20edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~guest~~|~~guest~~]] and made on <tt>2011-07-18 16:04:42 UTC</tt>.

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-18 23:18:40 UTC</tt>.

: The original revision id was <tt>~~241825239~~</tt>.

: The original revision id was <tt>241879197</tt>.

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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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">**20 tone equal temperament**

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated.

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.

[[toc|flat]]

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=Properties=

==Intervals==

|| ~~degrees of 20edo~~ || ~~cents value~~ ||

|| **Degree** || **Cents** ||= **Approximate**

|| 0 || 0 ||

**Ratios** ||= **Nearest**

|| 1 || 60 ||

**Harmonic** ||

|| 2 || 120 ||

|| 0 || 0 ||= 1/1 ||= 1 ||

|| 3 || 180 ||

|| 1 || 60 ||= ||= 33 ||

|| 4 || 240 ||

|| 2 || 120 ||= 14/13, 15/14 ||= 69 ||

|| 5 || 300 ||

|| 3 || 180 ||= 10/9 ||= 71 ||

|| 6 || 360 ||

|| 4 || 240 ||= 8/7, 15/13 ||= 37 ||

|| 7 || 420 ||

|| 5 || 300 ||= 13/11, 19/16 ||= 19 ||

|| 8 || 480 ||

|| 6 || 360 ||= 16/13, 5/4 ||= 79 ||

|| 9 || 540 ||

|| 7 || 420 ||= 14/11 ||= 41 ||

|| 10 || 600 ||

|| 8 || 480 ||= 25/19, 4/3 ||= 21 ||

|| 11 || 660 ||

|| 9 || 540 ||= 15/11, 11/8 ||= 11 ||

|| 12 || 720 ||

|| 10 || 600 ||= 7/5 ||= 91 ||

|| 13 || 780 ||

|| 11 || 660 ||= 22/15, 16/11 ||= 47 ||

|| 14 || 840 ||

|| 12 || 720 ||= 38/25, 3/2 ||= 97 ||

|| 15 || 900 ||

|| 13 || 780 ||= 11/7, 25/16 ||= 25 ||

|| 16 || 960 ||

|| 14 || 840 ||= 13/8, 8/5 ||= 13 ||

|| 17 || 1020 ||

|| 15 || 900 ||= 22/13, 32/19 ||= 27 ||

|| 18 || 1080 ||

|| 16 || 960 ||= 7/4, 26/15 ||= 7 ||

|| 19 || 1140 ||

|| 17 || 1020 ||= 9/5 ||= 115 ||

|| 18 || 1080 ||= 15/8, 13/7 ||= 15 ||

|| 19 || 1140 ||= ||= 31 ||

|| 20 || 1200 ||= 2/1 ||= 2 ||

==Modes==

20 tone equal modes:

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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>20edo</title></head><body>20 tone equal temperament

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 <a class="wiki_link" href="/cent">cent</a>s each. It contains smaller <a class="wiki_link" href="/edo">edo</a>s <a class="wiki_link" href="/2edo">2</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/5edo">5</a>, and <a class="wiki_link" href="/10edo">10</a> and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated.

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 <a class="wiki_link" href="/cent">cent</a>s each. It contains smaller <a class="wiki_link" href="/edo">edo</a>s <a class="wiki_link" href="/2edo">2</a>, <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/5edo">5</a>, and <a class="wiki_link" href="/10edo">10</a> and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.

<a href="#Compositions">Compositions</a> | <a href="#Properties">Properties</a> | <a href="#Books">Books</a>

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<tr>

<td>~~degrees of 20edo~~

<td>Degree

</td>

<td>Cents

</td>

<td style="text-align: center;">Approximate

Ratios

</td>

<td>~~cents value~~

<td style="text-align: center;">Nearest

Harmonic

</td>

</tr>

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</td>

<td>0

</td>

<td style="text-align: center;">1/1

</td>

<td style="text-align: center;">1

</td>

</tr>

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</td>

<td>60

</td>

</td>

<td style="text-align: center;">33

</td>

</tr>

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</td>

<td>120

</td>

<td style="text-align: center;">14/13, 15/14

</td>

<td style="text-align: center;">69

</td>

</tr>

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</td>

<td>180

</td>

<td style="text-align: center;">10/9

</td>

<td style="text-align: center;">71

</td>

</tr>

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</td>

<td>240

</td>

<td style="text-align: center;">8/7, 15/13

</td>

<td style="text-align: center;">37

</td>

</tr>

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</td>

<td>300

</td>

<td style="text-align: center;">13/11, 19/16

</td>

<td style="text-align: center;">19

</td>

</tr>

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</td>

<td>360

</td>

<td style="text-align: center;">16/13, 5/4

</td>

<td style="text-align: center;">79

</td>

</tr>

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</td>

<td>420

</td>

<td style="text-align: center;">14/11

</td>

<td style="text-align: center;">41

</td>

</tr>

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</td>

<td>480

</td>

<td style="text-align: center;">25/19, 4/3

</td>

<td style="text-align: center;">21

</td>

</tr>

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</td>

<td>540

</td>

<td style="text-align: center;">15/11, 11/8

</td>

<td style="text-align: center;">11

</td>

</tr>

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</td>

<td>600

</td>

<td style="text-align: center;">7/5

</td>

<td style="text-align: center;">91

</td>

</tr>

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</td>

<td>660

</td>

<td style="text-align: center;">22/15, 16/11

</td>

<td style="text-align: center;">47

</td>

</tr>

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</td>

<td>720

</td>

<td style="text-align: center;">38/25, 3/2

</td>

<td style="text-align: center;">97

</td>

</tr>

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</td>

<td>780

</td>

<td style="text-align: center;">11/7, 25/16

</td>

<td style="text-align: center;">25

</td>

</tr>

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</td>

<td>840

</td>

<td style="text-align: center;">13/8, 8/5

</td>

<td style="text-align: center;">13

</td>

</tr>

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</td>

<td>900

</td>

<td style="text-align: center;">22/13, 32/19

</td>

<td style="text-align: center;">27

</td>

</tr>

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</td>

<td>960

</td>

<td style="text-align: center;">7/4, 26/15

</td>

<td style="text-align: center;">7

</td>

</tr>

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</td>

<td>1020

</td>

<td style="text-align: center;">9/5

</td>

<td style="text-align: center;">115

</td>

</tr>

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</td>

<td>1080

</td>

<td style="text-align: center;">15/8, 13/7

</td>

<td style="text-align: center;">15

</td>

</tr>

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</td>

<td>1140

</td>

</td>

<td style="text-align: center;">31

</td>

</tr>

<tr>

<td>20

</td>

<td>1200

</td>

<td style="text-align: center;">2/1

</td>

<td style="text-align: center;">2

</td>

</tr>

</table>

~~ ~~

<h2 id="toc3"><a name="Properties-Modes"></a>Modes</h2>

20 tone equal modes:

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<h1 id="toc5"><a name="Books"></a>Books</h1>

<a href="http://www.ronsword.com/" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /></a><a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank">&quot;Icosaphonic Scales for Guitar&quot; - Theory / Scale book with above modes and more</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></body></html></pre></div>

<a href="http://www.ronsword.com/" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /></a><a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank">&quot;Icosaphonic Scales for Guitar&quot; - Theory / Scale book with above modes and more</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a></body></html></pre></div>

@@ 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>2011-07-18 16:04:42 UTC</tt>.<br>
+: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-18 23:18:40 UTC</tt>.<br>
-: The original revision id was <tt>241825239</tt>.<br>
+: The original revision id was <tt>241879197</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: #800038; font-size: 20px;"&gt;**20 tone equal temperament**&lt;/span&gt;
--tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated.
+-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
 [[toc|flat]]
@@ Line 20: / Line 20: @@
 =Properties=
 ==Intervals==
-|| degrees of 20edo || cents value ||
+|| **Degree** || **Cents** ||= **Approximate**
-|| 0 || 0 ||
+**Ratios** ||= **Nearest**
-|| 1 || 60 ||
+**Harmonic** ||
-|| 2 || 120 ||
+|| 0 || 0 ||= 1/1 ||= 1 ||
-|| 3 || 180 ||
+|| 1 || 60 ||=   ||= 33 ||
-|| 4 || 240 ||
+|| 2 || 120 ||= 14/13, 15/14 ||= 69 ||
-|| 5 || 300 ||
+|| 3 || 180 ||= 10/9 ||= 71 ||
-|| 6 || 360 ||
+|| 4 || 240 ||= 8/7, 15/13 ||= 37 ||
-|| 7 || 420 ||
+|| 5 || 300 ||= 13/11, 19/16 ||= 19 ||
-|| 8 || 480 ||
+|| 6 || 360 ||= 16/13, 5/4 ||= 79 ||
-|| 9 || 540 ||
+|| 7 || 420 ||= 14/11 ||= 41 ||
-|| 10 || 600 ||
+|| 8 || 480 ||= 25/19, 4/3 ||= 21 ||
-|| 11 || 660 ||
+|| 9 || 540 ||= 15/11, 11/8 ||= 11 ||
-|| 12 || 720 ||
+|| 10 || 600 ||= 7/5 ||= 91 ||
-|| 13 || 780 ||
+|| 11 || 660 ||= 22/15, 16/11 ||= 47 ||
-|| 14 || 840 ||
+|| 12 || 720 ||= 38/25, 3/2 ||= 97 ||
-|| 15 || 900 ||
+|| 13 || 780 ||= 11/7, 25/16 ||= 25 ||
-|| 16 || 960 ||
+|| 14 || 840 ||= 13/8, 8/5 ||= 13 ||
-|| 17 || 1020 ||
+|| 15 || 900 ||= 22/13, 32/19 ||= 27 ||
-|| 18 || 1080 ||
+|| 16 || 960 ||= 7/4, 26/15 ||= 7 ||
-|| 19 || 1140 ||
+|| 17 || 1020 ||= 9/5 ||= 115 ||
+|| 18 || 1080 ||= 15/8, 13/7 ||= 15 ||
+|| 19 || 1140 ||=   ||= 31 ||
+|| 20 || 1200 ||= 2/1 ||= 2 ||
 ==Modes==
 tone equal modes:
@@ Line 91: / Line 93: @@
 <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;20edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #800038; font-size: 20px;"&gt;&lt;strong&gt;20 tone equal temperament&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
--tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It contains smaller &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;s &lt;a class="wiki_link" href="/2edo"&gt;2&lt;/a&gt;, &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, and &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt; and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated.&lt;br /&gt;
+-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It contains smaller &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;s &lt;a class="wiki_link" href="/2edo"&gt;2&lt;/a&gt;, &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, and &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt; and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5 edo), 11, 13 (from 10 edo), 15, 19 (4 edo), 27 (4 edo), 29 and 31; as well as the other harmonics more loosely, while to some still functionally, approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Books"&gt;Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
@@ Line 104: / Line 106: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;degrees of 20edo&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Ratios&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;cents value&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Harmonic&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 113: / Line 121: @@
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 119: / Line 131: @@
 &lt;/td&gt;
          &lt;td&gt;60&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 125: / Line 141: @@
 &lt;/td&gt;
          &lt;td&gt;120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;14/13, 15/14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;69&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 131: / Line 151: @@
 &lt;/td&gt;
          &lt;td&gt;180&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;10/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 137: / Line 161: @@
 &lt;/td&gt;
          &lt;td&gt;240&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8/7, 15/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 143: / Line 171: @@
 &lt;/td&gt;
          &lt;td&gt;300&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;13/11, 19/16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 149: / Line 181: @@
 &lt;/td&gt;
          &lt;td&gt;360&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;16/13, 5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;79&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 155: / Line 191: @@
 &lt;/td&gt;
          &lt;td&gt;420&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;14/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 161: / Line 201: @@
 &lt;/td&gt;
          &lt;td&gt;480&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;25/19, 4/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 167: / Line 211: @@
 &lt;/td&gt;
          &lt;td&gt;540&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;15/11, 11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 173: / Line 221: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;91&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 179: / Line 231: @@
 &lt;/td&gt;
          &lt;td&gt;660&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;22/15, 16/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;47&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 185: / Line 241: @@
 &lt;/td&gt;
          &lt;td&gt;720&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;38/25, 3/2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;97&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 191: / Line 251: @@
 &lt;/td&gt;
          &lt;td&gt;780&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11/7, 25/16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 197: / Line 261: @@
 &lt;/td&gt;
          &lt;td&gt;840&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;13/8, 8/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 203: / Line 271: @@
 &lt;/td&gt;
          &lt;td&gt;900&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;22/13, 32/19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 209: / Line 281: @@
 &lt;/td&gt;
          &lt;td&gt;960&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7/4, 26/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 215: / Line 291: @@
 &lt;/td&gt;
          &lt;td&gt;1020&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;115&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 221: / Line 301: @@
 &lt;/td&gt;
          &lt;td&gt;1080&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;15/8, 13/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 227: / Line 311: @@
 &lt;/td&gt;
          &lt;td&gt;1140&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
-&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Properties-Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Modes&lt;/h2&gt;
 tone equal modes:&lt;br /&gt;
@@ Line 629: / Line 726: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Books&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:542:&amp;lt;a href=&amp;quot;http://www.ronsword.com/&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/20_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 114px; width: 82px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/" target="_blank" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:542 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank"&gt;&amp;quot;Icosaphonic Scales for Guitar&amp;quot; - Theory / Scale book with above modes and more&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+  &lt;!-- ws:start:WikiTextRemoteImageRule:636:&amp;lt;a href=&amp;quot;http://www.ronsword.com/&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/20_tet_Coversm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 114px; width: 82px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/" target="_blank" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/20_tet_Coversm.jpg" alt="external image 20_tet_Coversm.jpg" title="external image 20_tet_Coversm.jpg" style="height: 114px; width: 82px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:636 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/" rel="nofollow" target="_blank"&gt;&amp;quot;Icosaphonic Scales for Guitar&amp;quot; - Theory / Scale book with above modes and more&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>