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List of distinct EDO scales: Difference between revisions

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Wikispaces>Sarzadoce
**Imported revision 555135841 - Original comment: **
Wikispaces>Sarzadoce
**Imported revision 555136119 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-07-09 21:48:30 UTC</tt>.<br>
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-07-09 21:57:55 UTC</tt>.<br>
: The original revision id was <tt>555135841</tt>.<br>
: The original revision id was <tt>555136119</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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[[math]]
f(n) = \displaystyle \sum \limits_{d \mid n} \mu(n/d) (2^{n} - 1)
[[math]]


[[math]]
g(n) = \displaystyle \sum \limits_{m=1}^{n} \displaystyle \sum \limits_{d \mid m} \mu(m/d) (2^{m} - 1)
[[math]]




==List of Scales up to 10-EDO:==


&lt;span style="line-height: 1.5;"&gt; ∆ EDO (Variety = 1)&lt;/span&gt;
&lt;span style="line-height: 1.5;"&gt; ∆ EDO (Variety = 1)&lt;/span&gt;
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†† Strict MOS (Variety = 2)
†† Strict MOS (Variety = 2)


==1-EDO Scales==  
===1-EDO Scales===  


1 ∆
1 ∆


==2-EDO Scales==  
===2-EDO Scales===  


11 ∆
11 ∆


==3-EDO Scales==  
===3-EDO Scales===  


21 ††
21 ††
111 ∆
111 ∆


==4-EDO Scales==  
===4-EDO Scales===  


31 ††
31 ††
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1111 ∆
1111 ∆


==5-EDO Scales==  
===5-EDO Scales===  


32 ††
32 ††
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11111 ∆
11111 ∆


==6-EDO Scales==  
===6-EDO Scales===  


51 ††
51 ††
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111111 ∆
111111 ∆


==7-EDO Scales==  
===7-EDO Scales===  


43 ††
43 ††
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1111111 ∆
1111111 ∆


==8-EDO Scales==  
===8-EDO Scales===  


53 ††
53 ††
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11111111 ∆
11111111 ∆


==9-EDO Scales==  
===9-EDO Scales===  


54 ††
54 ††
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111111111 ∆
111111111 ∆


==10-EDO Scales==  
===10-EDO Scales===  


73 ††
73 ††
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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Breakdown of Scales by EDO and Number of Notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Breakdown of Scales by EDO and Number of Notes&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Breakdown of Scales by EDO and Number of Notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Breakdown of Scales by EDO and Number of Notes&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;


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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Breakdown of Scales by EDO Only"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Breakdown of Scales by EDO Only&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Breakdown of Scales by EDO Only"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Breakdown of Scales by EDO Only&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;


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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextMathRule:0:
[[math]]&amp;lt;br/&amp;gt;
f(n) = \displaystyle \sum \limits_{d \mid n} \mu(n/d) (2^{n} - 1)&amp;lt;br/&amp;gt;[[math]]
--&gt;&lt;script type="math/tex"&gt;f(n) = \displaystyle \sum \limits_{d \mid n} \mu(n/d) (2^{n} - 1)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextMathRule:1:
[[math]]&amp;lt;br/&amp;gt;
g(n) = \displaystyle \sum \limits_{m=1}^{n} \displaystyle \sum \limits_{d \mid m} \mu(m/d) (2^{m} - 1)&amp;lt;br/&amp;gt;[[math]]
--&gt;&lt;script type="math/tex"&gt;g(n) = \displaystyle \sum \limits_{m=1}^{n} \displaystyle \sum \limits_{d \mid m} \mu(m/d) (2^{m} - 1)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:1 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-List of Scales up to 10-EDO:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;List of Scales up to 10-EDO:&lt;/h2&gt;
&lt;br /&gt;
&lt;span style="line-height: 1.5;"&gt; ∆ EDO (Variety = 1)&lt;/span&gt;&lt;br /&gt;
&lt;span style="line-height: 1.5;"&gt; ∆ EDO (Variety = 1)&lt;/span&gt;&lt;br /&gt;
&lt;span style="line-height: 1.5;"&gt; ◊◊ Multi-MOS (Max Variety = 2)&lt;/span&gt;&lt;br /&gt;
&lt;span style="line-height: 1.5;"&gt; ◊◊ Multi-MOS (Max Variety = 2)&lt;/span&gt;&lt;br /&gt;
†† Strict MOS (Variety = 2)&lt;br /&gt;
†† Strict MOS (Variety = 2)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-1-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;1-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-List of Scales up to 10-EDO:-1-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;1-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
1 ∆&lt;br /&gt;
1 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-2-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;2-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-List of Scales up to 10-EDO:-2-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;2-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
11 ∆&lt;br /&gt;
11 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-3-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;3-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-List of Scales up to 10-EDO:-3-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;3-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
21 ††&lt;br /&gt;
21 ††&lt;br /&gt;
111 ∆&lt;br /&gt;
111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-4-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;4-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-List of Scales up to 10-EDO:-4-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;4-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
31 ††&lt;br /&gt;
31 ††&lt;br /&gt;
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1111 ∆&lt;br /&gt;
1111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-5-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;5-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-List of Scales up to 10-EDO:-5-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;5-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
32 ††&lt;br /&gt;
32 ††&lt;br /&gt;
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11111 ∆&lt;br /&gt;
11111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-6-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;6-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-List of Scales up to 10-EDO:-6-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;6-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
51 ††&lt;br /&gt;
51 ††&lt;br /&gt;
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111111 ∆&lt;br /&gt;
111111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-7-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;7-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-List of Scales up to 10-EDO:-7-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;7-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
43 ††&lt;br /&gt;
43 ††&lt;br /&gt;
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1111111 ∆&lt;br /&gt;
1111111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-8-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;8-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x-List of Scales up to 10-EDO:-8-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;8-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
53 ††&lt;br /&gt;
53 ††&lt;br /&gt;
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11111111 ∆&lt;br /&gt;
11111111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-9-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;9-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x-List of Scales up to 10-EDO:-9-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;9-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
54 ††&lt;br /&gt;
54 ††&lt;br /&gt;
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111111111 ∆&lt;br /&gt;
111111111 ∆&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-10-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;10-EDO Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x-List of Scales up to 10-EDO:-10-EDO Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;10-EDO Scales&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
73 ††&lt;br /&gt;
73 ††&lt;br /&gt;
Retrieved from "https://en.xen.wiki/w/List_of_distinct_EDO_scales"