15edo
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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
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<html><head><title>15edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 "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.<br /> <br /> ""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."<br /> <br /> <br /> <!-- ws:start:WikiTextRemoteImageRule:6:<img src="http://www.swordguitars.com/Sword_15edoclassicalsm.JPG" alt="" title="" /> --><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:<h2> --><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. "Pentadecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.<br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><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&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>