32/27: Difference between revisions

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**Imported revision 300946844 - Original comment: **
 
Mention alteraugment
 
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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 = Pythagorean minor third
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 13:06:35 UTC</tt>.<br>
| Color name = w3, wa 3rd
: The original revision id was <tt>300946844</tt>.<br>
| Sound = jid_32_27_pluck_adu_dr220.mp3
: The revision comment was: <tt></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>
The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] [[just intonation]].  Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8.
<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">The Pythagorean minor third of 32/27 is the interval between [[9_8|9/8]] and [[4_3|4/3]] which arises naturally in 3-limit just intonation. It is 352/351 sharp of [[13_11|13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].</pre></div>
 
<h4>Original HTML content:</h4>
It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].
<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;32_27&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The Pythagorean minor third of 32/27 is the interval between &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; and &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt; which arises naturally in 3-limit just intonation. It is 352/351 sharp of &lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt;, and tempering 352/351 out equates it with 13/11 and leads to &lt;a class="wiki_link" href="/minthmic%20chords"&gt;minthmic chords&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Temperaments ==
 
32/27 is treated as a comma in edos 3 & 6, where the best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations, producing [[alteraugment]]. Temperaments it can be interpreted as if used as a generator include [[Kleismic_family#Kleiboh|Kleiboh]] or [[Gariberttet]].
== Approximation ==
{{Interval edo approximation|32/27}}
== See also ==
* [[27/16]] – its [[octave complement]]
* [[81/64]] – its [[fifth complement]]
* [[9/8]] – its [[fourth complement]]
* [[Gallery of just intervals]]
* [[Pythagorean tuning]]
 
[[Category:Third]]
[[Category:Minor third]]