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Equal divisions of lengthFor an intervallic system with n divisions , **EDL** is considered as equal divisions of length by dividing string length to

nequal divisions ( So , we haven/2divisions per octave).If the first division isL1and the last,Ln, we have:L1 = L2 = L3 = …… = LnSo sum of the divisions is

Lor the string length. Note that the number of divisions in octave is half of the string length.By dividing string length ofLtondivision we have:n : n-1 : n-2 : n-3 : ……. : n-m : ….. : n-nwhich

n-misn/2.for example, by dividing string length to 12 equal divisions we have a series as:12:11:10:9:8:7:6:5:4:3:2:1:0or12 11 10 9 8 7 6 5 4 3 2 1 0which shows12-EDL:12:12means 12 from 12 divisions,12:11means 11 from 12 divisions and so on.Ratios as12:11shows active string length for each degree, which is vibrating.EDLsystem shows ascending trend of divisions sizes due to its inner structure and if compared withEDO:Relation between Utonality and EDL systemWe can consider

EDLsystem as **Utonal system** .Utonalityis 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.