AID: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:guest|guest]] and made on <tt>2013-01-17 08:48:33 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2013-01-17 11:24:10 UTC</tt>.

: The original revision id was <tt>~~399178006~~</tt>.

: The original revision id was <tt>399237864</tt>.

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

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<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">**Arithmetic irrational divisions**

For an intervallic system with __n__ divisions , [[http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29|~~__AID__~~]] is considered as [[http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html|arithmetic sequence]] with divisions of system as terms of sequence.

For an intervallic system with __n__ divisions , [[http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29|AID_]] is considered as [[http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html|arithmetic sequence]] with divisions of system as terms of sequence.

If the first division is __A1__ and the last , __An__ , with common difference of __d__ , we have :

A1 = A1

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By considering Sn=1200 , A1=70 , n=12 , d will be 5.454545455 and our 12-tone scale is equal to:

[[#TOC-0.070.0145.455226.364312.727404.545]] **0.0 70.0 145.455 226.364 312.727 404.545 501.818 604.545 712.727 826.364 945.455 1070.0 1200.0**

~~Scales based on AID can be subsets of EDO if :~~ Scales based on AID can be subsets of EDO if :1- we choose d=0 so , A1 = Sn/n .. Consider __n__=8 and __A1__=150 , then we have 8-EDO .

Scales based on AID can be subsets of EDO if :1- we choose d=0 so , A1 = Sn/n .. Consider __n__=8 and __A1__=150 , then we have 8-EDO .

2- for a constant __n__ and different __A1__, if __d__ and (Sn/A1) are Integer number , we have a susbet of EDO or EDI( Equal divisions of Interval) .Consider __Sn = 1400__ , __n__=8 and __A1__=70 , then we have a subset of a 140-ED(1400.) with Degrees as [[tel:7 17 30 46 65 87 112|7 17 30 46 65 87 112]] 140 :

2- for a constant __n__ and different __A1__, if __d__ and (Sn/A1) are Integer number , we have a susbet of EDO or EDI( Equal divisions of Interval) .Consider __Sn = 1400__ , __n__=8 and __A1__=70 , then we have a subset of a 140-ED(1400.) with Degrees as [[tel/7 17 30 46 65 87 112|7 17 30 46 65 87 112]] 140 :

**0.000 70.000 170.000 300.000 460.000 650.000 870.000 1120.000 1400.000**

[[#TOC-And-now-for:]]And now for Sn=1400 and n=8,

[[#TOC-If-A1-175.0-then-we-have-8-AID-1400]]If A1=175.0 then we have 8-AID(1400.)

[[#TOC-If-A1-56-then-we-have-700-AID-1400.]]If A1=56 then we have 700-AID(1400.) with Degrees as [[tel:28 73 135 214 310|28 73 135 214 310]] [[tel:423 553 700|423 553 700]]

[[#TOC-If-A1-56-then-we-have-700-AID-1400.]]If A1=56 then we have 700-AID(1400.) with Degrees as [[tel/28 73 135 214 310|28 73 135 214 310]] [[tel/423 553 700|423 553 700]]

[[#TOC-If-A1-87.5-then-we-have-112-AID-140]]If A1=87.5 then we have 112-AID(1400.) with Degrees as [[tel:7 16 27 40 55 72 91|7 16 27 40 55 72 91]] 112

[[#TOC-If-A1-87.5-then-we-have-112-AID-140]]If A1=87.5 then we have 112-AID(1400.) with Degrees as [[tel/7 16 27 40 55 72 91|7 16 27 40 55 72 91]] 112

__AID__ sytem shows different ascending , descending or linear trend of change in divisions sizes due to relation between n and A1 in __AID__ and __EDO__ with equal degree:

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<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>AID</title></head><body>Arithmetic irrational divisions

For an intervallic system with n divisions , <a class="wiki_link_ext" href="http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29" rel="nofollow">~~__AID__~~</a> is considered as <a class="wiki_link_ext" href="http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html" rel="nofollow">arithmetic sequence</a> with divisions of system as terms of sequence.

For an intervallic system with n divisions , <a class="wiki_link_ext" href="http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29" rel="nofollow">AID_</a> is considered as <a class="wiki_link_ext" href="http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html" rel="nofollow">arithmetic sequence</a> with divisions of system as terms of sequence.

If the first division is A1 and the last , An , with common difference of d , we have :

A1 = A1

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By considering Sn=1200 , A1=70 , n=12 , d will be 5.454545455 and our 12-tone scale is equal to:

<a name="TOC-0.070.0145.455226.364312.727404.545"></a> 0.0 70.0 145.455 226.364 312.727 404.545 501.818 604.545 712.727 826.364 945.455 1070.0 1200.0

~~Scales based on AID can be subsets of EDO if :~~ Scales based on AID can be subsets of EDO if :1- we choose d=0 so , A1 = Sn/n .. Consider n=8 and A1=150 , then we have 8-EDO .

Scales based on AID can be subsets of EDO if :1- we choose d=0 so , A1 = Sn/n .. Consider n=8 and A1=150 , then we have 8-EDO .

2- for a constant n and different A1, if d and (Sn/A1) are Integer number , we have a susbet of EDO or EDI( Equal divisions of Interval) .Consider Sn = 1400 , n=8 and A1=70 , then we have a subset of a 140-ED(1400.) with Degrees as <a class="wiki_link" href="http://tel.wikispaces.com/7%2017%2030%2046%2065%2087%20112">7 17 30 46 65 87 112</a> 140 :

0.000 70.000 170.000 300.000 460.000 650.000 870.000 1120.000 1400.000

@@ 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>2013-01-17 08:48:33 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2013-01-17 11:24:10 UTC</tt>.<br>
-: The original revision id was <tt>399178006</tt>.<br>
+: The original revision id was <tt>399237864</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>
@@ Line 8: / Line 8: @@
 <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: #000000; font-family: arial,sans-serif; font-size: 18px;"&gt;**Arithmetic irrational divisions**&lt;/span&gt;
-&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;&lt;span style="color: black; font-size: 11pt;"&gt;For an intervallic system with &lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt; divisions , &lt;/span&gt;&lt;span style="color: #be00ff; font-size: 11pt;"&gt;[[http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29|__AID__]]&lt;/span&gt;&lt;span style="color: black; font-size: 11pt;"&gt; is considered as [[http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html|arithmetic sequence]] with divisions of system as terms of sequence. &lt;/span&gt;&lt;/span&gt;
+&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;&lt;span style="color: black; font-size: 11pt;"&gt;For an intervallic system with &lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt; divisions , &lt;/span&gt;&lt;span style="color: #be00ff; font-size: 11pt;"&gt;[[http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29|AID_]]&lt;/span&gt;&lt;span style="color: black; font-size: 11pt;"&gt; is considered as [[http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html|arithmetic sequence]] with divisions of system as terms of sequence. &lt;/span&gt;&lt;/span&gt;
 &lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; text-align: left;"&gt;&lt;span style="color: black; font-size: 11pt;"&gt; If the first division is &lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt;A1&lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt; and the last , &lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt;An&lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt; , with common difference of &lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt;d&lt;/span&gt;__&lt;span style="color: black; font-size: 11pt;"&gt; , we have : &lt;/span&gt;&lt;/span&gt;
 &lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;A1 = A1&lt;/span&gt;
@@ Line 28: / Line 28: @@
 &lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;By considering Sn=1200 , A1=70 , n=12 , d will be 5.454545455 and our 12-tone scale is equal to:&lt;/span&gt;
 &lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;[[#TOC-0.070.0145.455226.364312.727404.545]] **0.0 70.0 145.455 226.364 312.727 404.545 501.818 604.545 712.727 826.364 945.455 1070.0 1200.0**&lt;/span&gt;
-&lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;Scales based on AID can be subsets of EDO if : Scales based on AID can be subsets of EDO if :&lt;/span&gt;&lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;1- we choose d=0 so ,&lt;span style="color: black; font-size: 11pt;"&gt; A1 = Sn/n&lt;/span&gt; .. Consider &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=150 , then we have 8-EDO .&lt;/span&gt;&lt;/span&gt;
+&lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;Scales based on AID can be subsets of EDO if :&lt;/span&gt;&lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;1- we choose d=0 so ,&lt;span style="color: black; font-size: 11pt;"&gt; A1 = Sn/n&lt;/span&gt; .. Consider &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=150 , then we have 8-EDO .&lt;/span&gt;&lt;/span&gt;
-&lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;2- for a constant &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt; and different __A1__, if __d__ and (Sn/A1) are Integer number , we have a susbet of EDO or EDI( Equal divisions of Interval) .Consider __Sn = 1400__ , &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=70 , then we have a subset of a 140-ED(1400.) with Degrees as [[tel:7 17 30 46 65 87 112|7 17 30 46 65 87 112]] 140 :&lt;/span&gt;&lt;/span&gt;
+&lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;2- for a constant &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt; and different __A1__, if __d__ and (Sn/A1) are Integer number , we have a susbet of EDO or EDI( Equal divisions of Interval) .Consider __Sn = 1400__ , &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;__&lt;span style="color: black; font-size: 10pt;"&gt;=70 , then we have a subset of a 140-ED(1400.) with Degrees as [[tel/7 17 30 46 65 87 112|7 17 30 46 65 87 112]] 140 :&lt;/span&gt;&lt;/span&gt;
 **0.000 70.000 170.000 300.000 460.000 650.000 870.000 1120.000 1400.000**
 &lt;span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;"&gt;[[#TOC-And-now-for:]]And now for &lt;/span&gt;&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;Sn=1400 and n=8,&lt;/span&gt;
 &lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt; [[#TOC-If-A1-175.0-then-we-have-8-AID-1400]]If A1=175.0 then we have 8-AID(1400.)&lt;/span&gt;
-&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt; [[#TOC-If-A1-56-then-we-have-700-AID-1400.]]If A1=56 then we have 700-AID(1400.) with Degrees as &lt;span style="color: black; font-size: 10pt;"&gt; [[tel:28 73 135 214 310|28 73 135 214 310]] [[tel:423 553 700|423 553 700]]&lt;/span&gt;&lt;/span&gt;
+&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt; [[#TOC-If-A1-56-then-we-have-700-AID-1400.]]If A1=56 then we have 700-AID(1400.) with Degrees as &lt;span style="color: black; font-size: 10pt;"&gt; [[tel/28 73 135 214 310|28 73 135 214 310]] [[tel/423 553 700|423 553 700]]&lt;/span&gt;&lt;/span&gt;
-&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt; [[#TOC-If-A1-87.5-then-we-have-112-AID-140]]&lt;span style="color: black; font-size: 10pt;"&gt;If A1=87.5 then we have 112-AID(1400.) with Degrees as &lt;span style="color: black; font-size: 10pt;"&gt; [[tel:7 16 27 40 55 72 91|7 16 27 40 55 72 91]] 112&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
+&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt; [[#TOC-If-A1-87.5-then-we-have-112-AID-140]]&lt;span style="color: black; font-size: 10pt;"&gt;If A1=87.5 then we have 112-AID(1400.) with Degrees as &lt;span style="color: black; font-size: 10pt;"&gt; [[tel/7 16 27 40 55 72 91|7 16 27 40 55 72 91]] 112&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
 &lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;__AID__ sytem shows different ascending , descending or linear trend of change in divisions sizes due to relation between n and A1 in __AID__&lt;span style="color: black; font-size: 10pt;"&gt; and __EDO__ with equal degree:&lt;/span&gt;&lt;/span&gt;
@@ Line 58: / Line 58: @@
 <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;AID&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #000000; font-family: arial,sans-serif; font-size: 18px;"&gt;&lt;strong&gt;Arithmetic irrational divisions&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;&lt;span style="color: black; font-size: 11pt;"&gt;For an intervallic system with &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 11pt;"&gt;n&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 11pt;"&gt; divisions , &lt;/span&gt;&lt;span style="color: #be00ff; font-size: 11pt;"&gt;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29" rel="nofollow"&gt;__AID__&lt;/a&gt;&lt;/span&gt;&lt;span style="color: black; font-size: 11pt;"&gt; is considered as &lt;a class="wiki_link_ext" href="http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html" rel="nofollow"&gt;arithmetic sequence&lt;/a&gt; with divisions of system as terms of sequence. &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;&lt;span style="color: black; font-size: 11pt;"&gt;For an intervallic system with &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 11pt;"&gt;n&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 11pt;"&gt; divisions , &lt;/span&gt;&lt;span style="color: #be00ff; font-size: 11pt;"&gt;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/240edo/arithmeticirrationaldivisions%28aid%29" rel="nofollow"&gt;AID_&lt;/a&gt;&lt;/span&gt;&lt;span style="color: black; font-size: 11pt;"&gt; is considered as &lt;a class="wiki_link_ext" href="http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html" rel="nofollow"&gt;arithmetic sequence&lt;/a&gt; with divisions of system as terms of sequence. &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; text-align: left;"&gt;&lt;span style="color: black; font-size: 11pt;"&gt; If the first division is &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 11pt;"&gt;A1&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 11pt;"&gt; and the last , &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 11pt;"&gt;An&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 11pt;"&gt; , with common difference of &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 11pt;"&gt;d&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 11pt;"&gt; , we have : &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;A1 = A1&lt;/span&gt;&lt;br /&gt;
@@ Line 78: / Line 78: @@
 &lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;By considering Sn=1200 , A1=70 , n=12 , d will be 5.454545455 and our 12-tone scale is equal to:&lt;/span&gt;&lt;br /&gt;
 &lt;span style="font-family: Tahoma,Geneva,sans-serif;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:2:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@TOC-0.070.0145.455226.364312.727404.545&amp;quot; title=&amp;quot;Anchor: TOC-0.070.0145.455226.364312.727404.545&amp;quot;/&amp;gt; --&gt;&lt;a name="TOC-0.070.0145.455226.364312.727404.545"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:2 --&gt; &lt;strong&gt;0.0 70.0 145.455 226.364 312.727 404.545 501.818 604.545 712.727 826.364 945.455 1070.0 1200.0&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
-&lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;Scales based on AID can be subsets of EDO if : Scales based on AID can be subsets of EDO if :&lt;/span&gt;&lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;1- we choose d=0 so ,&lt;span style="color: black; font-size: 11pt;"&gt; A1 = Sn/n&lt;/span&gt; .. Consider &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;=150 , then we have 8-EDO .&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span style="color: black; direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 11pt; text-align: left;"&gt;Scales based on AID can be subsets of EDO if :&lt;/span&gt;&lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;1- we choose d=0 so ,&lt;span style="color: black; font-size: 11pt;"&gt; A1 = Sn/n&lt;/span&gt; .. Consider &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;=150 , then we have 8-EDO .&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;span style="direction: ltr; display: block; font-family: Tahoma,Geneva,sans-serif; margin: 0cm 0cm 0pt; text-align: left;"&gt;&lt;span style="color: black; font-size: 10pt;"&gt;2- for a constant &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt; and different &lt;u&gt;A1&lt;/u&gt;, if &lt;u&gt;d&lt;/u&gt; and (Sn/A1) are Integer number , we have a susbet of EDO or EDI( Equal divisions of Interval) .Consider &lt;u&gt;Sn = 1400&lt;/u&gt; , &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;n&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;=8 and &lt;/span&gt;&lt;u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;A1&lt;/span&gt;&lt;/u&gt;&lt;span style="color: black; font-size: 10pt;"&gt;=70 , then we have a subset of a 140-ED(1400.) with Degrees as &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2017%2030%2046%2065%2087%20112"&gt;7 17 30 46 65 87 112&lt;/a&gt; 140 :&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;strong&gt;0.000 70.000 170.000 300.000 460.000 650.000 870.000 1120.000 1400.000&lt;/strong&gt;&lt;br /&gt;