64/63: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~hstraub~~|~~hstraub~~]] and made on <tt>~~2013~~-08-~~16 06~~:07:29 UTC</tt>.

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-04-22 21:51:08 UTC</tt>.

: The original revision id was <tt>~~445082582~~</tt>.

: The original revision id was <tt>503937862</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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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;white-space: pre-wrap ! important" class="old-revision-html">Other languages: [[xenharmonie/64_63|Deutsch]]

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 interval 64/63, called **septimal comma** or **Archytas' comma** or (in German) [[@http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma|**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 >.

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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"><html><head><title>64_63</title></head><body>Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/64_63">Deutsch</a>

The interval 64/63, called septimal or Archytas comma (in German <~~strong~~>Leipziger Komma</~~strong~~>), is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/superparticular">superparticular ratio</a> which equates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8">9/8</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7">8/7</a> if tempered out and has the eighth square number as a numerator. It also equates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4">7/4</a> with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_9">16/9</a>, 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 interval 64/63, called septimal comma or Archytas' comma or (in German) <a class="wiki_link_ext" href="http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma" rel="nofollow" target="_blank">**Leipziger Komma**</a>, is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/superparticular">superparticular ratio</a> which equates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8">9/8</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7">8/7</a> if tempered out and has the eighth square number as a numerator. It also equates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4">7/4</a> with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_9">16/9</a>, 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;.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2013-08-16 06:07:29 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-04-22 21:51:08 UTC</tt>.<br>
-: The original revision id was <tt>445082582</tt>.<br>
+: The original revision id was <tt>503937862</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>
@@ Line 8: / Line 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">&lt;span style="display: block; text-align: right;"&gt;Other languages: [[xenharmonie/64_63|Deutsch]]
 &lt;/span&gt;
-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 interval 64/63, called **septimal comma** or **Archytas' comma** or (in German) [[@http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma|**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;.
@@ Line 21: / Line 21: @@
 <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;&lt;span style="display: block; text-align: right;"&gt;Other languages: &lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/64_63"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
 &lt;/span&gt;&lt;br /&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;
+The interval 64/63, called &lt;strong&gt;septimal comma&lt;/strong&gt; or &lt;strong&gt;Archytas' comma&lt;/strong&gt; or (in German) &lt;a class="wiki_link_ext" href="http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma" rel="nofollow" target="_blank"&gt;**Leipziger Komma**&lt;/a&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;
 The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &amp;gt;.&lt;br /&gt;