Cluster MOS: 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:phylingual|phylingual]] and made on <tt>2012-05-12 18:44:35 UTC</tt>.

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-12 20:16:04 UTC</tt>.

: The original revision id was <tt>~~334237814~~</tt>.

: The original revision id was <tt>334261566</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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|| 6 || (22/13) || 7/4~16/9 || 9/5~11/6 || 40/21~15/8 ||

==~~Valentine~~==

==17-limit valentino==

Chroma: 49/48~55/54~56/55~64/63~128/125

Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150

|| Steps || "Minor" || "Major" ||

|| Steps || || "Diminished" || "Minor" || "Major" || "Augmented" || ||

|| 1 || 21/20~25/24 || 16/15 ||

|| 1 || || 36/35 || 21/20~25/24 || (17/16)~16/15 || 13/12 || ||

|| 2 || 12/11 || 10/9 ||

|| 2 || || 14/13 || 12/11~11/10 || 10/9 || 17/15 || 20/17 ||

|| 3 || 8/7 || 7/6 ||

|| 3 || || 9/8 || 8/7 || 7/6 || 32/27 || ||

|| 4 || 6/5 || 11/9 ||

|| 4 || || 13/11 || 6/5 || 11/9~17/14 || || ||

|| 5 || 5/4 || 14/11 ||

|| 5 || || 16/13~21/17 || 5/4 || 14/11 || 13/10 || 27/20 ||

|| 6 || 21/16 || 4/3 ||

|| 6 || || 9/7 || 21/16~17/13 || 4/3 || 34/25 || ||

|| 7 || 11/8 || 7/5 ||

|| 7 || || 27/20 || 11/8~15/11 || 7/5 || 17/12 || ||

|| 8 || 10/7 || 16/11 ||

|| 8 || || 24/17 || 10/7 || 16/11~22/15 || || ||

|| 9 || 3/2 || 32/21 ||

|| 9 || || 25/17 || 3/2 || 26/17~32/21 || 14/9 || ||

|| 10 || 11/7 || 8/5 ||

|| 10 || 40/27 || 20/13 || 11/7 || 8/5 || 13/8~34/21 || ||

|| 11 || 18/11 || 5/3 ||

|| 11 || || || 18/11~28/17 || 5/3 || 22/13 || ||

|| 12 || 12/7 || 7/4 ||

|| 12 || || 27/16 || 12/7 || 7/4 || 16/9 || ||

|| 13 || 9/5 || 11/6 ||

|| 13 || 17/10 || 30/14 || 9/5 || 11/6~20/11 || 13/7 || ||

|| 14 || 15/8 || 40/21~48/25 ||</pre></div>

|| 14 || || 24/13 || 15/8 || 40/21~48/25 || 35/18 || ||</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>Cluster temperament</title></head><body>A cluster temperament (named by <a class="wiki_link" href="/Keenan%20Pepper">Keenan Pepper</a>) is a very particular kind of rank-2 temperament whose generator is quite near a rational fraction of an octave. Therefore some MOS of the temperament is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma (&quot;diminished&quot;, &quot;minor&quot;, &quot;major&quot;, &quot;augmented&quot;...) include many nearby JI intervals that are individually recognizable, yet conceptually grouped into the same category (or &quot;cluster&quot;) because they're so close.

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<h2 id="toc7"><a name="Examples-~~Valentine~~"></a>~~Valentine~~</h2>

<h2 id="toc7"><a name="Examples-17-limit valentino"></a>17-limit valentino</h2>

Chroma: 49/48~55/54~56/55~64/63~128/125

Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150

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<tr>

<td>Steps

</td>

<td>

</td>

<td>&quot;Diminished&quot;

</td>

<td>&quot;Minor&quot;

</td>

<td>&quot;Major&quot;

</td>

<td>&quot;Augmented&quot;

</td>

<td>

</td>

</tr>

<tr>

<td>1

</td>

<td>

</td>

<td>36/35

</td>

<td>21/20~25/24

</td>

<td>16/15

<td>(17/16)~16/15

</td>

<td>13/12

</td>

<td>

</td>

</tr>

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<td>2

</td>

<td>12/11

<td>

</td>

<td>14/13

</td>

<td>12/11~11/10

</td>

<td>10/9

</td>

<td>17/15

</td>

<td>20/17

</td>

</tr>

<tr>

<td>3

</td>

<td>

</td>

<td>9/8

</td>

<td>8/7

</td>

<td>7/6

</td>

<td>32/27

</td>

<td>

</td>

</tr>

<tr>

<td>4

</td>

<td>

</td>

<td>13/11

</td>

<td>6/5

</td>

<td>11/9

<td>11/9~17/14

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>5

</td>

<td>

</td>

<td>16/13~21/17

</td>

<td>5/4

</td>

<td>14/11

</td>

<td>13/10

</td>

<td>27/20

</td>

</tr>

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<td>6

</td>

<td>21/16

<td>

</td>

<td>9/7

</td>

<td>21/16~17/13

</td>

<td>4/3

</td>

<td>34/25

</td>

<td>

</td>

</tr>

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<td>7

</td>

<td>11/8

<td>

</td>

<td>27/20

</td>

<td>11/8~15/11

</td>

<td>7/5

</td>

<td>17/12

</td>

<td>

</td>

</tr>

<tr>

<td>8

</td>

<td>

</td>

<td>24/17

</td>

<td>10/7

</td>

<td>16/11

<td>16/11~22/15

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>9

</td>

<td>

</td>

<td>25/17

</td>

<td>3/2

</td>

<td>32/21

<td>26/17~32/21

</td>

<td>14/9

</td>

<td>

</td>

</tr>

<tr>

<td>10

</td>

<td>40/27

</td>

<td>20/13

</td>

<td>11/7

</td>

<td>8/5

</td>

<td>13/8~34/21

</td>

<td>

</td>

</tr>

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<td>11

</td>

<td>18/11

<td>

</td>

<td>

</td>

<td>18/11~28/17

</td>

<td>5/3

</td>

<td>22/13

</td>

<td>

</td>

</tr>

<tr>

<td>12

</td>

<td>

</td>

<td>27/16

</td>

<td>12/7

</td>

<td>7/4

</td>

<td>16/9

</td>

<td>

</td>

</tr>

<tr>

<td>13

</td>

<td>17/10

</td>

<td>30/14

</td>

<td>9/5

</td>

<td>11/6

<td>11/6~20/11

</td>

<td>13/7

</td>

<td>

</td>

</tr>

<tr>

<td>14

</td>

<td>

</td>

<td>24/13

</td>

<td>15/8

</td>

<td>40/21~48/25

</td>

<td>35/18

</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:phylingual|phylingual]] and made on <tt>2012-05-12 18:44:35 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-12 20:16:04 UTC</tt>.<br>
-: The original revision id was <tt>334237814</tt>.<br>
+: The original revision id was <tt>334261566</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 74: / Line 74: @@
 || 6 || (22/13) || 7/4~16/9 || 9/5~11/6 || 40/21~15/8 ||
-==Valentine==
+==17-limit valentino==
-Chroma: 49/48~55/54~56/55~64/63~128/125
+Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150
-|| Steps || "Minor" || "Major" ||
+|| Steps ||   || "Diminished" || "Minor" || "Major" || "Augmented" ||   ||
-|| 1 || 21/20~25/24 || 16/15 ||
+|| 1 ||   || 36/35 || 21/20~25/24 || (17/16)~16/15 || 13/12 ||   ||
-|| 2 || 12/11 || 10/9 ||
+|| 2 ||   || 14/13 || 12/11~11/10 || 10/9 || 17/15 || 20/17 ||
-|| 3 || 8/7 || 7/6 ||
+|| 3 ||   || 9/8 || 8/7 || 7/6 || 32/27 ||   ||
-|| 4 || 6/5 || 11/9 ||
+|| 4 ||   || 13/11 || 6/5 || 11/9~17/14 ||   ||   ||
-|| 5 || 5/4 || 14/11 ||
+|| 5 ||   || 16/13~21/17 || 5/4 || 14/11 || 13/10 || 27/20 ||
-|| 6 || 21/16 || 4/3 ||
+|| 6 ||   || 9/7 || 21/16~17/13 || 4/3 || 34/25 ||   ||
-|| 7 || 11/8 || 7/5 ||
+|| 7 ||   || 27/20 || 11/8~15/11 || 7/5 || 17/12 ||   ||
-|| 8 || 10/7 || 16/11 ||
+|| 8 ||   || 24/17 || 10/7 || 16/11~22/15 ||   ||   ||
-|| 9 || 3/2 || 32/21 ||
+|| 9 ||   || 25/17 || 3/2 || 26/17~32/21 || 14/9 ||   ||
-|| 10 || 11/7 || 8/5 ||
+|| 10 || 40/27 || 20/13 || 11/7 || 8/5 || 13/8~34/21 ||   ||
-|| 11 || 18/11 || 5/3 ||
+|| 11 ||   ||   || 18/11~28/17 || 5/3 || 22/13 ||   ||
-|| 12 || 12/7 || 7/4 ||
+|| 12 ||   || 27/16 || 12/7 || 7/4 || 16/9 ||   ||
-|| 13 || 9/5 || 11/6 ||
+|| 13 || 17/10 || 30/14 || 9/5 || 11/6~20/11 || 13/7 ||   ||
-|| 14 || 15/8 || 40/21~48/25 ||</pre></div>
+|| 14 ||   || 24/13 || 15/8 || 40/21~48/25 || 35/18 ||   ||</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;Cluster temperament&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A cluster temperament (named by &lt;a class="wiki_link" href="/Keenan%20Pepper"&gt;Keenan Pepper&lt;/a&gt;) is a very particular kind of rank-2 temperament whose generator is quite near a rational fraction of an octave. Therefore some MOS of the temperament is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma (&amp;quot;diminished&amp;quot;, &amp;quot;minor&amp;quot;, &amp;quot;major&amp;quot;, &amp;quot;augmented&amp;quot;...) include many nearby JI intervals that are individually recognizable, yet conceptually grouped into the same category (or &amp;quot;cluster&amp;quot;) because they're so close.&lt;br /&gt;
@@ Line 719: / Line 719: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Examples-Valentine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Valentine&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Examples-17-limit valentino"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;17-limit valentino&lt;/h2&gt;
-  Chroma: 49/48~55/54~56/55~64/63~128/125&lt;br /&gt;
+  Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150&lt;br /&gt;
@@ Line 726: / Line 726: @@
      &lt;tr&gt;
          &lt;td&gt;Steps&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&amp;quot;Diminished&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&amp;quot;Minor&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&amp;quot;Major&amp;quot;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&amp;quot;Augmented&amp;quot;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;36/35&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;21/20~25/24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/15&lt;br /&gt;
+         &lt;td&gt;(17/16)~16/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 743: / Line 759: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12/11&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/13&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;12/11~11/10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20/17&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;32/27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;6/5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/9&lt;br /&gt;
+         &lt;td&gt;11/9~17/14&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&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/13~21/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;14/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27/20&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 775: / Line 823: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21/16&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/7&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;21/16~17/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;4/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;34/25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 783: / Line 839: @@
          &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/8&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27/20&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;11/8~15/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;24/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/11&lt;br /&gt;
+         &lt;td&gt;16/11~22/15&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&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;32/21&lt;br /&gt;
+         &lt;td&gt;26/17~32/21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;40/27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;11/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/8~34/21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 815: / Line 903: @@
          &lt;td&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;18/11&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;18/11~28/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27/16&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;12/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;30/14&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/6&lt;br /&gt;
+         &lt;td&gt;11/6~20/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;24/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;40/21~48/25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35/18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;