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 01:45:10 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-06-04 01:52:51 UTC</tt>.

: The original revision id was <tt>~~584785481~~</tt>.

: The original revision id was <tt>584785545</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 31-tone, X = 2, i = 1, G(^) = -12, and ^ = dim 2nd.

||= 5edo ||= ~~pentatonic ||= K(~~#) || || ||

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

||= ~~17edo ||= sweet~~ ||= || -5 || min 2nd ||

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

||= ~~19edo ||= sweet~~ ||= || || ||

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

||= ~~22edo ||= sweet~~ ||= || -5 || min 2nd ||

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

||= ~~26edo ||= sweet~~ ||= || || ||

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

||= ~~27edo ||= sweet~~ ||= || || ||

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

||= ~~29edo ||= sweet ||= || || ||~~

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

~~||= 31edo ||= sweet~~ ||= || -12 || dim 2nd ||

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

||= ~~32edo ||= sweet~~ ||= || || ||

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

||= ~~33edo ||= sweet~~ ||= || || ||

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

||= ~~34edo ||= sweet~~ ||= || || ||

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

||= ~~37edo ||= sweet~~ ||= || || ||

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

||= ~~38edo ||= sweet~~ ||= || || ||

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

||= ~~39edo ||= sweet~~ ||= || || ||

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

||= ~~40edo ||= sweet~~ ||= || || ||

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

||= ~~41edo ||= sweet~~ ||= || || ||

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

||= ~~42edo ||= sweet~~ ||= || || ||

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

||= ~~43edo ||= sweet ||= || || ||~~

</pre></div>

~~||= 44ddo ||= sweet ||= || || ||~~

~~||= 45edo ||= sweet~~ ||= || || ||

~~||= 46edo ||= sweet ||= || || ||~~

~~||= 47edo ||= sweet ||= || || ||~~

~~||= 49edo ||= sweet ||= || || ||~~

~~||= 50edo ||= sweet ||= || || ||~~

~~||= 51edo ||= sweet ||= || || ||~~

~~||= 52edo ||= sweet ||= || || ||~~

~~||= 53edo ||= sweet ||= || || ||~~</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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<td style="text-align: center;">5edo

</td>

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

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

</td>

~~<td style="text-align: center;">K(#) ~~

<td>genspan of ^

~~</td>~~

<td>

</td>

<td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

<td style="text-align: center;">~~26edo ~~

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

</td>

<td>

<td>-12

</td>

<td>

<td>dim 2nd

</td>

</tr>

<tr>

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

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

~~</td>~~

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

</td>

</td>

<td>~~-12~~

<td>

</td>

<td>~~dim 2nd~~

<td>

</td>

</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

<td style="text-align: center;">~~34edo ~~

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

<td style="text-align: center;">~~38edo ~~

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

<td style="text-align: center;">~~40edo ~~

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

</td>

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</tr>

<tr>

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

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">44ddo ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">46edo ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">51edo ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">52edo ~~

~~</td>~~

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

~~</td>~~

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

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

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

~~</td>~~

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

</td>

@@ 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 01:45:10 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-06-04 01:52:51 UTC</tt>.<br>
-: The original revision id was <tt>584785481</tt>.<br>
+: The original revision id was <tt>584785545</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 914: / Line 914: @@
 For 31-tone, X = 2, i = 1, G(^) = -12, and ^ = dim 2nd.
-||= 5edo ||= pentatonic ||= K(#) ||   ||   ||
+||= 5edo ||= Keyspan of # || genspan of ^ ||   ||
-||= 17edo ||= sweet ||=   || -5 || min 2nd ||
+||= 17-tone ||=   || -5 || min 2nd ||
-||= 19edo ||= sweet ||=   ||   ||   ||
+||= 19-tone ||=   ||   ||   ||
-||= 22edo ||= sweet ||=   || -5 || min 2nd ||
+||= 22-tone ||=   || -5 || min 2nd ||
-||= 26edo ||= sweet ||=   ||   ||   ||
+||= 27-tone ||=   ||   ||   ||
-||= 27edo ||= sweet ||=   ||   ||   ||
+||= 29-tone ||=   ||   ||   ||
-||= 29edo ||= sweet ||=   ||   ||   ||
+||= 31-tone ||=   || -12 || dim 2nd ||
-||= 31edo ||= sweet ||=   || -12 || dim 2nd ||
+||= 32-tone ||=   ||   ||   ||
-||= 32edo ||= sweet ||=   ||   ||   ||
+||= 37-tone ||=   ||   ||   ||
-||= 33edo ||= sweet ||=   ||   ||   ||
+||= 39-tone ||=   ||   ||   ||
-||= 34edo ||= sweet ||=   ||   ||   ||
+||= 41-tone ||=   ||   ||   ||
-||= 37edo ||= sweet ||=   ||   ||   ||
+||= 42-tone ||=   ||   ||   ||
-||= 38edo ||= sweet ||=   ||   ||   ||
+||= 43-tone ||=   ||   ||   ||
-||= 39edo ||= sweet ||=   ||   ||   ||
+||= 45-tone ||=   ||   ||   ||
-||= 40edo ||= sweet ||=   ||   ||   ||
+||= 49-tone ||=   ||   ||   ||
-||= 41edo ||= sweet ||=   ||   ||   ||
+||= 50-tone ||=   ||   ||   ||
-||= 42edo ||= sweet ||=   ||   ||   ||
+||= 53-tone ||=   ||   ||   ||
-||= 43edo ||= sweet ||=   ||   ||   ||
+</pre></div>
-||= 44ddo ||= sweet ||=   ||   ||   ||
-||= 45edo ||= sweet ||=   ||   ||   ||
-||= 46edo ||= sweet ||=   ||   ||   ||
-||= 47edo ||= sweet ||=   ||   ||   ||
-||= 49edo ||= sweet ||=   ||   ||   ||
-||= 50edo ||= sweet ||=   ||   ||   ||
-||= 51edo ||= sweet ||=   ||   ||   ||
-||= 52edo ||= sweet ||=   ||   ||   ||
-||= 53edo ||= sweet ||=   ||   ||   ||</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 1,032: / Line 1,023: @@
 fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2418:&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:2418 --&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;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 1,248: / Line 1,239: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2419:&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:2419 --&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;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:2420:&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:2420 --&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: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: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 3,820: / Line 3,811: @@
          &lt;td style="text-align: center;"&gt;5edo&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;pentatonic&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Keyspan of #&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;K(#)&lt;br /&gt;
+         &lt;td&gt;genspan of ^&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 3,830: / Line 3,819: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;17edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,842: / Line 3,829: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;19edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,854: / Line 3,839: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;22edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,866: / Line 3,849: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;26edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;27-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,878: / Line 3,859: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;27edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;29-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,890: / Line 3,869: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;29edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;31-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;-12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;dim 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;31edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;32-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-12&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;dim 2nd&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;32edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;37-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,926: / Line 3,899: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;33edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;39-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,938: / Line 3,909: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;34edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;41-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,950: / Line 3,919: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;37edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;42-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,962: / Line 3,929: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;38edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;43-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,974: / Line 3,939: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;39edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;45-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,986: / Line 3,949: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;40edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;49-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 3,998: / Line 3,959: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;41edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;50-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 4,010: / Line 3,969: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;42edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;53-tone&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;43edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;44ddo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;45edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;46edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;47edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;49edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;50edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;51edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;52edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&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&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;53edo&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;sweet&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;