171edo: Difference between revisions
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Wikispaces>hstraub **Imported revision 238142893 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 238828297 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-26 15:42:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238828297</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">//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 [[ | <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">//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 [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]] but not enough to make it a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|gap edo]]. | ||
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 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|. | ||
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[[nestoria12]]</pre></div> | [[nestoria12]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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>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=" | <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>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" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a> but not enough to make it a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">gap edo</a>.<br /> | ||
<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 &lt;59 -39 0 1|.<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 &lt;59 -39 0 1|.<br /> | ||
Revision as of 15:42, 26 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-06-26 15:42:22 UTC.
- The original revision id was 238828297.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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 [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]] but not enough to make it a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|gap edo]]. 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" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a> but not enough to make it a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">gap edo</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>