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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A scale is called '''chiral''' if reversing the order of the steps results in a different scale. The two scales form a '''chiral pair''' and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-06-10 20:32:55 UTC</tt>.<br>
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| : The original revision id was <tt>553639502</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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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">A scale is called **chiral** if reversing the order of the steps results in a different scale. The two scales form a **chiral pair** and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.
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| Scales for which this property does not hold are called **achiral**. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation. | | Scales for which this property does not hold are called '''achiral'''. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation. |
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| ==Properties:== | | ==Properties:== |
| # Chiral scales can only exist in EDO's larger than 5-EDO
| | <ol><li>Chiral scales can only exist in EDO's larger than 5-EDO</li><li>Chiral scales are at least max-variety 3 (they cannot be MOS or DE)</li><li>Chiral scales have at least 3 notes</li><li>Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)</li></ol> |
| # Chiral scales are at least max-variety 3 (they cannot be MOS or DE)
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| # Chiral scales have at least 3 notes
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| # Chiral scales have a [[http://en.wikipedia.org/wiki/Natural_density|density]] of 1 (see table below)
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| || **EDO** || **Number of** | | {| class="wikitable" |
| **Chiral Scales** || **Percentage of**
| | |- |
| **Chiral Scales** || **Corresponding Ratio** ||
| | | | '''EDO''' |
| || 1 || 0 || 0.0% || 0/1 || | | | | '''Number of''' |
| || 2 || 0 || 0.0% || 0/1 ||
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| || 3 || 0 || 0.0% || 0/1 ||
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| || 4 || 0 || 0.0% || 0/1 ||
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| || 5 || 0 || 0.0% || 0/1 ||
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| || 6 || 2 || 22.2% || 2/9 ||
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| || 7 || 4 || 22.2% || 2/9 ||
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| || 8 || 12 || 40.0% || 2/5 ||
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| || 9 || 28 || 50.0% || 1/2 ||
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| || 10 || 60 || 60.6% || 20/33 ||
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| || 11 || 124 || 66.7% || 2/3 ||
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| || 12 || 254 || 75.8% || 254/335 ||
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| || 13 || 504 || 80.0% || 4/5 ||
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| || 14 || 986 || 84.9% || 986/1161 ||
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| || 15 || 1936 || 88.7% || 968/1091 ||
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| || 16 || 3720 || 91.2% || 31/34 ||
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| || 17 || 7200 || 93.4% || 240/257 ||
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| || 18 || 13804 || 95.0% || 493/519 ||
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| || 19 || 26572 || 96.3% || 26/27 ||
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| || 20 || 50892 || 97.2% || 16964/17459 ||</pre></div>
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| <h4>Original HTML content:</h4>
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Chirality</title></head><body>A scale is called <strong>chiral</strong> if reversing the order of the steps results in a different scale. The two scales form a <strong>chiral pair</strong> and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.<br />
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| <br />
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| Scales for which this property does not hold are called <strong>achiral</strong>. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Properties:"></a><!-- ws:end:WikiTextHeadingRule:0 -->Properties:</h2>
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| <ol><li>Chiral scales can only exist in EDO's larger than 5-EDO</li><li>Chiral scales are at least max-variety 3 (they cannot be MOS or DE)</li><li>Chiral scales have at least 3 notes</li><li>Chiral scales have a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Natural_density" rel="nofollow">density</a> of 1 (see table below)</li></ol><br />
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| | '''Chiral Scales''' |
| | | | '''Percentage of''' |
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| <table class="wiki_table">
| | '''Chiral Scales''' |
| <tr>
| | | | '''Corresponding Ratio''' |
| <td><strong>EDO</strong><br />
| | |- |
| </td>
| | | | 1 |
| <td><strong>Number of</strong><br />
| | | | 0 |
| <strong>Chiral Scales</strong><br />
| | | | 0.0% |
| </td>
| | | | 0/1 |
| <td><strong>Percentage of</strong><br />
| | |- |
| <strong>Chiral Scales</strong><br />
| | | | 2 |
| </td>
| | | | 0 |
| <td><strong>Corresponding Ratio</strong><br />
| | | | 0.0% |
| </td>
| | | | 0/1 |
| </tr>
| | |- |
| <tr>
| | | | 3 |
| <td>1<br />
| | | | 0 |
| </td>
| | | | 0.0% |
| <td>0<br />
| | | | 0/1 |
| </td>
| | |- |
| <td>0.0%<br />
| | | | 4 |
| </td>
| | | | 0 |
| <td>0/1<br />
| | | | 0.0% |
| </td>
| | | | 0/1 |
| </tr>
| | |- |
| <tr>
| | | | 5 |
| <td>2<br />
| | | | 0 |
| </td>
| | | | 0.0% |
| <td>0<br />
| | | | 0/1 |
| </td>
| | |- |
| <td>0.0%<br />
| | | | 6 |
| </td>
| | | | 2 |
| <td>0/1<br />
| | | | 22.2% |
| </td>
| | | | 2/9 |
| </tr>
| | |- |
| <tr>
| | | | 7 |
| <td>3<br />
| | | | 4 |
| </td>
| | | | 22.2% |
| <td>0<br />
| | | | 2/9 |
| </td>
| | |- |
| <td>0.0%<br />
| | | | 8 |
| </td>
| | | | 12 |
| <td>0/1<br />
| | | | 40.0% |
| </td>
| | | | 2/5 |
| </tr>
| | |- |
| <tr>
| | | | 9 |
| <td>4<br />
| | | | 28 |
| </td>
| | | | 50.0% |
| <td>0<br />
| | | | 1/2 |
| </td>
| | |- |
| <td>0.0%<br />
| | | | 10 |
| </td>
| | | | 60 |
| <td>0/1<br />
| | | | 60.6% |
| </td>
| | | | 20/33 |
| </tr>
| | |- |
| <tr>
| | | | 11 |
| <td>5<br />
| | | | 124 |
| </td>
| | | | 66.7% |
| <td>0<br />
| | | | 2/3 |
| </td>
| | |- |
| <td>0.0%<br />
| | | | 12 |
| </td>
| | | | 254 |
| <td>0/1<br />
| | | | 75.8% |
| </td>
| | | | 254/335 |
| </tr>
| | |- |
| <tr>
| | | | 13 |
| <td>6<br />
| | | | 504 |
| </td>
| | | | 80.0% |
| <td>2<br />
| | | | 4/5 |
| </td>
| | |- |
| <td>22.2%<br />
| | | | 14 |
| </td>
| | | | 986 |
| <td>2/9<br />
| | | | 84.9% |
| </td>
| | | | 986/1161 |
| </tr>
| | |- |
| <tr>
| | | | 15 |
| <td>7<br />
| | | | 1936 |
| </td>
| | | | 88.7% |
| <td>4<br />
| | | | 968/1091 |
| </td>
| | |- |
| <td>22.2%<br />
| | | | 16 |
| </td>
| | | | 3720 |
| <td>2/9<br />
| | | | 91.2% |
| </td>
| | | | 31/34 |
| </tr>
| | |- |
| <tr>
| | | | 17 |
| <td>8<br />
| | | | 7200 |
| </td>
| | | | 93.4% |
| <td>12<br />
| | | | 240/257 |
| </td>
| | |- |
| <td>40.0%<br />
| | | | 18 |
| </td>
| | | | 13804 |
| <td>2/5<br />
| | | | 95.0% |
| </td>
| | | | 493/519 |
| </tr>
| | |- |
| <tr>
| | | | 19 |
| <td>9<br />
| | | | 26572 |
| </td>
| | | | 96.3% |
| <td>28<br />
| | | | 26/27 |
| </td>
| | |- |
| <td>50.0%<br />
| | | | 20 |
| </td>
| | | | 50892 |
| <td>1/2<br />
| | | | 97.2% |
| </td>
| | | | 16964/17459 |
| </tr>
| | |} |
| <tr>
| | [[Category:edo]] |
| <td>10<br />
| | [[Category:scales]] |
| </td>
| | [[Category:term]] |
| <td>60<br />
| | [[Category:theory]] |
| </td>
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| <td>60.6%<br />
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| </td>
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| <td>20/33<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11<br />
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| </td>
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| <td>124<br />
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| </td>
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| <td>66.7%<br />
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| </td>
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| <td>2/3<br />
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| </td>
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| </tr>
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| <tr>
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| <td>12<br />
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| </td>
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| <td>254<br />
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| </td>
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| <td>75.8%<br />
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| </td>
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| <td>254/335<br />
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| </td>
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| </tr>
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| <tr>
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| <td>13<br />
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| </td>
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| <td>504<br />
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| </td>
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| <td>80.0%<br />
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| </td>
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| <td>4/5<br />
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| </td>
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| </tr>
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| <tr>
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| <td>14<br />
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| </td>
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| <td>986<br />
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| </td>
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| <td>84.9%<br />
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| </td>
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| <td>986/1161<br />
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| </td>
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| </tr>
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| <tr>
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| <td>15<br />
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| </td>
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| <td>1936<br />
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| </td>
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| <td>88.7%<br />
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| </td>
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| <td>968/1091<br />
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| </td>
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| </tr>
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| <tr>
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| <td>16<br />
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| </td>
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| <td>3720<br />
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| </td>
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| <td>91.2%<br />
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| </td>
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| <td>31/34<br />
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| </td>
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| </tr>
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| <tr>
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| <td>17<br />
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| </td>
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| <td>7200<br />
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| </td>
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| <td>93.4%<br />
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| </td>
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| <td>240/257<br />
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| </td>
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| </tr>
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| <tr>
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| <td>18<br />
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| </td>
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| <td>13804<br />
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| </td>
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| <td>95.0%<br />
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| </td>
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| <td>493/519<br />
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| </td>
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| </tr>
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| <tr>
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| <td>19<br />
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| </td>
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| <td>26572<br />
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| </td>
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| <td>96.3%<br />
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| </td>
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| <td>26/27<br />
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| </td>
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| </tr>
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| <tr>
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| <td>20<br />
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| </td>
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| <td>50892<br />
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| </td>
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| <td>97.2%<br />
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| </td>
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| <td>16964/17459<br />
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| </td>
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| </tr>
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| </table>
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| </body></html></pre></div>
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