171edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~hstraub~~|~~hstraub~~]] and made on <tt>2011-06-~~22 07~~:03:54 UTC</tt>.<br>

: 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>~~238142893~~</tt>.<br>

: The original revision id was <tt>238828297</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>

<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 [[~~http://www.research.att.com/%7Enjas/sequences/A117538~~|Zeta ~~integral temperament~~]].

<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|.

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[[nestoria12]]</pre></div>

<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="~~wiki_link_ext~~" href="~~http://www.research.att.com~~/%~~7Enjas~~/~~sequences/A117538~~" ~~rel~~="~~nofollow~~">~~Zeta integral temperament~~</a>.<br />

<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 />

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 />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-22 07:03:54 UTC</tt>.<br>
+: 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>238142893</tt>.<br>
+: The original revision id was <tt>238828297</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>
 <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 [[http://www.research.att.com/%7Enjas/sequences/A117538|Zeta integral temperament]].
+<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]].
 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|.
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 [[nestoria12]]</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;171edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;171edo&lt;/em&gt; 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 &lt;a class="wiki_link_ext" href="http://www.research.att.com/%7Enjas/sequences/A117538" rel="nofollow"&gt;Zeta integral temperament&lt;/a&gt;.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;171edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;171edo&lt;/em&gt; 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 &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta integral edo&lt;/a&gt; but not enough to make it a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;gap edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 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 &amp;lt;59 -39 0 1|.&lt;br /&gt;