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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 = tridecimal 2/3-tone, trienthird, tridecimal supraminor second, sinaic |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-05 21:09:19 UTC</tt>.<br>
| | | Color name = 3uz2, thuzo 2nd |
| : The original revision id was <tt>318105244</tt>.<br>
| | | Sound = jid_14_13_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>
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| <h4>Original Wikitext content:</h4>
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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">14/13, the 2/3-tone or trienthird (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.
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| 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.)
| | '''14/13''', the '''tridecimal 2/3-tone''' or '''trienthird''' (one-third third) is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]]. |
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| 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.
| | The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor). Thus intervals close in size to it have been called '''sinaics''' by [[Zhea Erose]]. It may be called the '''tridecimal supraminor second''' as well, analogous to [[21/13]] being the ''tridecimal supraminor sixth''. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | In [[13-limit]] [[just intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[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. |
| <h4>Original HTML content:</h4>
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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>14_13</title></head><body>14/13, the 2/3-tone or trienthird (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 />
| | == See also == |
| <br />
| | * [[13/7]] – its [[octave complement]] |
| 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 />
| | * [[Gallery of just intervals]] |
| <br />
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| 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 />
| | [[Category:Second]] |
| <br />
| | [[Category:Neutral second]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | | [[Category:Supraminor second]] |
| | [[Category:Semitone]] |
14/13, the tridecimal 2/3-tone or trienthird (one-third third) is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a 5/4 major third- a stack of three trienthirds falling short of a 5/4 major third by a cantonisma.
The trienthird was a favorite interval of Avicenna (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor). Thus intervals close in size to it have been called sinaics by Zhea Erose. It may be called the tridecimal supraminor second as well, analogous to 21/13 being the tridecimal supraminor sixth.
In 13-limit just intonation, 14/13 represents the difference in size between the tridecimal minor third of 13/11 and undecimal major third of 14/11. It is also the difference between 13/10 and 7/5; 13/12 and 7/6; 13/9 and 14/9, and of course 13/8 and 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 also