32/27: Difference between revisions

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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:spt3125~~|~~spt3125]] and made on <tt>2014-06-08 15:12:56 UTC</tt>.<br>~~

| Color name = w3, wa 3rd

~~: The original revision id was <tt>513254024</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>~~

<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">**32/27**

|~~5 -3>~~

~~294.135 cents~~

~~[[media type="file" key~~="jid_32_27_pluck_adu_dr220.mp3~~"]] [[file:xenharmonic/jid_32_27_pluck_adu_dr220.mp3|sound sample]]~~

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>~~

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.

~~<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"><html><head><title>32_27</title></head><body><strong>~~32/27&~~lt;/strong><br />~~

It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].

|~~5 -3&gt;<br />~~

~~294~~.~~135 cents<br />~~

== Temperaments ==

~~<embed src~~=~~"/s/mediaplayer.swf" pluginspage~~=~~"http://www.macromedia.com/go/getflashplayer" type~~=~~"application/x-shockwave-flash" quality~~="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_32_27_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed> <a href="http://xenharmonic.wikispaces.com/file/view/jid_32_27_pluck_adu_dr220.mp3/513250248/jid_32_27_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_32_27_pluck_adu_dr220.mp3/513250248/jid_32_27_pluck_adu_dr220.mp3');">sound sample</a><br />

~~<br~~ /~~>~~

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]].

~~The Pythagorean minor third of 32/27 is the interval between <a class="wiki_link" href="/9_8">~~9/8~~</a> and <a class="wiki_link" href="/4_3">4/3</a> which arises naturally in 3-limit~~ just intonation. It is 352/351 sharp of <a class="wiki_link" href="/13_11">13/11</a>, and tempering 352/351 out equates it with 13/11 and leads to <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>.</body></html></pre></div>

== Approximation ==

== 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]]

@@ Line 1: / Line 1: @@
-<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:spt3125|spt3125]] and made on <tt>2014-06-08 15:12:56 UTC</tt>.<br>
+| Color name = w3, wa 3rd
-: The original revision id was <tt>513254024</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>
-<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">**32/27**
-|5 -3&gt;
-.135 cents
-[[media type="file" key="jid_32_27_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_32_27_pluck_adu_dr220.mp3|sound sample]]
-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>
+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.
-<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;32_27&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;32/27&lt;/strong&gt;&lt;br /&gt;
+It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].
-|5 -3&amp;gt;&lt;br /&gt;
-.135 cents&lt;br /&gt;
+== Temperaments ==
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_32_27_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_32_27_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_32_27_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_32_27_pluck_adu_dr220.mp3/513250248/jid_32_27_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_32_27_pluck_adu_dr220.mp3/513250248/jid_32_27_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
+/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]].
-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>
+== 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]]