81/80
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenjacob and made on 2011-09-14 23:42:36 UTC.
- The original revision id was 254214124.
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Original Wikitext content:
The **syntonic** or **Didymus comma**, 81/80, is the smallest [[superparticular|superparticular interval]] which belongs to the [[5-limit]]. Like [[16_15|16/15]], [[625_624|625/624]], [[2401_2400|2401/2400]] and [[4096_4095|4096/4095]] it has a fourth power as a numerator, marking it as a comma which is the ratio between two larger successive superparticular intervals; it is in fact the difference between [[10_9|10/9]] and [[9_8|9/8]], the product of which is the just major third, [[5_4|5/4]]. Tempering it out gives a tuning for the whole tone which is intermediate between 10/9 and 9/8, and leads to [[Meantone family|meantone temperament]]. Youtube video of "[[http://www.youtube.com/watch?v=IpWiEWFRGAY|Five senses of 81/80]]", demonstratory video by Jacob Barton. According to [[http://untwelve.org/interviews/golden.html|this interview]], Monroe Golden's //Incongruity// uses just-intonation chord progressions that exploit this comma. [[http://en.wikipedia.org/wiki/Syntonic_comma]]
Original HTML content:
<html><head><title>81_80</title></head><body>The <strong>syntonic</strong> or <strong>Didymus comma</strong>, 81/80, is the smallest <a class="wiki_link" href="/superparticular">superparticular interval</a> which belongs to the <a class="wiki_link" href="/5-limit">5-limit</a>. Like <a class="wiki_link" href="/16_15">16/15</a>, <a class="wiki_link" href="/625_624">625/624</a>, <a class="wiki_link" href="/2401_2400">2401/2400</a> and <a class="wiki_link" href="/4096_4095">4096/4095</a> it has a fourth power as a numerator, marking it as a comma which is the ratio between two larger successive superparticular intervals; it is in fact the difference between <a class="wiki_link" href="/10_9">10/9</a> and <a class="wiki_link" href="/9_8">9/8</a>, the product of which is the just major third, <a class="wiki_link" href="/5_4">5/4</a>. Tempering it out gives a tuning for the whole tone which is intermediate between 10/9 and 9/8, and leads to <a class="wiki_link" href="/Meantone%20family">meantone temperament</a>.<br /> <br /> Youtube video of "<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=IpWiEWFRGAY" rel="nofollow">Five senses of 81/80</a>", demonstratory video by Jacob Barton.<br /> <br /> According to <a class="wiki_link_ext" href="http://untwelve.org/interviews/golden.html" rel="nofollow">this interview</a>, Monroe Golden's <em>Incongruity</em> uses just-intonation chord progressions that exploit this comma.<br /> <br /> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">http://en.wikipedia.org/wiki/Syntonic_comma</a></body></html>