14/13: 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:<br>

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-08-~~25 14~~:41:22 UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 16:35:21 UTC</tt>.<br>

: The original revision id was <tt>~~248474547~~</tt>.<br>

: The original revision id was <tt>260511346</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>

<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">14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which is almost exactly 1/3 of a major third of 5/4. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable ~~divisions~~ as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.

<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">14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which, measuring about 128.3¢, is almost exactly 1/3 of a major third of [[5_4|5/4]]. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable [[EDO]]s as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.

The trienthird was a favorite interval of [[http://en.wikipedia.org/wiki/Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)</pre></div>

The trienthird was a favorite interval of [[http://en.wikipedia.org/wiki/Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)

In [[13-limit]] [[Just Intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13_11|13/11]] and tridecimal supermajor third of [[14_11|14/11]]. It is also the difference between [[13_10|13/10]] and [[7_5|7/5]]; [[13_12|13/12]] and [[7_6|7/6]]; [[13_9|13/9]] and [[14_9|14/9]], and of course [[13_8|13/8]] and [[7_4|7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.

See: [[Gallery of Just Intervals]]</pre></div>

<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>14_13</title></head><body>14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which is almost exactly 1/3 of a major third of 5/4. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable ~~divisions~~ as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.<br />

<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>14_13</title></head><body>14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which, measuring about 128.3¢, is almost exactly 1/3 of a major third of <a class="wiki_link" href="/5_4">5/4</a>. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable <a class="wiki_link" href="/EDO">EDO</a>s as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.<br />

<br />

The trienthird was a favorite interval of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Avicenna" rel="nofollow">Avicenna</a> (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)<br />

<br />

In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 14/13 represents the difference in size between the tridecimal minor third of <a class="wiki_link" href="/13_11">13/11</a> and tridecimal supermajor third of <a class="wiki_link" href="/14_11">14/11</a>. It is also the difference between <a class="wiki_link" href="/13_10">13/10</a> and <a class="wiki_link" href="/7_5">7/5</a>; <a class="wiki_link" href="/13_12">13/12</a> and <a class="wiki_link" href="/7_6">7/6</a>; <a class="wiki_link" href="/13_9">13/9</a> and <a class="wiki_link" href="/14_9">14/9</a>, and of course <a class="wiki_link" href="/13_8">13/8</a> and <a class="wiki_link" href="/7_4">7/4</a> and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.<br />

<br />

~~The trienthird was a favorite interval of~~ <a class="~~wiki_link_ext~~" href="~~http://en.wikipedia.org/wiki~~/~~Avicenna" rel="nofollow~~">~~Avicenna~~</a> ~~(Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)~~</body></html></pre></div>

See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>

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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:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-25 14:41:22 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 16:35:21 UTC</tt>.<br>
-: The original revision id was <tt>248474547</tt>.<br>
+: The original revision id was <tt>260511346</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>
 <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">14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which is almost exactly 1/3 of a major third of 5/4. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable divisions as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.
+<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">14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which, measuring about 128.3¢, is almost exactly 1/3 of a major third of [[5_4|5/4]]. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable [[EDO]]s as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.
-The trienthird was a favorite interval of [[http://en.wikipedia.org/wiki/Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)</pre></div>
+The trienthird was a favorite interval of [[http://en.wikipedia.org/wiki/Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)
+In [[13-limit]] [[Just Intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13_11|13/11]] and tridecimal supermajor third of [[14_11|14/11]]. It is also the difference between [[13_10|13/10]] and [[7_5|7/5]]; [[13_12|13/12]] and [[7_6|7/6]]; [[13_9|13/9]] and [[14_9|14/9]], and of course [[13_8|13/8]] and [[7_4|7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.
+See: [[Gallery of Just Intervals]]</pre></div>
 <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;14_13&lt;/title&gt;&lt;/head&gt;&lt;body&gt;14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which is almost exactly 1/3 of a major third of 5/4. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable divisions as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.&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;14_13&lt;/title&gt;&lt;/head&gt;&lt;body&gt;14/13, the 2/3-tone or trienthrid (one-third third) interval is a somewhat exotic 13-limit interval which, measuring about 128.3¢, is almost exactly 1/3 of a major third of &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;. The small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.&lt;br /&gt;
+&lt;br /&gt;
+The trienthird was a favorite interval of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Avicenna" rel="nofollow"&gt;Avicenna&lt;/a&gt; (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)&lt;br /&gt;
+&lt;br /&gt;
+In &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 14/13 represents the difference in size between the tridecimal minor third of &lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt; and tridecimal supermajor third of &lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;. It is also the difference between &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; and &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;; &lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt; and &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;; &lt;a class="wiki_link" href="/13_9"&gt;13/9&lt;/a&gt; and &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, and of course &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; and &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.&lt;br /&gt;
 &lt;br /&gt;
-The trienthird was a favorite interval of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Avicenna" rel="nofollow"&gt;Avicenna&lt;/a&gt; (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)&lt;/body&gt;&lt;/html&gt;</pre></div>
+See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>