt;13/9&lt;/a&gt;, a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.&lt;br /&gt;
== See also ==
&lt;br /&gt;
 
Other just tritones include &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, &lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;, &lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;, &lt;a class="wiki_link" href="/24_17"&gt;24/17&lt;/a&gt;, &lt;a class="wiki_link" href="/17_12"&gt;17/12&lt;/a&gt;, &lt;a class="wiki_link" href="/23_16"&gt;23/16&lt;/a&gt;, &lt;a class="wiki_link" href="/32_23"&gt;32/23&lt;/a&gt;, and, of course, infinitely many more intervals.&lt;br /&gt;
* [[13/9]] – its [[octave complement]]
&lt;br /&gt;
* [[13/12]] – its [[fifth complement]]
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[Gallery of just intervals]]
 
[[Category:Tritone]]