EDL: Difference between revisions

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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:

: This revision was by author [[User:~~guest~~|~~guest~~]] and made on <tt>2012-02-~~12 06~~:29:59 UTC</tt>.

: This revision was by author [[User:acousticsoftombak|acousticsoftombak]] and made on <tt>2012-02-17 01:37:12 UTC</tt>.

: The original revision id was <tt>~~300893018~~</tt>.

: The original revision id was <tt>302667494</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<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">~~EDL stands for~~ Equal ~~Division~~ of [~~String~~] ~~Length~~. ~~If you place frets at~~ equal ~~distances on a fretboard~~, the ~~string lengths will be an arithmetic sequence~~, ~~for example 24~~/24, 23/~~24, 22~~/24... ~~Therefore~~ the ~~frequencies, which are inversely proportional to~~ string length~~, are~~ the ~~inverse~~ of ~~an arithmetic sequence~~; ~~that~~ is, ~~undertones~~, ~~or a~~ [[~~Otonality~~ and ~~utonality~~|~~utonality~~]]. ~~For example 24EDL~~ is ~~the pitches 24~~/24=1/~~1, 24~~/~~23, 24~~/22=12/11, 8/7, 6/5, 24/~~19, 4~~/3...</pre></div>

<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">**Equal divisions of length**

For an intervallic system with n divisions , [[http://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29|**EDL**]] is considered as equal divisions of length by dividing string length to** n** equal divisions ( So , we have **n/2** divisions per octave).If the first division is **L1** and the last, **Ln** , we have:

**L1 = L2 = L3 = …… = Ln**

So sum of the divisions is **L** or the string length. Note that the number of divisions in octave is half of the string length.By dividing string length of **L** to **n** division we have: **n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-n **

which **n-m **is **n/2.** for example, by dividing string length to 12 equal divisions we have a series as:

**12:11:10:9:8:7:6:5:4:3:2:1:0** or **12 11 10 9 8 7 6 5 4 3 2 1 0 **which shows **12-EDL**:

[[image:http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg align="center"]]

**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 **EDO** :

[[image:http://sites.google.com/site/240edo/edl2.JPG width="347" height="224" align="center"]]

**__Relation between Utonality and EDL system__**

We can consider **EDL** system as [[@http://en.wikipedia.org/wiki/Otonal|**Utonal system**]] .**Utonality** is a term introduced by [[@http://en.wikipedia.org/wiki/Harry_Partch|**Harry Partch**]] to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.

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 "[[@http://tonalsoft.com/enc/n/nexus.aspx|**Numerary nexus**]]".

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 [[@http://tonalsoft.com/enc/e/epimorios.aspx|**epimorios**]] **(**[[http://en.wikipedia.org/wiki/Superparticular_number|**Superparticular**]]**)** divisions which show descending series with ascending sizes.

</pre></div>

<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>EDL</title></head><body>~~EDL stands for~~ Equal ~~Division~~ of ~~[String] Length~~. ~~If you place frets at equal distances on~~ a ~~fretboard~~, ~~the~~ string ~~lengths will be an arithmetic sequence~~, ~~for example 24~~/24, 23/24, 22/24... ~~Therefore~~ the ~~frequencies, which are inversely proportional to~~ string length~~, are~~ the ~~inverse~~ of ~~an arithmetic sequence~~; ~~that~~ is, ~~undertones~~, ~~or a~~ <a class="~~wiki_link~~" href="/~~Otonality%20and%20utonality~~">~~utonality~~</a>. ~~For example 24EDL~~ is ~~the pitches 24~~/24=1/~~1, 24~~/~~23, 24~~/22=12/11, 8/7, 6/5, 24/~~19, 4~~/3...</body></html></pre></div>

<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"><html><head><title>EDL</title></head><body>Equal divisions of length

For an intervallic system with n divisions , <a class="wiki_link_ext" href="http://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29" rel="nofollow">**EDL**</a> is considered as equal divisions of length by dividing string length to n equal divisions ( So , we have n/2 divisions per octave).If the first division is L1 and the last, Ln , we have:

L1 = L2 = L3 = …… = Ln

So sum of the divisions is L or the string length. Note that the number of divisions in octave is half of the string length.By dividing string length of L to n division we have: n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-n

which n-m is n/2. for example, by dividing string length to 12 equal divisions we have a series as:

12:11:10:9:8:7:6:5:4:3:2:1:0 or 12 11 10 9 8 7 6 5 4 3 2 1 0 which shows 12-EDL:

<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>

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 EDO :

<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>

Relation between Utonality and EDL system

We can consider EDL system as <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Otonal" rel="nofollow" target="_blank">**Utonal system**</a> .Utonality is a term introduced by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow" target="_blank">**Harry Partch**</a> to describe chords whose notes are the &quot;undertones&quot; (divisors) of a given fixed tone.

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 &quot;<a class="wiki_link_ext" href="http://tonalsoft.com/enc/n/nexus.aspx" rel="nofollow" target="_blank">**Numerary nexus**</a>&quot;.

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 <a class="wiki_link_ext" href="http://tonalsoft.com/enc/e/epimorios.aspx" rel="nofollow" target="_blank">**epimorios**</a> (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Superparticular_number" rel="nofollow">**Superparticular**</a>) divisions which show descending series with ascending sizes.

</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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>2012-02-12 06:29:59 UTC</tt>.<br>
+: This revision was by author [[User:acousticsoftombak|acousticsoftombak]] and made on <tt>2012-02-17 01:37:12 UTC</tt>.<br>
-: The original revision id was <tt>300893018</tt>.<br>
+: The original revision id was <tt>302667494</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">EDL stands for Equal Division of [String] Length. If you place frets at equal distances on a fretboard, the string lengths will be an arithmetic sequence, for example 24/24, 23/24, 22/24... Therefore the frequencies, which are inversely proportional to string length, are the inverse of an arithmetic sequence; that is, undertones, or a [[Otonality and utonality|utonality]]. For example 24EDL is the pitches 24/24=1/1, 24/23, 24/22=12/11, 8/7, 6/5, 24/19, 4/3...</pre></div>
+<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">&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;&lt;span style="font-family: arial,sans-serif;"&gt;&lt;span style="font-family: arial,sans-serif;"&gt;**&lt;span style="color: #000000;"&gt;Equal divisions of length&lt;/span&gt;**&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;For an intervallic system with n divisions , &lt;/span&gt;[[http://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29|**EDL**]]&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; is &lt;span style="font-family: arial,sans-serif;"&gt;considered as equal divisions of length&lt;/span&gt; by dividing string length to&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; n&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; equal divisions ( So , we have **n/2** divisions per octave).If the first division is &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L1&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; and the last, &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;Ln&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; , we have: &lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L1 = L2 = L3 = …… = Ln&lt;/span&gt;**&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;So sum of the divisions is &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; or the string length. Note that the number of divisions in octave is half of the string length.By dividing string length of &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; to &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; division we have: &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-n &lt;/span&gt;**&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; which &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n-m &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;is &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n/2.&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; for example, by dividing string length to 12 equal divisions we have a series as:&lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;12:11:10:9:8:7:6:5:4:3:2:1:0&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; or &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;12 11 10 9 8 7 6 5 4 3 2 1 0 &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;which shows &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;12-EDL&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;:&lt;/span&gt;&lt;/span&gt;
+&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; &lt;/span&gt;
+[[image:http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg align="center"]]
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;**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 &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;EDO&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; :&lt;/span&gt;&lt;/span&gt;
+&lt;span style="display: block; text-align: center;"&gt;
+&lt;/span&gt;
+[[image:http://sites.google.com/site/240edo/edl2.JPG width="347" height="224" align="center"]]
+&lt;span style="display: block; text-align: center;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 14.6667px;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; &lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: center;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 14.6667px;"&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;__Relation between Utonality and EDL system__&lt;/span&gt;**&lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;We can consider &lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;EDL&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; system as &lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;[[@http://en.wikipedia.org/wiki/Otonal|**Utonal system**]]&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; .&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;Utonality&lt;/span&gt;**&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; is a term introduced by &lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;[[@http://en.wikipedia.org/wiki/Harry_Partch|**Harry Partch**]]&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; to describe chords whose notes are the "undertones" (divisors) of a given fixed tone.&lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;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 "&lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;[[@http://tonalsoft.com/enc/n/nexus.aspx|**Numerary nexus**]]&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;".&lt;/span&gt;&lt;/span&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;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 &lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;[[@http://tonalsoft.com/enc/e/epimorios.aspx|**epimorios**]]&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; **(**[[http://en.wikipedia.org/wiki/Superparticular_number|**Superparticular**]]**)** divisions which show descending series with ascending sizes.&lt;/span&gt;&lt;/span&gt;
+&lt;/span&gt;</pre></div>
 <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;EDL&lt;/title&gt;&lt;/head&gt;&lt;body&gt;EDL stands for Equal Division of [String] Length. If you place frets at equal distances on a fretboard, the string lengths will be an arithmetic sequence, for example 24/24, 23/24, 22/24... Therefore the frequencies, which are inversely proportional to string length, are the inverse of an arithmetic sequence; that is, undertones, or a &lt;a class="wiki_link" href="/Otonality%20and%20utonality"&gt;utonality&lt;/a&gt;. For example 24EDL is the pitches 24/24=1/1, 24/23, 24/22=12/11, 8/7, 6/5, 24/19, 4/3...&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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;EDL&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;&lt;span style="font-family: arial,sans-serif;"&gt;&lt;span style="font-family: arial,sans-serif;"&gt;&lt;strong&gt;&lt;span style="color: #000000;"&gt;Equal divisions of length&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;For an intervallic system with n divisions , &lt;/span&gt;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/240edo/equaldivisionsoflength%28edl%29" rel="nofollow"&gt;**EDL**&lt;/a&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; is &lt;span style="font-family: arial,sans-serif;"&gt;considered as equal divisions of length&lt;/span&gt; by dividing string length to&lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; n&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; equal divisions ( So , we have &lt;strong&gt;n/2&lt;/strong&gt; divisions per octave).If the first division is &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L1&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; and the last, &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;Ln&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; , we have: &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L1 = L2 = L3 = …… = Ln&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;So sum of the divisions is &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; or the string length. Note that the number of divisions in octave is half of the string length.By dividing string length of &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;L&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; to &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; division we have: &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-n &lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; which &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n-m &lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;is &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;n/2.&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; for example, by dividing string length to 12 equal divisions we have a series as:&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;12:11:10:9:8:7:6:5:4:3:2:1:0&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; or &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;12 11 10 9 8 7 6 5 4 3 2 1 0 &lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;which shows &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;12-EDL&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;:&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; &lt;/span&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:0:&amp;lt;div style=&amp;quot;text-align: center&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/div&amp;gt; --&gt;&lt;div style="text-align: center"&gt;&lt;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" /&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:0 --&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;&lt;strong&gt;12:12&lt;/strong&gt; means 12 from 12 divisions,&lt;strong&gt;12:11&lt;/strong&gt; means 11 from 12 divisions and so on.Ratios as &lt;strong&gt;12:11&lt;/strong&gt; shows active string length for each degree, which is vibrating.&lt;strong&gt;EDL&lt;/strong&gt; system shows ascending trend of divisions sizes due to its inner structure and if compared with &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;EDO&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; :&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="display: block; text-align: center;"&gt;&lt;br /&gt;
+&lt;/span&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:1:&amp;lt;div style=&amp;quot;text-align: center&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://sites.google.com/site/240edo/edl2.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 224px; width: 347px;&amp;quot; /&amp;gt;&amp;lt;/div&amp;gt; --&gt;&lt;div style="text-align: center"&gt;&lt;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;" /&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:1 --&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 14.6667px;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: center;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 14.6667px;"&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;&lt;u&gt;Relation between Utonality and EDL system&lt;/u&gt;&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;We can consider &lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;EDL&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; system as &lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Otonal" rel="nofollow" target="_blank"&gt;**Utonal system**&lt;/a&gt;&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; .&lt;/span&gt;&lt;strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;Utonality&lt;/span&gt;&lt;/strong&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; is a term introduced by &lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow" target="_blank"&gt;**Harry Partch**&lt;/a&gt;&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; to describe chords whose notes are the &amp;quot;undertones&amp;quot; (divisors) of a given fixed tone.&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;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 &amp;quot;&lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/n/nexus.aspx" rel="nofollow" target="_blank"&gt;**Numerary nexus**&lt;/a&gt;&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;&amp;quot;.&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="text-align: left;"&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt;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 &lt;/span&gt;&lt;span style="color: #0000ff; font-family: Arial; font-size: 13.3333px;"&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/e/epimorios.aspx" rel="nofollow" target="_blank"&gt;**epimorios**&lt;/a&gt;&lt;/span&gt;&lt;span style="color: #000000; font-family: Arial; font-size: 13.3333px;"&gt; &lt;strong&gt;(&lt;/strong&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Superparticular_number" rel="nofollow"&gt;**Superparticular**&lt;/a&gt;&lt;strong&gt;)&lt;/strong&gt; divisions which show descending series with ascending sizes.&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>