7/4: 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:<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-05-~~26 02~~:57:04 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-05-31 17:24:11 UTC</tt>.<br>

: The original revision id was <tt>~~231979670~~</tt>.<br>

: The original revision id was <tt>233284800</tt>.<br>

: The revision comment was: <tt>~~sorry, I failed the right position ;~~)</tt><br>

: The revision comment was: <tt>re-ordered after relative delta (in relative cents)</tt><br>

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

<h4>Original Wikitext content:</h4>

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=Approximations=

Edos containing good approximations of the interval 7:4 are:

* [EDO; Delta; Multiples]

* [[~~11edo~~]]~~, 12~~.~~9923 ct,~~ [[~~22edo~~]]

||~ [[EDO]] ||~ abs Delta ||~ rel Delta ||~ Prominent Multiples ||

* [[~~5edo~~]]~~, -8.8259 ct,~~ [[~~10edo~~]], [[~~15edo~~]], [[~~20edo~~]], [[~~25edo~~]]

|| [[26edo]] || 0.40486 [[cent|ct]] || 0.87720 [[relative cent|rct]] || [[78edo]] ||

* [[~~16edo~~]]~~, 6~~.~~1741~~ ct

|| [[83edo]] || 0.15121 ct || 1.0459 rct || [[166edo]] ||

* [[~~69edo~~]]~~, 5~~.~~0871~~ ct

|| [[57edo]] || 0.40485 ct || 1.9231 rct || ||

* [[~~21edo~~]], ~~2.6026 ct~~

|| [[31edo]] || 1.0839 ct || 2.8003 rct || ||

* [[~~36edo~~]], ~~-2.1592 ct~~, [[~~72edo~~]]

|| [[5edo]] || 8.8259 ct || 3.6775 rct || [[10edo]], [[15edo]], [[20edo]], [[25edo]] ||

* [[~~89edo~~]]~~, 1~~.~~9606~~ ct

|| [[21edo]] || 2.6026 ct || 4.5547 rct || ||

* [[47edo]], 1.3868 ct, [[94edo]]

|| [[88edo]] || 0.6441 ct || 4.7233 rct || ||

* [[~~31edo~~]], 1.~~0839~~ ct

|| [[47edo]] || 1.3868 ct || 5.4319 rct || [[94edo]] ||

* [[~~73edo~~]]~~, 1~~.~~0371~~ ct

|| [[73edo]] || 1.0371 ct || 6.3091 rct || ||

* [[~~88edo~~]]~~, -0~~.~~6441~~ ct

|| [[36edo]] || 2.1592 ct || 6.4777 rct || [[72edo]] ||

* [[~~26edo~~]]~~, 0~~.~~40486~~ ct, [[~~78edo~~]]

|| [[16edo]] || 6.1741 ct || 8.2321 rct || ||

* [[~~57edo~~]]~~, -0~~.~~40485~~ ct

|| [[11edo]] || 12.992 ct || 11.910 rct || [[22edo]] ||

* [[~~83edo~~]]~~, -0~~.~~1512~~ ct~~, [[166edo]]~~</pre></div>

|| [[89edo]] || 1.9606 ct || 14.541 rct || ||

|| [[69edo]] || 5.0871 ct || 29.251 rct || ||

</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>7_4</title></head><body>Frequency ratio 7:4, measuring approximately 968.8259064691249 cents, has been given the name &quot;harmonic seventh.&quot; It represents the interval between the 4th and 7th harmonics in the <a class="wiki_link" href="/OverToneSeries">overtone series</a>. It is also called a &quot;septimal subminor seventh&quot; -- the word &quot;septimal&quot; referring to the presence of a 7 as the highest prime in the ratio, and the word &quot;subminor&quot; referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as <a class="wiki_link" href="/9_5">9:5</a> or <a class="wiki_link" href="/16_9">16:9</a>, <a class="wiki_link" href="/12edo">12edo</a>'s 1000-cent interval, or a minor seventh found in a meantone system).<br />

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<h1 id="toc2"><a name="Approximations"></a>Approximations</h1>

Edos containing good approximations of the interval 7:4 are:<br />

<ul><li>[EDO; Delta; Multiples]</li><li><a class="wiki_link" href="/~~11edo~~">~~11edo~~</a>~~, 12~~.~~9923 ct,~~ <a class="wiki_link" href="/~~22edo~~">~~22edo~~</a></li><li><a class="wiki_link" href="/~~5edo~~">~~5edo~~</a>~~, -8.8259 ct,~~ <a class="wiki_link" href="/~~10edo~~">~~10edo~~</a>, <a class="wiki_link" href="/~~15edo~~">~~15edo~~</a>, <a class="wiki_link" href="/~~20edo~~">~~20edo~~</a>, <a class="wiki_link" href="/~~25edo~~">~~25edo~~</a></li><li><a class="wiki_link" href="/~~16edo~~">~~16edo~~</a>~~, 6~~.~~1741~~ ct</li><li><a class="wiki_link" href="/~~69edo~~">~~69edo~~</a>~~, 5~~.~~0871~~ ct</li><li><a class="wiki_link" href="/~~21edo~~">~~21edo~~</a>, ~~2.6026 ct~~</li><li><a class="wiki_link" href="/~~36edo~~">~~36edo~~</a>, ~~-2.1592 ct,~~ <a class="wiki_link" href="/~~72edo~~">~~72edo~~</a></li><li><a class="wiki_link" href="/~~89edo~~">~~89edo~~</a>~~, 1~~.~~9606~~ ct</li><li><a class="wiki_link" href="/47edo">47edo</a>, 1.3868 ct, <a class="wiki_link" href="/94edo">94edo</a></li><li><a class="wiki_link" href="/~~31edo~~">~~31edo~~</a>, 1.~~0839~~ ct</li><li><a class="wiki_link" href="/~~73edo~~">~~73edo~~</a>~~, 1~~.~~0371~~ ct</li><li><a class="wiki_link" href="/~~88edo~~">~~88edo~~</a>~~, -0.6441 ct~~</li><li><a class="wiki_link" href="/~~26edo~~">~~26edo~~</a>~~, 0~~.~~40486~~ ct, <a class="wiki_link" href="/~~78edo~~">~~78edo~~</a></li><li><a class="wiki_link" href="/~~57edo~~">~~57edo~~</a>~~, -0.40485 ct~~</li><li><a class="wiki_link" href="/~~83edo~~">~~83edo~~</a>~~, -0~~.~~1512~~ ct, <a class="wiki_link" href="/~~166edo~~">~~166edo~~</a></li></ul></body></html></pre></div>

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<tr>

</th>

<th>abs Delta<br />

</th>

<th>rel Delta<br />

</th>

<th>Prominent Multiples<br />

</th>

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</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:xenwolf|xenwolf]] and made on <tt>2011-05-26 02:57:04 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-05-31 17:24:11 UTC</tt>.<br>
-: The original revision id was <tt>231979670</tt>.<br>
+: The original revision id was <tt>233284800</tt>.<br>
-: The revision comment was: <tt>sorry, I failed the right position ;)</tt><br>
+: The revision comment was: <tt>re-ordered after relative delta (in relative cents)</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 38: / Line 38: @@
 =Approximations=
 Edos containing good approximations of the interval 7:4 are:
-* [EDO; Delta; Multiples]
-* [[11edo]], 12.9923 ct, [[22edo]]
+||~ [[EDO]] ||~ abs Delta ||~ rel Delta ||~ Prominent Multiples ||
-* [[5edo]], -8.8259 ct, [[10edo]], [[15edo]], [[20edo]], [[25edo]]
+|| [[26edo]] || 0.40486 [[cent|ct]] || 0.87720 [[relative cent|rct]] || [[78edo]] ||
-* [[16edo]], 6.1741 ct
+|| [[83edo]] || 0.15121 ct || 1.0459 rct || [[166edo]] ||
-* [[69edo]], 5.0871 ct
+|| [[57edo]] || 0.40485 ct || 1.9231 rct || ||
-* [[21edo]], 2.6026 ct
+|| [[31edo]] ||  1.0839 ct || 2.8003 rct || ||
-* [[36edo]], -2.1592 ct, [[72edo]]
+|| [[5edo]]  ||  8.8259 ct || 3.6775 rct || [[10edo]], [[15edo]], [[20edo]], [[25edo]] ||
-* [[89edo]], 1.9606 ct
+|| [[21edo]] ||  2.6026 ct || 4.5547 rct || ||
-* [[47edo]], 1.3868 ct, [[94edo]]
+|| [[88edo]] ||  0.6441 ct || 4.7233 rct || ||
-* [[31edo]], 1.0839 ct
+|| [[47edo]] ||  1.3868 ct || 5.4319 rct || [[94edo]] ||
-* [[73edo]], 1.0371 ct
+|| [[73edo]] ||  1.0371 ct || 6.3091 rct || ||
-* [[88edo]], -0.6441 ct
+|| [[36edo]] ||  2.1592 ct || 6.4777 rct || [[72edo]] ||
-* [[26edo]], 0.40486 ct, [[78edo]]
+|| [[16edo]] ||  6.1741 ct || 8.2321 rct || ||
-* [[57edo]], -0.40485 ct
+|| [[11edo]] ||  12.992 ct || 11.910 rct || [[22edo]] ||
-* [[83edo]], -0.1512 ct, [[166edo]]</pre></div>
+|| [[89edo]] ||  1.9606 ct || 14.541 rct || ||
+|| [[69edo]] ||  5.0871 ct || 29.251 rct || ||
+</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;7_4&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Frequency ratio 7:4, measuring approximately 968.8259064691249 cents, has been given the name &amp;quot;harmonic seventh.&amp;quot; It represents the interval between the 4th and 7th harmonics in the &lt;a class="wiki_link" href="/OverToneSeries"&gt;overtone series&lt;/a&gt;. It is also called a &amp;quot;septimal subminor seventh&amp;quot; -- the word &amp;quot;septimal&amp;quot; referring to the presence of a 7 as the highest prime in the ratio, and the word &amp;quot;subminor&amp;quot; referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as &lt;a class="wiki_link" href="/9_5"&gt;9:5&lt;/a&gt; or &lt;a class="wiki_link" href="/16_9"&gt;16:9&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s 1000-cent interval, or a minor seventh found in a meantone system).&lt;br /&gt;
@@ Line 86: / Line 88: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Approximations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Approximations&lt;/h1&gt;
   Edos containing good approximations of the interval 7:4 are:&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;[EDO; Delta; Multiples]&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;, 12.9923 ct, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, -8.8259 ct, &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;, 6.1741 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/69edo"&gt;69edo&lt;/a&gt;, 5.0871 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt;, 2.6026 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, -2.1592 ct, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/89edo"&gt;89edo&lt;/a&gt;, 1.9606 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/47edo"&gt;47edo&lt;/a&gt;, 1.3868 ct, &lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, 1.0839 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/73edo"&gt;73edo&lt;/a&gt;, 1.0371 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt;, -0.6441 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;, 0.40486 ct, &lt;a class="wiki_link" href="/78edo"&gt;78edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/57edo"&gt;57edo&lt;/a&gt;, -0.40485 ct&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/83edo"&gt;83edo&lt;/a&gt;, -0.1512 ct, &lt;a class="wiki_link" href="/166edo"&gt;166edo&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;abs Delta&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;rel Delta&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Prominent Multiples&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.40486 &lt;a class="wiki_link" href="/cent"&gt;ct&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.87720 &lt;a class="wiki_link" href="/relative%20cent"&gt;rct&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/78edo"&gt;78edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/83edo"&gt;83edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.15121 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.0459 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/166edo"&gt;166edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/57edo"&gt;57edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.40485 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.9231 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.0839 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.8003 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.8259 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.6775 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.6026 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.5547 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.6441 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.7233 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/47edo"&gt;47edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.3868 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.4319 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/73edo"&gt;73edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.0371 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.3091 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.1592 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.4777 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.1741 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.2321 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12.992 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11.910 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/89edo"&gt;89edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.9606 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.541 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;a class="wiki_link" href="/69edo"&gt;69edo&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.0871 ct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29.251 rct&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>