14/13
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2012-04-05 21:09:19 UTC.
- The original revision id was 318105244.
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Original Wikitext content:
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. 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]]
Original HTML content:
<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 /> <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 /> See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html>