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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>
| | #redirect [[IFDO #Equal divisions of length]] |
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| <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>
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| <span style="text-align: left;">'''<span style="color: #000000; font-family: Arial; font-size: 13.3333px;">L1 = L2 = L3 = …… = Ln</span>'''</span>
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| <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>
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| <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>
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| <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>
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| <span style="color: #000000; font-family: Arial; font-size: 13.3333px;"> </span>
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| External image: http://sites.google.com/site/240edo/edl1-custom-size-381-249.jpg<br>
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| : <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br>
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| : <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
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| </div>
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| [[Category:IMPORTDEBUG - Change External Images]]
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| <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>
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| <div class='external-image-warning' style='background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block'>
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| External image: http://sites.google.com/site/240edo/edl2.JPG<br>
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| : <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br>
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| : <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
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| </div>
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| [[Category:IMPORTDEBUG - Change External Images]]
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| <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>
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| <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;"><u>Relation between Utonality and EDL system</u></span>'''</span></span>
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| <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>
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| <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>
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| <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>
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| </span> [[Category:edl]]
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