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: | : 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> | : The original revision id was <tt>263901793</tt>.<br> | ||
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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> | ||
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=Z function= | =Z function= | ||
72edo is the ninth [[The Riemann Zeta Function and Tuning#Zeta | 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:// | * [[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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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:2 -->Z function</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:2 -->Z function</h1> | ||
72edo is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta | 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.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule:373:&lt;img src=&quot;/file/view/plot72.png/219772696/plot72.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" /><!-- ws:end:WikiTextLocalImageRule:373 --><br /> | <!-- ws:start:WikiTextLocalImageRule:373:&lt;img src=&quot;/file/view/plot72.png/219772696/plot72.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/plot72.png/219772696/plot72.png" alt="plot72.png" title="plot72.png" /><!-- ws:end:WikiTextLocalImageRule:373 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:6 -->External links</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:6 -->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://en.wikipedia.org/wiki/72_tone_equal_temperament" 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:// | <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://en.wikipedia.org/wiki/72_tone_equal_temperament" 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> | ||