15edo: Difference between revisions

Revision as of 06:15, 19 February 2010

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=15 tone equal temperament= 

15-edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.
15-edo has been labeled a "Porcupine" temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the "Mizarian Porcupine Overture" by Herman Miller. It also falls into the catagory of kleisma tunings along with 53 and 19.

""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone."


[[image:http://www.swordguitars.com/Sword_15edoclassicalsm.JPG]](15-tone Classical Guitar by Ron Sword)



==Theory== 
[[http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html|15-EDO Tutorial]] by Brent Carson.
Sword, Ronald. "Pentadecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.
==**Compositions**== 
[[http://teamouse.googlepages.com/MizarianPorcupineOverture.mp3|Mizarian Porcupine Overture]] by [[http://teamouse.googlepages.com/home|Herman Miller]] ([[Regular Temperaments#porcupine|porcupine]] chord progressions)
[[http://www.microtonalmusic.net/audio/15edostudy.mp3|Study for Bells]] by [[http://danielthompson.blogspot.com/|Daniel Thompson]] (Jan. 2007)
Study for Kyle Gann by [[http://www.akjmusic.com/works.html|Aaron K. Johnson]] (12-out-of-15)
[[http://rm-and-jo.laughingsquid.org/Music/index.html|Rick McGowan]]: a lot of music, for example [[http://rm-and-jo.laughingsquid.org/Music/McGowan-FourBalletScenes.mp3|Four Ballet Scenes]] and [[http://rm-and-jo.laughingsquid.org/temp/sgs-4-a.mp3|Four]]
Brian McLaren: 5 piano pieces
Easley Blackwood: Suite for Guitar in 15 equal tuning
[[http://absurdistlover.com/music/my-first-succesful-foray-into-microtonal-music/|sketch]] by AbsurdistLover (Jan. 2007 )
[[http://www.soundclick.com/bands/songInfo.cfm?bandID=145852&songID=2920478|Hyperimprovisation 3.3]] by Jacob Barton (2003)
[[http://www.h-pi.com/midi/15ET.mid|Elegy in 15ET]] by Aaron Andrew Hunt
[[http://www.h-pi.com/midi/15ETa3fugue2.mid|Fugue a3 in 15ET]] by Aaron Andrew Hunt

Original HTML content:

<html><head><title>15edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x15 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->15 tone equal temperament</h1>
 <br />
15-edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.<br />
15-edo has been labeled a &quot;Porcupine&quot; temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the &quot;Mizarian Porcupine Overture&quot; by Herman Miller. It also falls into the catagory of kleisma tunings along with 53 and 19.<br />
<br />
&quot;&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone.&quot;<br />
<br />
<br />
<!-- ws:start:WikiTextRemoteImageRule:6:&lt;img src=&quot;http://www.swordguitars.com/Sword_15edoclassicalsm.JPG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="external image Sword_15edoclassicalsm.JPG" title="external image Sword_15edoclassicalsm.JPG" /><!-- ws:end:WikiTextRemoteImageRule:6 -->(15-tone Classical Guitar by Ron Sword)<br />
<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x15 tone equal temperament-Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h2>
 <a class="wiki_link_ext" href="http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html" rel="nofollow">15-EDO Tutorial</a> by Brent Carson.<br />
Sword, Ronald. &quot;Pentadecaphonic Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: June 2009.<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x15 tone equal temperament-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>Compositions</strong></h2>
 <a class="wiki_link_ext" href="http://teamouse.googlepages.com/MizarianPorcupineOverture.mp3" rel="nofollow">Mizarian Porcupine Overture</a> by <a class="wiki_link_ext" href="http://teamouse.googlepages.com/home" rel="nofollow">Herman Miller</a> (<a class="wiki_link" href="/Regular%20Temperaments#porcupine">porcupine</a> chord progressions)<br />
<a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/15edostudy.mp3" rel="nofollow">Study for Bells</a> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a> (Jan. 2007)<br />
Study for Kyle Gann by <a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">Aaron K. Johnson</a> (12-out-of-15)<br />
<a class="wiki_link_ext" href="http://rm-and-jo.laughingsquid.org/Music/index.html" rel="nofollow">Rick McGowan</a>: a lot of music, for example <a class="wiki_link_ext" href="http://rm-and-jo.laughingsquid.org/Music/McGowan-FourBalletScenes.mp3" rel="nofollow">Four Ballet Scenes</a> and <a class="wiki_link_ext" href="http://rm-and-jo.laughingsquid.org/temp/sgs-4-a.mp3" rel="nofollow">Four</a><br />
Brian McLaren: 5 piano pieces<br />
Easley Blackwood: Suite for Guitar in 15 equal tuning<br />
<a class="wiki_link_ext" href="http://absurdistlover.com/music/my-first-succesful-foray-into-microtonal-music/" rel="nofollow">sketch</a> by AbsurdistLover (Jan. 2007 )<br />
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/songInfo.cfm?bandID=145852&amp;songID=2920478" rel="nofollow">Hyperimprovisation 3.3</a> by Jacob Barton (2003)<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/15ET.mid" rel="nofollow">Elegy in 15ET</a> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/15ETa3fugue2.mid" rel="nofollow">Fugue a3 in 15ET</a> by Aaron Andrew Hunt</body></html>

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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:guest|guest]] and made on <tt>2009-06-03 17:59:09 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 06:15:39 UTC</tt>.<br>
-: The original revision id was <tt>76664493</tt>.<br>
+: The original revision id was <tt>121498917</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">=15 tone equal temperament=
+-edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.
+-edo has been labeled a "Porcupine" temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the "Mizarian Porcupine Overture" by Herman Miller. It also falls into the catagory of kleisma tunings along with 53 and 19.
+""In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone."
+[[image:http://www.swordguitars.com/Sword_15edoclassicalsm.JPG]](15-tone Classical Guitar by Ron Sword)
 ==Theory==
@@ Line 25: / Line 35: @@
 <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;15edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x15 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;15 tone equal temperament&lt;/h1&gt;
   &lt;br /&gt;
+-edo is a 7-limit tuning because of the amount of septimal intervals, but it does contain 11-limit intervals.&lt;br /&gt;
+-edo has been labeled a &amp;quot;Porcupine&amp;quot; temperament by Paul Erlich, which has stuck ever since. The name comes from a piece called the &amp;quot;Mizarian Porcupine Overture&amp;quot; by Herman Miller. It also falls into the catagory of kleisma tunings along with 53 and 19.&lt;br /&gt;
+&lt;br /&gt;
+&amp;quot;&amp;quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 cents. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave. 15-ET matches the 11:8 and 16:11 ratios, and does not match the 7:5 or 10:7 tritone.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:6:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_15edoclassicalsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="external image Sword_15edoclassicalsm.JPG" title="external image Sword_15edoclassicalsm.JPG" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:6 --&gt;(15-tone Classical Guitar by Ron Sword)&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x15 tone equal temperament-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
   &lt;a class="wiki_link_ext" href="http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html" rel="nofollow"&gt;15-EDO Tutorial&lt;/a&gt; by Brent Carson.&lt;br /&gt;

15edo: Difference between revisions

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