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6edo: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 575345733 - Original comment: **
Wikispaces>PiotrGrochowski
**Imported revision 590343118 - Original comment: 6edo's circle of fifths fails to close by 32/27, not 256/243**
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-20 11:43:36 UTC</tt>.<br>
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-29 12:15:01 UTC</tt>.<br>
: The original revision id was <tt>575345733</tt>.<br>
: The original revision id was <tt>590343118</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>6edo's circle of fifths fails to close by 32/27, not 256/243</tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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>
<h4>Original Wikitext content:</h4>
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**6-edo** divides the 1200-[[cents|cent]] octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.
**6-edo** divides the 1200-[[cents|cent]] octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.


==Related EDOs ==  
==Related EDOs==  
* Superset: [[2edo]], [[3edo]]
* Superset: [[2edo]], [[3edo]]
* Supersets: [[12edo]], [[18edo]], [[24edo]]...
* Supersets: [[12edo]], [[18edo]], [[24edo]]...
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6 EDO tempers out the following commas. (Note: This assumes val &lt; 6 10 14 17 21 22 |.)
6 EDO tempers out the following commas. (Note: This assumes val &lt; 6 10 14 17 21 22 |.)
||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Val ||
||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Val ||
||= 256/243 ||&gt; 90.22 || Limma || Pythagorean Minor 2nd || | 8 -5 &gt; ||
||= 32/27 ||&gt; 294.13 || Pythagorean minor third ||   || | 5 -3 &gt; ||
||= 128/125 ||&gt; 41.06 || Diesis || Augmented Comma || | 7 0 -3 &gt; ||
||= 128/125 ||&gt; 41.06 || Diesis || Augmented Comma || | 7 0 -3 &gt; ||
||= 3125/3072 ||&gt; 29.61 || Small Diesis || Magic Comma || | -10 -1 5 &gt; ||
||= 3125/3072 ||&gt; 29.61 || Small Diesis || Magic Comma || | -10 -1 5 &gt; ||
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&lt;strong&gt;6-edo&lt;/strong&gt; divides the 1200-&lt;a class="wiki_link" href="/cents"&gt;cent&lt;/a&gt; octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.&lt;br /&gt;
&lt;strong&gt;6-edo&lt;/strong&gt; divides the 1200-&lt;a class="wiki_link" href="/cents"&gt;cent&lt;/a&gt; octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x6 Equal Divisions of the Octave-Related EDOs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Related EDOs &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x6 Equal Divisions of the Octave-Related EDOs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Related EDOs&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;Superset: &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Supersets: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;Neighbours: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;Superset: &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Supersets: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;Neighbours: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x6 Equal Divisions of the Octave-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Notation&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x6 Equal Divisions of the Octave-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Notation&lt;/h2&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;256/243&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;32/27&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: right;"&gt;90.22&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;294.13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Limma&lt;br /&gt;
         &lt;td&gt;Pythagorean minor third&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Pythagorean Minor 2nd&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;| 8 -5 &amp;gt;&lt;br /&gt;
         &lt;td&gt;| 5 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Retrieved from "https://en.xen.wiki/w/6edo"