72edo: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 238827829 - Original comment: **
Wikispaces>hstraub
**Imported revision 263901793 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-06-26 15:36:35 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-10-12 02:43:39 UTC</tt>.<br>
: The original revision id was <tt>238827829</tt>.<br>
: The original revision id was <tt>263901793</tt>.<br>
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=Z function=  
=Z function=  
72edo is the ninth [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[The Riemann Zeta Function and Tuning#The Z function|Z function]] 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.
72edo is the ninth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[The Riemann Zeta Function and Tuning#The%20Z%20function|Z function]] 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.


[[image:plot72.png]]
[[image:plot72.png]]
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* [[http://en.wikipedia.org/wiki/72_tone_equal_temperament|OrthodoxWiki Article on Byzantine chant, which uses 72edo]]
* [[http://en.wikipedia.org/wiki/72_tone_equal_temperament|OrthodoxWiki Article on Byzantine chant, which uses 72edo]]
* [[http://en.wikipedia.org/wiki/Joe_Maneri|Wikipedia article on Joe Maneri (1927-2009)]]
* [[http://en.wikipedia.org/wiki/Joe_Maneri|Wikipedia article on Joe Maneri (1927-2009)]]
* [[http://members.aon.at/ekmelischemusik/|Gesellschaft für Ekmelische Musik]], a group of composers and researchers dedicated to 72edo music
* [[http://www.ekmelic-music.org/en/index.htmmusik/|Ekmelic Music Society/Gesellschaft für Ekmelische Musik]], a group of composers and researchers dedicated to 72edo music
* [[http://sonic-arts.org/tagawa/72edo.htm|Rick Tagawa's 72edo site]], including theory and composers' list
* [[http://sonic-arts.org/tagawa/72edo.htm|Rick Tagawa's 72edo site]], including theory and composers' list
* [[http://dannywier.ucoz.com|Danny Wier, composer and musician who specializes in 72-edo]]</pre></div>
* [[http://dannywier.ucoz.com|Danny Wier, composer and musician who specializes in 72-edo]]</pre></div>
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&lt;br /&gt;
&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="Z function"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Z function&lt;/h1&gt;
  72edo is the ninth &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&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 Z function"&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;
  72edo 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;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: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;
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&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: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;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://en.wikipedia.org/wiki/72_tone_equal_temperament" 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://members.aon.at/ekmelischemusik/" rel="nofollow"&gt;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>
  &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://en.wikipedia.org/wiki/72_tone_equal_temperament" 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>