72edo: Difference between revisions
Wikispaces>guest **Imported revision 288351900 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 298249420 - Original comment: ** |
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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>2012-02-03 14:21:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>298249420</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> | ||
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=Music= | =Music= | ||
[[http://www.archive.org/details/Kotekant|Kotekant]] [[http://www.archive.org/download/Kotekant/kotekant.mp3|play]] by [[Gene Ward Smith]] | [[http://www.archive.org/details/Kotekant|Kotekant]] [[http://www.archive.org/download/Kotekant/kotekant.mp3|play]] by [[Gene Ward Smith]] | ||
=Scales= | |||
[[genus24255et72|Euler(24255) genus in 72 equal]] | |||
=External links= | =External links= | ||
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* [[http://soundcloud.com/dawiertx|Danny Wier, composer and musician who specializes in 72-edo]]</pre></div> | * [[http://soundcloud.com/dawiertx|Danny Wier, composer and musician who specializes in 72-edo]]</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>72edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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><!-- ws:start:WikiTextTocRule:16:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#toc2"> </a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Z function">Z function</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
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72-tone equal temperament (or 72-edo) divides the octave into 72 steps or <em>moria</em>. 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.<br /> | 72-tone equal temperament (or 72-edo) divides the octave into 72 steps or <em>moria</em>. 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.<br /> | ||
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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 /> | 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: | <!-- ws:start:WikiTextLocalImageRule:1277:&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:1277 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:10 -->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><br /> | <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><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->Scales</h1> | ||
<a class="wiki_link" href="/genus24255et72">Euler(24255) genus in 72 equal</a><br /> | |||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:14 -->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://soundcloud.com/dawiertx" rel="nofollow">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div> | <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://soundcloud.com/dawiertx" rel="nofollow">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div> | ||