EDL
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<span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"><span style="font-family: arial,sans-serif;"><span style="font-family: arial,sans-serif;">**<span style="color: #000000;">Equal divisions of length</span>**</span></span></span> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">For an intervallic system with n divisions , </span>[[http://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29|**EDL**]]<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> is <span style="font-family: arial,sans-serif;">considered as equal divisions of length</span> by dividing string length to</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> n</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> equal divisions ( So , we have **n/2** divisions per octave).If the first division is </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L1</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> and the last, </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">Ln</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> , we have: </span></span> <span style="text-align: left;">**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L1 = L2 = L3 = …… = Ln</span>**</span> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">So sum of the divisions is </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> or the string length. Note that the number of divisions in octave is half of the string length.By dividing string length of </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> to </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> division we have: </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-n </span>**</span> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> which </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n-m </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">is </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n/2.</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> for example, by dividing string length to 12 equal divisions we have a series as:</span></span> <span style="text-align: left;">**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">12:11:10:9:8:7:6:5:4:3:2:1:0</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> or </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">12 11 10 9 8 7 6 5 4 3 2 1 0 </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">which shows </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">12-EDL</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">:</span></span> <span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> </span> [[image:http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg align="center"]] <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">**12:12** means 12 from 12 divisions,**12:11** means 11 from 12 divisions and so on.Ratios as **12:11** shows active string length for each degree, which is vibrating.**EDL** system shows ascending trend of divisions sizes due to its inner structure and if compared with </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">EDO</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> :</span></span> <span style="display: block; text-align: center;"> </span> [[image:http://sites.google.com/site/240edo/edl2.JPG width="347" height="224" align="center"]] <span style="display: block; text-align: center;"><span style="color: #000000; font-family: Arial; font-size: 14.6667px;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> </span></span> <span style="text-align: center;"><span style="color: #000000; font-family: Arial; font-size: 14.6667px;">**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">__Relation between Utonality and EDL system__</span>**</span></span> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">We can consider </span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">EDL</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> system as </span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;">[[@http://en.wikipedia.org/wiki/Otonal|**Utonal system**]]</span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> .</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">Utonality</span>**<span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> is a term introduced by </span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;">[[@http://en.wikipedia.org/wiki/Harry_Partch|**Harry Partch**]]</span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.</span></span> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">In the other hand , an utonality is a collection of pitches which can be expressedin ratios that have the same nominators. For example, 7/4, 7/5, 7/6 form an utonality which 7 as nominator is called "</span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;">[[@http://tonalsoft.com/enc/n/nexus.aspx|**Numerary nexus**]]</span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">".</span></span> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">If a string is divided into equal parts, it will produce an utonality and so we have EDL system.EDL systems are classified as systems with unequal </span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;">[[@http://tonalsoft.com/enc/e/epimorios.aspx|**epimorios**]]</span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> **(**[[http://en.wikipedia.org/wiki/Superparticular_number|**Superparticular**]]**)** divisions which show descending series with ascending sizes.</span></span> </span>
Original HTML content:
<html><head><title>EDL</title></head><body><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"><span style="font-family: arial,sans-serif;"><span style="font-family: arial,sans-serif;"><strong><span style="color: #000000;">Equal divisions of length</span></strong></span></span></span><br /> <br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">For an intervallic system with n divisions , </span><a class="wiki_link_ext" href="http://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29" rel="nofollow">**EDL**</a><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> is <span style="font-family: arial,sans-serif;">considered as equal divisions of length</span> by dividing string length to</span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> n</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> equal divisions ( So , we have <strong>n/2</strong> divisions per octave).If the first division is </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L1</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> and the last, </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">Ln</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> , we have: </span></span><br /> <span style="text-align: left;"><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L1 = L2 = L3 = …… = Ln</span></strong></span><br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">So sum of the divisions is </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> or the string length. Note that the number of divisions in octave is half of the string length.By dividing string length of </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> to </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> division we have: </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-n </span></strong></span><br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> which </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n-m </span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">is </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">n/2.</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> for example, by dividing string length to 12 equal divisions we have a series as:</span></span><br /> <span style="text-align: left;"><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">12:11:10:9:8:7:6:5:4:3:2:1:0</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> or </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">12 11 10 9 8 7 6 5 4 3 2 1 0 </span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">which shows </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">12-EDL</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">:</span></span><br /> <br /> <span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> </span><br /> <!-- ws:start:WikiTextRemoteImageRule:0:<div style="text-align: center"><img src="http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg" alt="" title="" /></div> --><div style="text-align: center"><img src="http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg" alt="external image edl1-custom-size-381-249.jpg" title="external image edl1-custom-size-381-249.jpg" /></div><!-- ws:end:WikiTextRemoteImageRule:0 --><br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"><strong>12:12</strong> means 12 from 12 divisions,<strong>12:11</strong> means 11 from 12 divisions and so on.Ratios as <strong>12:11</strong> shows active string length for each degree, which is vibrating.<strong>EDL</strong> system shows ascending trend of divisions sizes due to its inner structure and if compared with </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">EDO</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> :</span></span><br /> <br /> <span style="display: block; text-align: center;"><br /> </span><br /> <!-- ws:start:WikiTextRemoteImageRule:1:<div style="text-align: center"><img src="http://sites.google.com/site/240edo/edl2.JPG" alt="" title="" style="height: 224px; width: 347px;" /></div> --><div style="text-align: center"><img src="http://sites.google.com/site/240edo/edl2.JPG" alt="external image edl2.JPG" title="external image edl2.JPG" style="height: 224px; width: 347px;" /></div><!-- ws:end:WikiTextRemoteImageRule:1 --><span style="display: block; text-align: center;"><span style="color: #000000; font-family: Arial; font-size: 14.6667px;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> </span></span><br /> <span style="text-align: center;"><span style="color: #000000; font-family: Arial; font-size: 14.6667px;"><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"><u>Relation between Utonality and EDL system</u></span></strong></span></span><br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">We can consider </span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">EDL</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> system as </span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Otonal" rel="nofollow" target="_blank">**Utonal system**</a></span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> .</span><strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">Utonality</span></strong><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> is a term introduced by </span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow" target="_blank">**Harry Partch**</a></span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.</span></span><br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">In the other hand , an utonality is a collection of pitches which can be expressedin ratios that have the same nominators. For example, 7/4, 7/5, 7/6 form an utonality which 7 as nominator is called "</span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/n/nexus.aspx" rel="nofollow" target="_blank">**Numerary nexus**</a></span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">".</span></span><br /> <span style="text-align: left;"><span style="color: #000000; font-family: Arial; font-size: 13.3333px;">If a string is divided into equal parts, it will produce an utonality and so we have EDL system.EDL systems are classified as systems with unequal </span><span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/e/epimorios.aspx" rel="nofollow" target="_blank">**epimorios**</a></span><span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> <strong>(</strong><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Superparticular_number" rel="nofollow">**Superparticular**</a><strong>)</strong> divisions which show descending series with ascending sizes.</span></span><br /> </span></body></html>