65/64: Difference between revisions

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{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = wilsorma
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-14 19:40:16 UTC</tt>.<br>
| Color name = 3oy1, thoyo 1sn,<br>Thoyo comma
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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>
In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].  
<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 [[Just Intonation]], 65/64 is a [[superparticular]] interval of around 26., nearly a quarter of a semitone or eighth of a tone. It belongs to the 13-prime limit, which means that the highest prime in the ratio is 13. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5_4|5/4]] and [[16_13|16/13]]; [[8_5|8/5]] and [[13_8|13/8]]; [[13_12|13/12]] and [[16_15|16/15]]; [[15_8||15/8]] and [[24_13|24/13]], [[13_10|13/10]] and [[32_25|32/25]]; [[20/13|20/13]] and [[25_16|25/16]], and of course, infinitely many other pairs of just intervals.


See: [[Gallery of Just Intervals|Galley of Just Intervals]]</pre></div>
Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.
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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;65_64&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 65/64 is a &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval of around 26.8¢, nearly a quarter of a semitone or eighth of a tone. It belongs to the 13-prime limit, which means that the highest prime in the ratio is 13. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; and &lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;; &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt; and &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;; &lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt; and &lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;; &lt;a class="wiki_link" href="/15_8"&gt;|15/8&lt;/a&gt; and &lt;a class="wiki_link" href="/24_13"&gt;24/13&lt;/a&gt;, &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; and &lt;a class="wiki_link" href="/32_25"&gt;32/25&lt;/a&gt;; [[20/13|20/13]] and &lt;a class="wiki_link" href="/25_16"&gt;25/16&lt;/a&gt;, and of course, infinitely many other pairs of just intervals.&lt;br /&gt;
This interval is the 13th-partial chroma (13-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "13", while its reciprocal is denoted as "{{invert|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13.  
&lt;br /&gt;
 
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Galley of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Tempering it out leads to the rank-2 2.5.13 '''wilsormatic''' temperament, which has a generator tuned to abut 370-375 cents that represents both 5/4 and 16/13, or the rank-5 '''wilsormic''' temperament. 
 
== See also ==
* [[Gallery of just intervals]]
* [[64/63]]
 
[[Category:Commas with unknown etymology]]
{{todo|research|comment=Is it named after Erv Wilson?}}