72edo: 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:

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-~~24 02~~:03:56 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-03 14:20:40 UTC</tt>.

: The original revision id was <tt>~~267798768~~</tt>.

: The original revision id was <tt>271608782</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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|| Nearest degree of 72edo: || || 12 || || 11 || || 10 || || 9 || || 8 || || 8 || || 7 || || 7 || ||

|| ...in cents: || || 200.0 || || 183.3 || || 166.7 || || 150.0 || || 133.3 || || 133.3 || || 116.7 || || 116.7 || ||

=Linear temperaments=

||~ Periods per octave ||~ Generator ||~ Names ||

|| 1 || 1\72 || [[quincy]] ||

|| 1 || 5\72 || ||

|| 1 || 7\72 || [[miracle]]/benediction/manna ||

|| 1 || 11\72 || ||

|| 1 || 13\72 || ||

|| 1 || 17\72 || [[neominor]] ||

|| 1 || 19\72 || [[catakleismic]] ||

|| 1 || 23\72 || ||

|| 1 || 25\72 || [[sqrtphi]] ||

|| 1 || 29\72 || ||

|| 1 || 31\72 || [[marvo]]/zarvo ||

|| 1 || 35\72 || [[cotritone]] ||

|| 2 || 1\72 || ||

|| 2 || 5\72 || [[harry]] ||

|| 2 || 7\72 || ||

|| 2 || 11\72 || [[unidec]]/hendec ||

|| 2 || 13\72 || [[wizard]]/lizard/gizzard ||

|| 2 || 17\72 || ||

|| 3 || 1\72 || ||

|| 3 || 5\72 || [[tritikleismic]] ||

|| 3 || 7\72 || ||

|| 3 || 11\72 || [[mirkat]] ||

|| 4 || 1\72 || [[quadritikleismic]] ||

|| 4 || 5\72 || ||

|| 4 || 7\72 || ||

|| 6 || 1\72 || ||

|| 6 || 5\72 || ||

|| 8 || 1\72 || [[octoid]] ||

|| 8 || 2\72 || [[octowerck]] ||

|| 8 || 4\72 || ||

|| 9 || 1\72 || ||

|| 9 || 3\72 || [[ennealimmal]]/ennealimmic ||

|| 12 || 1\72 || [[compton]] ||

|| 18 || 1\72 || [[hemiennealimmal]] ||

|| 24 || 1\72 || ||

|| 36 || 1\72 || ||

=Z function=

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* [[http://dannywier.ucoz.com|Danny Wier, composer and musician who specializes in 72-edo]]</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>72edo</title></head><body><a href="#Harmonic Scale">Harmonic Scale</a> | <a href="#Z function">Z function</a> | <a href="#Music">Music</a> | <a href="#External links">External links</a>

<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>72edo</title></head><body><a href="#Harmonic Scale">Harmonic Scale</a> | <a href="#Linear temperaments">Linear temperaments</a> | <a href="#Z function">Z function</a> | <a href="#Music">Music</a> | <a href="#External links">External links</a>

<hr />

<hr />

72-tone equal temperament (or 72-edo) divides the octave into 72 steps or moria. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of <a class="wiki_link" href="/24edo">24-tone equal temperament</a>, a common and standard tuning of <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic</a> music, and has itself been used to tune Turkish music.

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<h1 id="toc1"><a name="Z function"></a>Z function</h1>

<h1 id="toc1"><a name="Linear temperaments"></a>Linear temperaments</h1>

<tr>

<th>Periods per octave

</th>

<th>Generator

</th>

<th>Names

</th>

</tr>

<tr>

<td>1

</td>

<td>1\72

</td>

<td><a class="wiki_link" href="/quincy">quincy</a>

</td>

</tr>

<tr>

<td>1

</td>

<td>5\72

</td>

<td>

</td>

</tr>

<tr>

<td>1

</td>

<td>7\72

</td>

<td><a class="wiki_link" href="/miracle">miracle</a>/benediction/manna

</td>

</tr>

<tr>

<td>1

</td>

<td>11\72

</td>

<td>

</td>

</tr>

<tr>

<td>1

</td>

<td>13\72

</td>

<td>

</td>

</tr>

<tr>

<td>1

</td>

<td>17\72

</td>

<td><a class="wiki_link" href="/neominor">neominor</a>

</td>

</tr>

<tr>

<td>1

</td>

<td>19\72

</td>

<td><a class="wiki_link" href="/catakleismic">catakleismic</a>

</td>

</tr>

<tr>

<td>1

</td>

<td>23\72

</td>

<td>

</td>

</tr>

<tr>

<td>1

</td>

<td>25\72

</td>

<td><a class="wiki_link" href="/sqrtphi">sqrtphi</a>

</td>

</tr>

<tr>

<td>1

</td>

<td>29\72

</td>

<td>

</td>

</tr>

<tr>

<td>1

</td>

<td>31\72

</td>

<td><a class="wiki_link" href="/marvo">marvo</a>/zarvo

</td>

</tr>

<tr>

<td>1

</td>

<td>35\72

</td>

<td><a class="wiki_link" href="/cotritone">cotritone</a>

</td>

</tr>

<tr>

<td>2

</td>

<td>1\72

</td>

<td>

</td>

</tr>

<tr>

<td>2

</td>

<td>5\72

</td>

<td><a class="wiki_link" href="/harry">harry</a>

</td>

</tr>

<tr>

<td>2

</td>

<td>7\72

</td>

<td>

</td>

</tr>

<tr>

<td>2

</td>

<td>11\72

</td>

<td><a class="wiki_link" href="/unidec">unidec</a>/hendec

</td>

</tr>

<tr>

<td>2

</td>

<td>13\72

</td>

<td><a class="wiki_link" href="/wizard">wizard</a>/lizard/gizzard

</td>

</tr>

<tr>

<td>2

</td>

<td>17\72

</td>

<td>

</td>

</tr>

<tr>

<td>3

</td>

<td>1\72

</td>

<td>

</td>

</tr>

<tr>

<td>3

</td>

<td>5\72

</td>

<td><a class="wiki_link" href="/tritikleismic">tritikleismic</a>

</td>

</tr>

<tr>

<td>3

</td>

<td>7\72

</td>

<td>

</td>

</tr>

<tr>

<td>3

</td>

<td>11\72

</td>

<td><a class="wiki_link" href="/mirkat">mirkat</a>

</td>

</tr>

<tr>

<td>4

</td>

<td>1\72

</td>

<td><a class="wiki_link" href="/quadritikleismic">quadritikleismic</a>

</td>

</tr>

<tr>

<td>4

</td>

<td>5\72

</td>

<td>

</td>

</tr>

<tr>

<td>4

</td>

<td>7\72

</td>

<td>

</td>

</tr>

<tr>

<td>6

</td>

<td>1\72

</td>

<td>

</td>

</tr>

<tr>

<td>6

</td>

<td>5\72

</td>

<td>

</td>

</tr>

<tr>

<td>8

</td>

<td>1\72

</td>

<td><a class="wiki_link" href="/octoid">octoid</a>

</td>

</tr>

<tr>

<td>8

</td>

<td>2\72

</td>

<td><a class="wiki_link" href="/octowerck">octowerck</a>

</td>

</tr>

<tr>

<td>8

</td>

<td>4\72

</td>

<td>

</td>

</tr>

<tr>

<td>9

</td>

<td>1\72

</td>

<td>

</td>

</tr>

<tr>

<td>9

</td>

<td>3\72

</td>

<td><a class="wiki_link" href="/ennealimmal">ennealimmal</a>/ennealimmic

</td>

</tr>

<tr>

<td>12

</td>

<td>1\72

</td>

<td><a class="wiki_link" href="/compton">compton</a>

</td>

</tr>

<tr>

<td>18

</td>

<td>1\72

</td>

<td><a class="wiki_link" href="/hemiennealimmal">hemiennealimmal</a>

</td>

</tr>

<tr>

<td>24

</td>

<td>1\72

</td>

<td>

</td>

</tr>

<tr>

<td>36

</td>

<td>1\72

</td>

<td>

</td>

</tr>

</table>

<h1 id="toc2"><a name="Z function"></a>Z function</h1>

72edo is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>, as well as being a peak and gap edo, and the maximum value of the <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#The%20Z%20function">Z function</a> in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.

<img src="/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" />

<img src="/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" />

<h1 id="~~toc2~~"><a name="Music"></a>Music</h1>

<h1 id="toc3"><a name="Music"></a>Music</h1>

<a class="wiki_link_ext" href="http://www.archive.org/details/Kotekant" rel="nofollow">Kotekant</a> <a class="wiki_link_ext" href="http://www.archive.org/download/Kotekant/kotekant.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a>

<h1 id="~~toc3~~"><a name="External links"></a>External links</h1>

<h1 id="toc4"><a name="External links"></a>External links</h1>

<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/72_tone_equal_temperament" rel="nofollow">Wikipedia article on 72edo</a></li><li><a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant" rel="nofollow">OrthodoxWiki Article on Byzantine chant, which uses 72edo</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joe_Maneri" rel="nofollow">Wikipedia article on Joe Maneri (1927-2009)</a></li><li><a class="wiki_link_ext" href="http://www.ekmelic-music.org/en/index.htmmusik/" rel="nofollow">Ekmelic Music Society/Gesellschaft für Ekmelische Musik</a>, a group of composers and researchers dedicated to 72edo music</li><li><a class="wiki_link_ext" href="http://sonic-arts.org/tagawa/72edo.htm" rel="nofollow">Rick Tagawa's 72edo site</a>, including theory and composers' list</li><li><a class="wiki_link_ext" href="http://dannywier.ucoz.com" rel="nofollow">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div>

@@ 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:keenanpepper|keenanpepper]] and made on <tt>2011-10-24 02:03:56 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-03 14:20:40 UTC</tt>.<br>
-: The original revision id was <tt>267798768</tt>.<br>
+: The original revision id was <tt>271608782</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>
@@ Line 28: / Line 28: @@
 || Nearest degree of 72edo: ||   || 12 ||   || 11 ||   || 10 ||   || 9 ||   || 8 ||   || 8 ||   || 7 ||   || 7 ||   ||
 || ...in cents: ||   || 200.0 ||   || 183.3 ||   || 166.7 ||   || 150.0 ||   || 133.3 ||   || 133.3 ||   || 116.7 ||   || 116.7 ||   ||
+=Linear temperaments=
+||~ Periods per octave ||~ Generator ||~ Names ||
+|| 1 || 1\72 || [[quincy]] ||
+|| 1 || 5\72 ||   ||
+|| 1 || 7\72 || [[miracle]]/benediction/manna ||
+|| 1 || 11\72 ||   ||
+|| 1 || 13\72 ||   ||
+|| 1 || 17\72 || [[neominor]] ||
+|| 1 || 19\72 || [[catakleismic]] ||
+|| 1 || 23\72 ||   ||
+|| 1 || 25\72 || [[sqrtphi]] ||
+|| 1 || 29\72 ||   ||
+|| 1 || 31\72 || [[marvo]]/zarvo ||
+|| 1 || 35\72 || [[cotritone]] ||
+|| 2 || 1\72 ||   ||
+|| 2 || 5\72 || [[harry]] ||
+|| 2 || 7\72 ||   ||
+|| 2 || 11\72 || [[unidec]]/hendec ||
+|| 2 || 13\72 || [[wizard]]/lizard/gizzard ||
+|| 2 || 17\72 ||   ||
+|| 3 || 1\72 ||   ||
+|| 3 || 5\72 || [[tritikleismic]] ||
+|| 3 || 7\72 ||   ||
+|| 3 || 11\72 || [[mirkat]] ||
+|| 4 || 1\72 || [[quadritikleismic]] ||
+|| 4 || 5\72 ||   ||
+|| 4 || 7\72 ||   ||
+|| 6 || 1\72 ||   ||
+|| 6 || 5\72 ||   ||
+|| 8 || 1\72 || [[octoid]] ||
+|| 8 || 2\72 || [[octowerck]] ||
+|| 8 || 4\72 ||   ||
+|| 9 || 1\72 ||   ||
+|| 9 || 3\72 || [[ennealimmal]]/ennealimmic ||
+|| 12 || 1\72 || [[compton]] ||
+|| 18 || 1\72 || [[hemiennealimmal]] ||
+|| 24 || 1\72 ||   ||
+|| 36 || 1\72 ||   ||
 =Z function=
@@ Line 45: / Line 84: @@
 * [[http://dannywier.ucoz.com|Danny Wier, composer and musician who specializes in 72-edo]]</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;72edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt; | &lt;a href="#Z function"&gt;Z function&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&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;72edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:10:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Linear temperaments"&gt;Linear temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt; | &lt;a href="#Z function"&gt;Z function&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;hr /&gt;
 -tone equal temperament (or 72-edo) divides the octave into 72 steps or &lt;em&gt;moria&lt;/em&gt;. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of &lt;a class="wiki_link" href="/24edo"&gt;24-tone equal temperament&lt;/a&gt;, a common and standard tuning of &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic&lt;/a&gt; music, and has itself been used to tune Turkish music.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 406: / Line 445: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Z function"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Z function&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Linear temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Linear temperaments&lt;/h1&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Periods per octave&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Generator&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Names&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/quincy"&gt;quincy&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/miracle"&gt;miracle&lt;/a&gt;/benediction/manna&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/neominor"&gt;neominor&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/catakleismic"&gt;catakleismic&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;23\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/sqrtphi"&gt;sqrtphi&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/marvo"&gt;marvo&lt;/a&gt;/zarvo&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+        &lt;td&gt;&lt;a class="wiki_link" href="/cotritone"&gt;cotritone&lt;/a&gt;&lt;br /&gt;
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+    &lt;tr&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/harry"&gt;harry&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
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+    &lt;tr&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/unidec"&gt;unidec&lt;/a&gt;/hendec&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/wizard"&gt;wizard&lt;/a&gt;/lizard/gizzard&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/tritikleismic"&gt;tritikleismic&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
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+&lt;/td&gt;
+        &lt;td&gt;11\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/mirkat"&gt;mirkat&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/quadritikleismic"&gt;quadritikleismic&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/octoid"&gt;octoid&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/octowerck"&gt;octowerck&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/ennealimmal"&gt;ennealimmal&lt;/a&gt;/ennealimmic&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/compton"&gt;compton&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/hemiennealimmal"&gt;hemiennealimmal&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1\72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Z function"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Z function&lt;/h1&gt;
 edo is the ninth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt;, as well as being a peak and gap edo, and the maximum value of the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#The%20Z%20function"&gt;Z function&lt;/a&gt; in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:373:&amp;lt;img src=&amp;quot;/file/view/plot72.png/219772696/plot72.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:373 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:674:&amp;lt;img src=&amp;quot;/file/view/plot72.png/219772696/plot72.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:674 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Music&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Music&lt;/h1&gt;
   &lt;a class="wiki_link_ext" href="http://www.archive.org/details/Kotekant" rel="nofollow"&gt;Kotekant&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/Kotekant/kotekant.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;External links&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;External links&lt;/h1&gt;
   &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/72_tone_equal_temperament" rel="nofollow"&gt;Wikipedia article on 72edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant" rel="nofollow"&gt;OrthodoxWiki Article on Byzantine chant, which uses 72edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joe_Maneri" rel="nofollow"&gt;Wikipedia article on Joe Maneri (1927-2009)&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ekmelic-music.org/en/index.htmmusik/" rel="nofollow"&gt;Ekmelic Music Society/Gesellschaft für Ekmelische Musik&lt;/a&gt;, a group of composers and researchers dedicated to 72edo music&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/tagawa/72edo.htm" rel="nofollow"&gt;Rick Tagawa's 72edo site&lt;/a&gt;, including theory and composers' list&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://dannywier.ucoz.com" rel="nofollow"&gt;Danny Wier, composer and musician who specializes in 72-edo&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>