64/63: Difference between revisions

Wikispaces>hstraub
**Imported revision 434004772 - Original comment: **
Wikispaces>xenwolf
**Imported revision 434005032 - Original comment: **
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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:hstraub|hstraub]] and made on <tt>2013-05-24 06:36:22 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-05-24 06:38:30 UTC</tt>.<br>
: The original revision id was <tt>434004772</tt>.<br>
: The original revision id was <tt>434005032</tt>.<br>
: The revision comment was: <tt></tt><br>
: 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>
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>
<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 interval 64/63, called **septimal** or **Archytas comma** (in german **Leipziger Komma**), is a [[xenharmonic/superparticular|superparticular ratio]] which equates [[xenharmonic/9_8|9/8]] and [[xenharmonic/8_7|8/7]] if tempered out and has the eighth square number as a numerator. It also equates [[xenharmonic/7_4|7/4]] with [[xenharmonic/16_9|16/9]], so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59.
<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 interval 64/63, called **septimal** or **Archytas comma** (in German **Leipziger Komma**), is a [[xenharmonic/superparticular|superparticular ratio]] which equates [[xenharmonic/9_8|9/8]] and [[xenharmonic/8_7|8/7]] if tempered out and has the eighth square number as a numerator. It also equates [[xenharmonic/7_4|7/4]] with [[xenharmonic/16_9|16/9]], so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59.


The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &gt;.
The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &gt;.
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[[http://en.wikipedia.org/wiki/Septimal_comma]]</pre></div>
[[http://en.wikipedia.org/wiki/Septimal_comma]]</pre></div>
<h4>Original HTML content:</h4>
<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;64_63&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The interval 64/63, called &lt;strong&gt;septimal&lt;/strong&gt; or &lt;strong&gt;Archytas comma&lt;/strong&gt; (in german &lt;strong&gt;Leipziger Komma&lt;/strong&gt;), is a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/superparticular"&gt;superparticular ratio&lt;/a&gt; which equates &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8"&gt;9/8&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7"&gt;8/7&lt;/a&gt; if tempered out and has the eighth square number as a numerator. It also equates &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4"&gt;7/4&lt;/a&gt; with &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_9"&gt;16/9&lt;/a&gt;, so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59.&lt;br /&gt;
<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;64_63&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The interval 64/63, called &lt;strong&gt;septimal&lt;/strong&gt; or &lt;strong&gt;Archytas comma&lt;/strong&gt; (in German &lt;strong&gt;Leipziger Komma&lt;/strong&gt;), is a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/superparticular"&gt;superparticular ratio&lt;/a&gt; which equates &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8"&gt;9/8&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7"&gt;8/7&lt;/a&gt; if tempered out and has the eighth square number as a numerator. It also equates &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4"&gt;7/4&lt;/a&gt; with &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_9"&gt;16/9&lt;/a&gt;, so that the just dominant seventh chord, 1-5/4-3/2-16/9, and the otonal tetrad, 1-5/4-3/2-7/4, are equated to the same chord when 64/63 is tempered out. Equal divisions of the octave tempering out 64/63 include 12, 15, 22, 27, 37, 49 and 59.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &amp;gt;.&lt;br /&gt;
The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &amp;gt;.&lt;br /&gt;