171edo
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- This revision was by author hstraub and made on 2011-06-22 07:03:54 UTC.
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Original Wikitext content:
//171edo// is a remarkable division of the octave which serves as a microtemperament for the 7-limit, approximating the 9-limit tonality diamond within about 2/5 of a cent. It divides the octave into 171 parts of 7.016 cents each. The excellence of its 7-limit approximations is good enough to make it the eleventh [[http://www.research.att.com/%7Enjas/sequences/A117538|Zeta integral temperament]]. 171 supports a number of 7-limit rank-two temperaments: pontiac, with commas 4375/4374 and 32805/32768; sesquiquartififths, with 2401/2400 and 32805/32768; term, with 32805/32768 and 250047/250000; ennealimmal, with 2401/2400 and 4375/4374; tertiaseptal with 2401/2400 and 65635/65536; supermajor, with 4375/4374 and 52734275/52706752; enneadecal with 4375/4374 and 703125/702464; neptune, with 2401/2400 and 48828125/488771072; mitonic, with 4375/4374 and 2100875/2097152; and mutt, with 65635/65536 and 250047/250000. It is also an excellent tuning for the 5-limit schismatic microtemperament, tempering out 32805/32768, and the no-fives temperament tempering out <59 -39 0 1|. 171 factors into primes as 3^2 * 19, and it shares the nearly pure 7/6 of [[9edo]] and the nearly pure 6/5 of [[19edo]], with every 7-limit interval expressible in terms of 2, 6/5 and 7/6. 171 is much less accurate in the 11-limit, but still quite useful as it is a good tuning (emphasizing accuracy in the 7-limit) for the important rank-three temperament jove, which tempers out 243/242 and 441/440, not to mention 540/539 and 2401/2400. Jove can be extended by adding 364/363 for the 13 limit and 595/594 for the 17 limit, which 171 also supports. =Scales= [[nestoria7]] [[nestoria12]]
Original HTML content:
<html><head><title>171edo</title></head><body><em>171edo</em> is a remarkable division of the octave which serves as a microtemperament for the 7-limit, approximating the 9-limit tonality diamond within about 2/5 of a cent. It divides the octave into 171 parts of 7.016 cents each. The excellence of its 7-limit approximations is good enough to make it the eleventh <a class="wiki_link_ext" href="http://www.research.att.com/%7Enjas/sequences/A117538" rel="nofollow">Zeta integral temperament</a>.<br /> <br /> 171 supports a number of 7-limit rank-two temperaments: pontiac, with commas 4375/4374 and 32805/32768; sesquiquartififths, with 2401/2400 and 32805/32768; term, with 32805/32768 and 250047/250000; ennealimmal, with 2401/2400 and 4375/4374; tertiaseptal with 2401/2400 and 65635/65536; supermajor, with 4375/4374 and 52734275/52706752; enneadecal with 4375/4374 and 703125/702464; neptune, with 2401/2400 and 48828125/488771072; mitonic, with 4375/4374 and 2100875/2097152; and mutt, with 65635/65536 and 250047/250000. It is also an excellent tuning for the 5-limit schismatic microtemperament, tempering out 32805/32768, and the no-fives temperament tempering out <59 -39 0 1|.<br /> <br /> 171 factors into primes as 3^2 * 19, and it shares the nearly pure 7/6 of <a class="wiki_link" href="/9edo">9edo</a> and the nearly pure 6/5 of <a class="wiki_link" href="/19edo">19edo</a>, with every 7-limit interval expressible in terms of 2, 6/5 and 7/6. 171 is much less accurate in the 11-limit, but still quite useful as it is a good tuning (emphasizing accuracy in the 7-limit) for the important rank-three temperament jove, which tempers out 243/242 and 441/440, not to mention 540/539 and 2401/2400. Jove can be extended by adding 364/363 for the 13 limit and 595/594 for the 17 limit, which 171 also supports.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1> <a class="wiki_link" href="/nestoria7">nestoria7</a><br /> <a class="wiki_link" href="/nestoria12">nestoria12</a></body></html>