5edo: Difference between revisions

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5-edo divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two. 5-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)

==Listen to the sound of the 5-edo scale==  

** "[[@http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele|True Island]]" (album) by Small Scale Revolution (2011)

** Ralph Jarzombek: [[http://webzoom.freewebs.com/ralphjarzombek/micro12.mp3|Micro12]]

==Ear Training==  

==Notation==  

** via Reinhard's cents notation

** a four-line hybrid treble/bass staff.

  &lt;br /&gt;

5-edo divides the 1200-&lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt; octave into 5 equal parts, making its smallest interval exactly 240 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt;, or the fifth root of two. 5-edo is the 3rd &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, after &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt; and &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;. Most importantly, 5-edo is the smallest &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt; containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)&lt;br /&gt;

&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x5 Equal Divisions of the Octave: Theory-Listen to the sound of the 5-edo scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Listen to the sound of the 5-edo scale&lt;/h2&gt;

  &lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x5-edo in Musicmaking-Compositions, improvisations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;&lt;strong&gt;Compositions&lt;/strong&gt;, improvisations&lt;/h2&gt;

  &lt;ul&gt;&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/" rel="nofollow"&gt;Herman Miller&lt;/a&gt;: &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/herman_miller/Daybreak.mp3" rel="nofollow"&gt;Daybreak on Slendro Mountain&lt;/a&gt;&lt;/em&gt; (2000)&lt;/li&gt;&lt;li&gt;Aaron K. Johnson: &lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow"&gt;5tet funk&lt;/a&gt;&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;amp;songID=1519939" rel="nofollow"&gt;Andrew Heathwaite: //Pinta Penta// (2004)&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3" rel="nofollow"&gt;play&lt;/a&gt; (rendered in 6 alternative pentatonics as well)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hans%20Straub"&gt;Hans Straub&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow"&gt;Asîmchômsaia&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Brian%20Wong"&gt;Brian Wong&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://bwong.ca/template1.php?sub=3" rel="nofollow"&gt;Slendronica#1b&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg" rel="nofollow"&gt;play&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Brian McLaren: various and sundry&lt;/li&gt;&lt;li&gt;Paul Rubenstein: various, with electric guitars in 10- and 15-edo&lt;/li&gt;&lt;li&gt;X.J.Scott: &lt;em&gt;Sleeping Through It All&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;Bill Sethares: &lt;em&gt;5-tet funk&lt;/em&gt; (2004), &lt;em&gt;Pentacle&lt;/em&gt; (2004)&lt;/li&gt;&lt;li&gt;&amp;quot;Cenobyte&amp;quot; Ukulele &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=UKUCRnEJKKU" rel="nofollow"&gt; http://www.youtube.com/watch?v=UKUCRnEJKKU&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele" rel="nofollow" target="_blank"&gt;True Island&lt;/a&gt;&amp;quot; (album) by Small Scale Revolution (2011)&lt;/li&gt;&lt;li&gt;Ralph Jarzombek: &lt;a class="wiki_link_ext" href="http://webzoom.freewebs.com/ralphjarzombek/micro12.mp3" rel="nofollow"&gt;Micro12&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/ul&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x5-edo in Musicmaking-Ear Training"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Ear Training&lt;/h2&gt;

  5edo ear-training exercises by Alex Ness available &lt;a class="wiki_link_ext" href="https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&amp;amp;usp=drive_web" rel="nofollow" target="_blank"&gt;here&lt;/a&gt;.&lt;br /&gt;

&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x5-edo in Musicmaking-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Notation&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x5-edo in Musicmaking-Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Harmony&lt;/h2&gt;

  5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather &amp;quot;dirty&amp;quot; but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.&lt;br /&gt;