15edo: Difference between revisions

Revision as of 11:07, 31 March 2011

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This revision was by author genewardsmith and made on 2011-03-31 11:07:21 UTC.

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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.

from //wikipedia//:
""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 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]]). 15-ET matches the [[11_8|11:8]] and [[16_11|16:11]] ratios, and does not match the [[7_5|7:5]] or [[10_7|10:7]] tritone."

Additional notes:

In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modualted anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. .


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

=Theory= 
[[http://www.webcitation.org/5xZyzKBEW|The 15-Tone Scale System]] by [[Ivor Darreg]].
[[http://www.inteas.com/Penta01.htm|The Pentadecaphonic System]]
[[http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html|15-EDO Tutorial]] by [[Brent Carson]].

=Practical Theory / Books= 
[[image:http://ronsword.com/images/Pendecaphonic_coversm.jpg width="112" height="149" link="http://www.ronsword.com"]][[http://www.ronsword.com|Sword, Ronald. "Pendecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.]] - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions
==**Compositions**== 
[[http://teamouse.googlepages.com/MizarianPorcupineOverture.mp3|Mizarian Porcupine Overture]] by [[Herman Miller]] ([[http://teamouse.googlepages.com/home|Herman Miller]]) ([[Regular Temperaments#porcupine|porcupine]] chord progressions)
[[http://www.microtonalmusic.net/audio/15edostudy.mp3|Study for Bells]] by [[Daniel Thompson]] ([[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://azuma-asobi.com/Music/index.html|Rick McGowan]]: [[http://azuma-asobi.com/Music/Music-FullWorks.html|Four Ballet Scenes]]
[[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 />
<br />
15-edo is a <a class="wiki_link" href="/7-limit">7-limit</a> tuning because of the amount of septimal intervals, but it does contain <a class="wiki_link" href="/11-limit">11-limit</a> intervals.<br />
<br />
from <em>wikipedia</em>:<br />
&quot;&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 15 equal steps. Each step represents a frequency ratio of 2 1/15, or 80 <a class="wiki_link" href="/cent">cent</a>s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of <a class="wiki_link" href="/5edo">5 equal divisions of the octave</a> (or five scales of <a class="wiki_link" href="/3edo">3edo</a>). 15-ET matches the <a class="wiki_link" href="/11_8">11:8</a> and <a class="wiki_link" href="/16_11">16:11</a> ratios, and does not match the <a class="wiki_link" href="/7_5">7:5</a> or <a class="wiki_link" href="/10_7">10:7</a> tritone.&quot;<br />
<br />
Additional notes:<br />
<br />
In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modualted anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. .<br />
<br />
<br />
<!-- ws:start:WikiTextRemoteImageRule:8:&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:8 -->(<em>15-tone Classical Guitar by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></em> / <em>Sword Guitars</em>)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h1>
 <a class="wiki_link_ext" href="http://www.webcitation.org/5xZyzKBEW" rel="nofollow">The 15-Tone Scale System</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a>.<br />
<a class="wiki_link_ext" href="http://www.inteas.com/Penta01.htm" rel="nofollow">The Pentadecaphonic System</a><br />
<a class="wiki_link_ext" href="http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html" rel="nofollow">15-EDO Tutorial</a> by <a class="wiki_link" href="/Brent%20Carson">Brent Carson</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:4 -->Practical Theory / Books</h1>
 <!-- ws:start:WikiTextRemoteImageRule:10:&lt;a href=&quot;http://www.ronsword.com&quot; rel=&quot;nofollow&quot;&gt;&lt;img src=&quot;http://ronsword.com/images/Pendecaphonic_coversm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 149px; width: 112px;&quot; /&gt;&lt;/a&gt; --><a href="http://www.ronsword.com" rel="nofollow"><img src="http://ronsword.com/images/Pendecaphonic_coversm.jpg" alt="external image Pendecaphonic_coversm.jpg" title="external image Pendecaphonic_coversm.jpg" style="height: 149px; width: 112px;" /></a><!-- ws:end:WikiTextRemoteImageRule:10 --><a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ronald. &quot;Pendecaphonic Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: June 2009.</a> - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Practical Theory / Books-Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 --><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" href="/Herman%20Miller">Herman Miller</a> (<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" href="/Daniel%20Thompson">Daniel Thompson</a> (<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://azuma-asobi.com/Music/index.html" rel="nofollow">Rick McGowan</a>: <a class="wiki_link_ext" href="http://azuma-asobi.com/Music/Music-FullWorks.html" rel="nofollow">Four Ballet Scenes</a><br />
<a class="wiki_link" href="/Brian%20McLaren">Brian McLaren</a>: 5 piano pieces<br />
<a class="wiki_link" href="/Easley%20Blackwood">Easley Blackwood</a>: 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 <a class="wiki_link" href="/Jacob%20Barton">Jacob Barton</a> (2003)<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/15ET.mid" rel="nofollow">Elegy in 15ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><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:xenwolf|xenwolf]] and made on <tt>2011-03-31 02:58:54 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-31 11:07:21 UTC</tt>.<br>
-: The original revision id was <tt>215733824</tt>.<br>
+: The original revision id was <tt>215850762</tt>.<br>
-: The revision comment was: <tt>5x3edo and some links added</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>
@@ Line 32: / Line 32: @@
 [[http://www.microtonalmusic.net/audio/15edostudy.mp3|Study for Bells]] by [[Daniel Thompson]] ([[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]]
+[[http://azuma-asobi.com/Music/index.html|Rick McGowan]]: [[http://azuma-asobi.com/Music/Music-FullWorks.html|Four Ballet Scenes]]
 [[Brian McLaren]]: 5 piano pieces
 [[Easley Blackwood]]: Suite for Guitar in 15 equal tuning
@@ Line 66: / Line 66: @@
 &lt;a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/15edostudy.mp3" rel="nofollow"&gt;Study for Bells&lt;/a&gt; by &lt;a class="wiki_link" href="/Daniel%20Thompson"&gt;Daniel Thompson&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow"&gt;Daniel Thompson&lt;/a&gt;) (Jan. 2007)&lt;br /&gt;
 Study for Kyle Gann by &lt;a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow"&gt;Aaron K. Johnson&lt;/a&gt; (12-out-of-15)&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://rm-and-jo.laughingsquid.org/Music/index.html" rel="nofollow"&gt;Rick McGowan&lt;/a&gt;: a lot of music, for example &lt;a class="wiki_link_ext" href="http://rm-and-jo.laughingsquid.org/Music/McGowan-FourBalletScenes.mp3" rel="nofollow"&gt;Four Ballet Scenes&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://rm-and-jo.laughingsquid.org/temp/sgs-4-a.mp3" rel="nofollow"&gt;Four&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://azuma-asobi.com/Music/index.html" rel="nofollow"&gt;Rick McGowan&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://azuma-asobi.com/Music/Music-FullWorks.html" rel="nofollow"&gt;Four Ballet Scenes&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/Brian%20McLaren"&gt;Brian McLaren&lt;/a&gt;: 5 piano pieces&lt;br /&gt;
 &lt;a class="wiki_link" href="/Easley%20Blackwood"&gt;Easley Blackwood&lt;/a&gt;: Suite for Guitar in 15 equal tuning&lt;br /&gt;

15edo: Difference between revisions

Revision as of 11:07, 31 March 2011

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