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Equal divisions of length

For an intervallic system with n divisions , **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:


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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 :



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Relation between Utonality and EDL system
We can consider EDL system as **Utonal system** .Utonality is a term introduced by **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 "**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 **epimorios** (**Superparticular**) divisions which show descending series with ascending sizes.