Kite's ups and downs notation: 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:TallKite|TallKite]] and made on <tt>2016-06-04 01:52:51 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-06-04 02:00:22 UTC</tt>.

: The original revision id was <tt>~~584785545~~</tt>.

: The original revision id was <tt>584785603</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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For 22-tone, X = 3 and N = 22. We choose i to be the smallest (least absolute value) number that avoids fractions. Thus i = 1, G(^) = -5, and ^ = min 2nd.

~~For 17-tone, X = 2, i = 1, G(^) = -5, and ^ = min 2nd~~

||= ||= Keyspan of # ||= value of i ||= genspan of ^ ||= stepspan &

quality of ^ ||

~~For 31-tone, X = 2, i = 1, G(^) = -12, and ^ = dim 2nd.~~

||= 17-tone ||= 2 ||= 1 ||= -5 ||= min 2nd ||

||= 22-tone ||= 3 ||= 1 ||= -5 ||= min 2nd ||

||= ~~5edo~~ ||= Keyspan of # || genspan of ^ || ||

||= 27-tone ||= 4 ||= ||= ||= ||

||= 17-tone ||= || -5 || min 2nd ||

||= 29-tone ||= 3 ||= ||= ||= ||

||= 19-tone ||= ~~|| || ||~~

||= 31-tone ||= 2 ||= 1 ||= -12 ||= dim 2nd ||

||= ~~22-tone~~ ||= || -5 || min 2nd ||

||= 32-tone ||= 5 ||= ||= ||= ||

||= 27-tone ||= || || ||

||= 37-tone ||= 6 ||= ||= ||= ||

||= 29-tone ||= || || ||

||= 39-tone ||= 5 ||= ||= ||= ||

||= 31-tone ||= || -12 || dim 2nd ||

||= 41-tone ||= 4 ||= ||= ||= ||

||= 32-tone ||= || || ||

||= 42-tone ||= 7 ||= ||= ||= ||

||= 37-tone ||= || || ||

||= 43-tone ||= 3 ||= ||= ||= ||

||= 39-tone ||= || || ||

||= 45-tone ||= 5 ||= ||= ||= ||

||= 41-tone ||= || || ||

||= 49-tone ||= 7 ||= ||= ||= ||

||= 42-tone ||= || || ||

||= 50-tone ||= 3 ||= ||= ||= ||

||= 43-tone ||= || || ||

||= 53-tone ||= 5 ||= ||= ||= ||</pre></div>

||= 45-tone ||= || || ||

||= 49-tone ||= || || ||

||= 50-tone ||= || || ||

||= 53-tone ||= || || ||

</pre></div>

<h4>Original HTML content:</h4>

<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>Ups and Downs Notation</title></head><body><h1 id="toc0"><a name="x&quot;Ups and Downs&quot; Notation"></a>&quot;Ups and Downs&quot; Notation</h1>

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fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢

<img src="/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png" alt="The fifth of EDOs 5-53.png" title="The fifth of EDOs 5-53.png" style="height: 1035px; width: 800px;" />

<img src="/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png" alt="The fifth of EDOs 5-53.png" title="The fifth of EDOs 5-53.png" style="height: 1035px; width: 800px;" />

This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.

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<img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" />

<img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" />

<h2 id="toc3"><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg" alt="Tibia in G with ^v, rygb 2.jpg" title="Tibia in G with ^v, rygb 2.jpg" style="height: 957px; width: 800px;" /></h2>

<h2 id="toc3"><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg" alt="Tibia in G with ^v, rygb 2.jpg" title="Tibia in G with ^v, rygb 2.jpg" style="height: 957px; width: 800px;" /></h2>

<h2 id="toc4"> </h2>

<h2 id="toc5"> </h2>

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For 22-tone, X = 3 and N = 22. We choose i to be the smallest (least absolute value) number that avoids fractions. Thus i = 1, G(^) = -5, and ^ = min 2nd.

~~ ~~

~~For 17-tone, X = 2, i = 1, G(^) = -5, and ^ = min 2nd ~~

~~ ~~

~~For 31-tone, X = 2, i = 1, G(^) = -12, and ^ = dim 2nd. ~~

Line 3,809:

Line 3,800:

<tr>

<td style="text-align: center;">~~5edo~~

</td>

<td style="text-align: center;">Keyspan of #

</td>

<td>~~genspan~~ of ^

<td style="text-align: center;">value of i

</td>

<td>

<td style="text-align: center;">genspan of ^

</td>

<td style="text-align: center;">stepspan &amp;

quality of ^

</td>

</tr>

Line 3,821:

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<td style="text-align: center;">17-tone

</td>

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

</td>

<td>-5

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

</td>

~~<td>min 2nd ~~

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

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

</td>

<td~~> ~~

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

~~</td>~~

~~&lt~~;td>

</td>

</tr>

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<td style="text-align: center;">22-tone

</td>

<td style="text-align: center;">3

</td>

<td>-5

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

</td>

<td>min 2nd

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

</td>

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

</td>

</tr>

<tr>

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

</td>

<td style="text-align: center;">4

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">29-tone

</td>

<td style="text-align: center;">3

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

Line 3,871:

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

</td>

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

</td>

<td>~~-12~~

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

</td>

<td>dim 2nd

<td style="text-align: center;">-12

</td>

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

</td>

</tr>

<tr>

<td style="text-align: center;">32-tone

</td>

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

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

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

</td>

<td style="text-align: center;">6

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">39-tone

</td>

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

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

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

</td>

<td style="text-align: center;">4

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">42-tone

</td>

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

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">43-tone

</td>

<td style="text-align: center;">3

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">45-tone

</td>

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

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">49-tone

</td>

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

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">50-tone

</td>

<td style="text-align: center;">3

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td style="text-align: center;">53-tone

</td>

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

</td>

</td>

<td>

</td>

<td>

</td>

</tr>

@@ 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:TallKite|TallKite]] and made on <tt>2016-06-04 01:52:51 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-06-04 02:00:22 UTC</tt>.<br>
-: The original revision id was <tt>584785545</tt>.<br>
+: The original revision id was <tt>584785603</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 910: / Line 910: @@
 For 22-tone, X = 3 and N = 22. We choose i to be the smallest (least absolute value) number that avoids fractions. Thus i = 1, G(^) = -5, and ^ = min 2nd.
-For 17-tone, X = 2, i = 1, G(^) = -5, and ^ = min 2nd
+||=   ||= Keyspan of # ||= value of i ||= genspan of ^ ||= stepspan &amp;
+quality of ^ ||
-For 31-tone, X = 2, i = 1, G(^) = -12, and ^ = dim 2nd.
+||= 17-tone ||= 2 ||= 1 ||= -5 ||= min 2nd ||
+||= 22-tone ||= 3 ||= 1 ||= -5 ||= min 2nd ||
-||= 5edo ||= Keyspan of # || genspan of ^ ||   ||
+||= 27-tone ||= 4 ||=   ||=   ||=   ||
-||= 17-tone ||=   || -5 || min 2nd ||
+||= 29-tone ||= 3 ||=   ||=   ||=   ||
-||= 19-tone ||=   ||   ||   ||
+||= 31-tone ||= 2 ||= 1 ||= -12 ||= dim 2nd ||
-||= 22-tone ||=   || -5 || min 2nd ||
+||= 32-tone ||= 5 ||=   ||=   ||=   ||
-||= 27-tone ||=   ||   ||   ||
+||= 37-tone ||= 6 ||=   ||=   ||=   ||
-||= 29-tone ||=   ||   ||   ||
+||= 39-tone ||= 5 ||=   ||=   ||=   ||
-||= 31-tone ||=   || -12 || dim 2nd ||
+||= 41-tone ||= 4 ||=   ||=   ||=   ||
-||= 32-tone ||=   ||   ||   ||
+||= 42-tone ||= 7 ||=   ||=   ||=   ||
-||= 37-tone ||=   ||   ||   ||
+||= 43-tone ||= 3 ||=   ||=   ||=   ||
-||= 39-tone ||=   ||   ||   ||
+||= 45-tone ||= 5 ||=   ||=   ||=   ||
-||= 41-tone ||=   ||   ||   ||
+||= 49-tone ||= 7 ||=   ||=   ||=   ||
-||= 42-tone ||=   ||   ||   ||
+||= 50-tone ||= 3 ||=   ||=   ||=   ||
-||= 43-tone ||=   ||   ||   ||
+||= 53-tone ||= 5 ||=   ||=   ||=   ||</pre></div>
-||= 45-tone ||=   ||   ||   ||
-||= 49-tone ||=   ||   ||   ||
-||= 50-tone ||=   ||   ||   ||
-||= 53-tone ||=   ||   ||   ||
-</pre></div>
 <h4>Original HTML content:</h4>
 <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;Ups and Downs Notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x&amp;quot;Ups and Downs&amp;quot; Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&amp;quot;Ups and Downs&amp;quot; Notation&lt;/h1&gt;
@@ Line 1,023: / Line 1,018: @@
 fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2264:&amp;lt;img src=&amp;quot;/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 1035px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png" alt="The fifth of EDOs 5-53.png" title="The fifth of EDOs 5-53.png" style="height: 1035px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2264 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:2286:&amp;lt;img src=&amp;quot;/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 1035px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png" alt="The fifth of EDOs 5-53.png" title="The fifth of EDOs 5-53.png" style="height: 1035px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2286 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.&lt;br /&gt;
@@ Line 1,239: / Line 1,234: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2265:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 1035px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2265 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:2287:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 1035px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2287 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:2266:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 957px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg" alt="Tibia in G with ^v, rygb 2.jpg" title="Tibia in G with ^v, rygb 2.jpg" style="height: 957px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2266 --&gt;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:2288:&amp;lt;img src=&amp;quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 957px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg" alt="Tibia in G with ^v, rygb 2.jpg" title="Tibia in G with ^v, rygb 2.jpg" style="height: 957px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2288 --&gt;&lt;/h2&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt; &lt;/h2&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt; &lt;/h2&gt;
@@ Line 3,800: / Line 3,795: @@
 &lt;br /&gt;
 For 22-tone, X = 3 and N = 22. We choose i to be the smallest (least absolute value) number that avoids fractions. Thus i = 1, G(^) = -5, and ^ = min 2nd.&lt;br /&gt;
-&lt;br /&gt;
-For 17-tone, X = 2, i = 1, G(^) = -5, and ^ = min 2nd&lt;br /&gt;
-&lt;br /&gt;
-For 31-tone, X = 2, i = 1, G(^) = -12, and ^ = dim 2nd.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 3,809: / Line 3,800: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;5edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Keyspan of #&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;genspan of ^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;value of i&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;genspan of ^&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;stepspan &amp;amp;&lt;br /&gt;
+quality of ^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,821: / Line 3,815: @@
          &lt;td style="text-align: center;"&gt;17-tone&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;min 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-5&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;19-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;min 2nd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,841: / Line 3,827: @@
          &lt;td style="text-align: center;"&gt;22-tone&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;min 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;min 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;27-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;29-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 3,871: / Line 3,863: @@
          &lt;td style="text-align: center;"&gt;31-tone&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;dim 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;-12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;dim 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;32-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;37-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;39-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;41-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;42-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;43-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;45-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;49-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;50-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td style="text-align: center;"&gt;53-tone&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;