4L 3s: 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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-03-~~10 23~~:08:51 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 05:17:40 UTC</tt>.

: The original revision id was <tt>~~209493438~~</tt>.

: The original revision id was <tt>222633992</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">4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). The spectrum looks like this:

|| || || || || ~~scale~~ || g in cents || 2g || 3g || 4g ||

There are two notable harmonic entropy minima: [[Kleismic family|hanson/keemun]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling temperaments|myna]], in which the generator is also 6/5 but now **10** of them make a 6/1.

|| 1\4 || || || || 1 0 1 0 1 0 1 || 300.000 || 600.000 || 900.000 || 0.000 ||

||||||||||||||~ Generator ||~ Scale ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||

|| || || || 5\19 || 4 1 4 1 4 1 4 || 315.789 || 631.579 || 947.368 || 63.158 ||

|| 1\4 || || || || || || || 1 0 1 0 1 0 1 || 300.000 || 600.000 || 900.000 || 0.000 ||= ||

|| || || 4\15 || || 3 1 3 1 3 1 3 || 320.000 || 640.000 || 960.000 || 80.000 ||

|| || || || || || || 8\31 || 7 1 7 1 7 1 7 || 309.677 || || || ||= Myna is around here ||

|| || || || 7\26 || 5 2 5 2 5 2 5 || 323.077 || 646.154 || 969.231 || 92.308 ||

|| || || || || || 7\27 || || 6 1 6 1 6 1 6 || 311.111 || || || ||= ||

|| || 3\11 || || || 2 1 2 1 2 1 2 || 327.273 || 654.545 || 981.818 || 109.091 ||

|| || || || || 6\23 || || || 5 1 5 1 5 1 5 || 313.043 || || || ||= ||

|| || || || 8\29 || 5 3 5 3 5 3 5 || 331.034 || 662.069 || 993.013 || 124.138 ||

|| || || || 5\19 || || || || 4 1 4 1 4 1 4 || 315.789 || 631.579 || 947.368 || 63.158 ||= ||

|| || || 5\18 || || 3 2 3 2 3 2 3 || 333.333 || 666.667 || 1000.000 || 133.333 ||

|| || || || || 9\34 || || || 7 2 7 2 7 2 7 || 317.647 || || || ||= Hanson/Keemun is around here ||

|| || || || 7\25 || 4 3 4 3 4 3 4 || 336.000 || 672.000 || 1008.000 || 144.000 ||

|| || || 4\15 || || || || || 3 1 3 1 3 1 3 || 320.000 || 640.000 || 960.000 || 80.000 ||= ||

|| 2\7 || || || || 1 1 1 1 1 1 1 || 342.857 || 685.714 || 1028.571 || 171.429 ||

|| || || || 7\26 || || || || 5 2 5 2 5 2 5 || 323.077 || 646.154 || 969.231 || 92.308 ||= ||

|| || 3\11 || || || || || || 2 1 2 1 2 1 2 || 327.273 || 654.545 || 981.818 || 109.091 ||= Boundary of propriety (generators

~~The "northernmost" range, near 5\19, could be called the keemun range or region, representing [[Kleismic family~~|~~keemun temperament]].~~</pre></div>

larger than this are proper) ||

|| || || || 8\29 || || || || 5 3 5 3 5 3 5 || 331.034 || 662.069 || 993.013 || 124.138 ||= ||

|| || || 5\18 || || || || || 3 2 3 2 3 2 3 || 333.333 || 666.667 || 1000.000 || 133.333 ||= ||

|| || || || 7\25 || || || || 4 3 4 3 4 3 4 || 336.000 || 672.000 || 1008.000 || 144.000 ||= ||

|| 2\7 || || || || || || || 1 1 1 1 1 1 1 || 342.857 || 685.714 || 1028.571 || 171.429 ||= ||</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>4L 3s</title></head><body>4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of <a class="wiki_link" href="/4edo">4edo</a>, 300¢) to 2\7edo (two degrees of <a class="wiki_link" href="/7edo">7edo</a>, or approx. 342.857¢). The spectrum looks like this:

There are two notable harmonic entropy minima: <a class="wiki_link" href="/Kleismic%20family">hanson/keemun</a>, in which the generator is 6/5 and 6 of them make a 3/1, and <a class="wiki_link" href="/Starling%20temperaments">myna</a>, in which the generator is also 6/5 but now 10 of them make a 6/1.

<tr>

<th colspan="7">Generator

</th>

<th>Scale

</th>

<th>g in cents

</th>

<th>2g

</th>

<th>3g

</th>

<th>4g

</th>

<th>Comments

</th>

</tr>

<tr>

<td>1\4

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1 0 1 0 1 0 1

</td>

<td>300.000

</td>

<td>600.000

</td>

<td>900.000

</td>

<td>0.000

</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>8\31

</td>

<td>7 1 7 1 7 1 7

</td>

<td>309.677

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">Myna is around here

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

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<td>

</td>

<td>~~scale~~

<td>7\27

</td>

<td>

</td>

<td>6 1 6 1 6 1 6

</td>

<td>311.111

</td>

<td>~~g in cents~~

<td>

</td>

<td>2g

<td>

</td>

<td>3g

<td>

</td>

<td>4g

</td>

</tr>

<tr>

<td>~~1\4~~

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>6\23

</td>

<td>

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<td>

</td>

<td>1 0 1 ~~0 1 0~~ 1

<td>5 1 5 1 5 1 5

</td>

<td>313.043

</td>

<td>~~300.000~~

<td>

</td>

<td>~~600.000~~

<td>

</td>

<td>~~900.000~~

<td>

</td>

<td>~~0.000~~

</td>

</tr>

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</td>

<td>5\19

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>4 1 4 1 4 1 4

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</td>

<td>63.158

</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>9\34

</td>

<td>

</td>

<td>

</td>

<td>7 2 7 2 7 2 7

</td>

<td>317.647

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">Hanson/Keemun is around here

</td>

</tr>

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</td>

<td>4\15

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>80.000

</td>

</td>

</tr>

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</td>

<td>7\26

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>5 2 5 2 5 2 5

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</td>

<td>92.308

</td>

</td>

</tr>

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</td>

<td>3\11

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>109.091

</td>

<td style="text-align: center;">Boundary of propriety (generators

larger than this are proper)

</td>

</tr>

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</td>

<td>8\29

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>5 3 5 3 5 3 5

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</td>

<td>124.138

</td>

</td>

</tr>

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</td>

<td>5\18

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>133.333

</td>

</td>

</tr>

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</td>

<td>7\25

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>4 3 4 3 4 3 4

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</td>

<td>144.000

</td>

</td>

</tr>

<tr>

<td>2\7

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>171.429

</td>

</td>

</tr>

</table>

~~ ~~

</body></html></pre></div>

~~The &quot;northernmost&quot; range, near 5\19, could be called the keemun range or region, representing <a class="wiki_link" href="/Kleismic%20family">keemun temperament</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:genewardsmith|genewardsmith]] and made on <tt>2011-03-10 23:08:51 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 05:17:40 UTC</tt>.<br>
-: The original revision id was <tt>209493438</tt>.<br>
+: The original revision id was <tt>222633992</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">4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). The spectrum looks like this:
-||   ||   ||   ||   || scale || g in cents || 2g || 3g || 4g ||
+There are two notable harmonic entropy minima: [[Kleismic family|hanson/keemun]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling temperaments|myna]], in which the generator is also 6/5 but now **10** of them make a 6/1.
-|| 1\4 ||   ||   ||   || 1 0 1 0 1 0 1 || 300.000 || 600.000 || 900.000 || 0.000 ||
+||||||||||||||~ Generator ||~ Scale ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||
-||   ||   ||   || 5\19 || 4 1 4 1 4 1 4 || 315.789 || 631.579 || 947.368 || 63.158 ||
+|| 1\4 ||   ||   ||   ||   ||   ||   || 1 0 1 0 1 0 1 || 300.000 || 600.000 || 900.000 || 0.000 ||=   ||
-||   ||   || 4\15 ||   || 3 1 3 1 3 1 3 || 320.000 || 640.000 || 960.000 || 80.000 ||
+||   ||   ||   ||   ||   ||   || 8\31 || 7 1 7 1 7 1 7 || 309.677 ||   ||   ||   ||= Myna is around here ||
-||   ||   ||   || 7\26 || 5 2 5 2 5 2 5 || 323.077 || 646.154 || 969.231 || 92.308 ||
+||   ||   ||   ||   ||   || 7\27 ||   || 6 1 6 1 6 1 6 || 311.111 ||   ||   ||   ||=   ||
-||   || 3\11 ||   ||   || 2 1 2 1 2 1 2 || 327.273 || 654.545 || 981.818 || 109.091 ||
+||   ||   ||   ||   || 6\23 ||   ||   || 5 1 5 1 5 1 5 || 313.043 ||   ||   ||   ||=   ||
-||   ||   ||   || 8\29 || 5 3 5 3 5 3 5 || 331.034 || 662.069 || 993.013 || 124.138 ||
+||   ||   ||   || 5\19 ||   ||   ||   || 4 1 4 1 4 1 4 || 315.789 || 631.579 || 947.368 || 63.158 ||=   ||
-||   ||   || 5\18 ||   || 3 2 3 2 3 2 3 || 333.333 || 666.667 || 1000.000 || 133.333 ||
+||   ||   ||   ||   || 9\34 ||   ||   || 7 2 7 2 7 2 7 || 317.647 ||   ||   ||   ||= Hanson/Keemun is around here ||
-||   ||   ||   || 7\25 || 4 3 4 3 4 3 4 || 336.000 || 672.000 || 1008.000 || 144.000 ||
+||   ||   || 4\15 ||   ||   ||   ||   || 3 1 3 1 3 1 3 || 320.000 || 640.000 || 960.000 || 80.000 ||=   ||
-|| 2\7 ||   ||   ||   || 1 1 1 1 1 1 1 || 342.857 || 685.714 || 1028.571 || 171.429 ||
+||   ||   ||   || 7\26 ||   ||   ||   || 5 2 5 2 5 2 5 || 323.077 || 646.154 || 969.231 || 92.308 ||=   ||
+||   || 3\11 ||   ||   ||   ||   ||   || 2 1 2 1 2 1 2 || 327.273 || 654.545 || 981.818 || 109.091 ||= Boundary of propriety (generators
-The "northernmost" range, near 5\19, could be called the keemun range or region, representing [[Kleismic family|keemun temperament]].</pre></div>
+larger than this are proper) ||
+||   ||   ||   || 8\29 ||   ||   ||   || 5 3 5 3 5 3 5 || 331.034 || 662.069 || 993.013 || 124.138 ||=   ||
+||   ||   || 5\18 ||   ||   ||   ||   || 3 2 3 2 3 2 3 || 333.333 || 666.667 || 1000.000 || 133.333 ||=   ||
+||   ||   ||   || 7\25 ||   ||   ||   || 4 3 4 3 4 3 4 || 336.000 || 672.000 || 1008.000 || 144.000 ||=   ||
+|| 2\7 ||   ||   ||   ||   ||   ||   || 1 1 1 1 1 1 1 || 342.857 || 685.714 || 1028.571 || 171.429 ||=   ||</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;4L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;, 300¢) to 2\7edo (two degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, or approx. 342.857¢). The spectrum looks like this:&lt;br /&gt;
 &lt;br /&gt;
+There are two notable harmonic entropy minima: &lt;a class="wiki_link" href="/Kleismic%20family"&gt;hanson/keemun&lt;/a&gt;, in which the generator is 6/5 and 6 of them make a 3/1, and &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;myna&lt;/a&gt;, in which the generator is also 6/5 but now &lt;strong&gt;10&lt;/strong&gt; of them make a 6/1.&lt;br /&gt;
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
+        &lt;th colspan="7"&gt;Generator&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Scale&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;g in cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;2g&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;3g&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;4g&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Comments&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\4&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;td&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;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1 0 1 0 1 0 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;300.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;600.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;900.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&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;td&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;td&gt;8\31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7 1 7 1 7 1 7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;309.677&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;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Myna is around here&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
@@ Line 35: / Line 114: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;scale&lt;br /&gt;
+         &lt;td&gt;7\27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6 1 6 1 6 1 6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;311.111&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;g in cents&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2g&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3g&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4g&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1\4&lt;br /&gt;
+         &lt;td&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;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6\23&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 55: / Line 146: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1 0 1 0 1 0 1&lt;br /&gt;
+         &lt;td&gt;5 1 5 1 5 1 5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;313.043&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;300.000&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600.000&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;900.000&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0.000&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 74: / Line 167: @@
 &lt;/td&gt;
          &lt;td&gt;5\19&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;td&gt;&lt;br /&gt;
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          &lt;td&gt;4 1 4 1 4 1 4&lt;br /&gt;
@@ Line 84: / Line 183: @@
 &lt;/td&gt;
          &lt;td&gt;63.158&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;9\34&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;td&gt;7 2 7 2 7 2 7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;317.647&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;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Hanson/Keemun is around here&lt;br /&gt;
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      &lt;/tr&gt;
@@ Line 92: / Line 221: @@
 &lt;/td&gt;
          &lt;td&gt;4\15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
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@@ Line 104: / Line 239: @@
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          &lt;td&gt;80.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 114: / Line 251: @@
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          &lt;td&gt;7\26&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;5 2 5 2 5 2 5&lt;br /&gt;
@@ Line 124: / Line 267: @@
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          &lt;td&gt;92.308&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 130: / Line 275: @@
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          &lt;td&gt;3\11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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@@ Line 144: / Line 295: @@
 &lt;/td&gt;
          &lt;td&gt;109.091&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
+larger than this are proper)&lt;br /&gt;
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      &lt;/tr&gt;
@@ Line 154: / Line 308: @@
 &lt;/td&gt;
          &lt;td&gt;8\29&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;5 3 5 3 5 3 5&lt;br /&gt;
@@ Line 164: / Line 324: @@
 &lt;/td&gt;
          &lt;td&gt;124.138&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 172: / Line 334: @@
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          &lt;td&gt;5\18&lt;br /&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
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@@ Line 184: / Line 352: @@
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          &lt;td&gt;133.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 194: / Line 364: @@
 &lt;/td&gt;
          &lt;td&gt;7\25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;4 3 4 3 4 3 4&lt;br /&gt;
@@ Line 204: / Line 380: @@
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          &lt;td&gt;144.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;2\7&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;td&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
@@ Line 224: / Line 408: @@
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          &lt;td&gt;171.429&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
-&lt;br /&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>
-The &amp;quot;northernmost&amp;quot; range, near 5\19, could be called the keemun range or region, representing &lt;a class="wiki_link" href="/Kleismic%20family"&gt;keemun temperament&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>