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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =Division of the tritave (3/1) into 27 equal parts= |
| 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:hstraub|hstraub]] and made on <tt>2013-08-13 06:53:28 UTC</tt>.<br>
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| : The original revision id was <tt>444570578</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">=[[#Division of the tritave (3/1) into 12 equal parts]]Division of the tritave (3/1) into 27 equal parts=
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| Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. | | Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 [[cent|cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo|17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime_number|prime number]]. |
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| 27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too. | | 27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too. |
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| See, e.g., [[http://launch.dir.groups.yahoo.com/group/tuning/message/86909]] and [[http://www.klingon.org/smboard/index.php?topic=1810.0]]. | | See, e.g., [http://launch.dir.groups.yahoo.com/group/tuning/message/86909 http://launch.dir.groups.yahoo.com/group/tuning/message/86909] and [http://www.klingon.org/smboard/index.php?topic=1810.0 http://www.klingon.org/smboard/index.php?topic=1810.0]. |
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| ==Intervals== | | ==Intervals== |
| ||~ degrees of 27edt ||~ cents value ||~ approximation in 17edo ||
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| || 0 || 0.00 || 0.00 ||
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| || 1 || 70.44 || 70.59 ||
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| || 2 || 140.89 || 141.18 ||
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| || 3 || 211.33 || 211.76 ||
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| || 4 || 281.77 || 282.35 ||
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| || 5 || 352.21 || 352.94 ||
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| || 6 || 422.66 || 423.53 ||
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| || 7 || 493.10 || 494.12 ||
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| || 8 || 563.54 || 564.71 ||
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| || 9 || 633.99 || 635.29 ||
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| || 10 || 704.43 || 705.88 ||
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| || 11 || 774.87 || 776.47 ||
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| || 12 || 845.31 || 847.06 ||
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| || 13 || 915.76 || 917.65 ||
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| || 14 || 986.20 || 988.24 ||
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| || 15 || 1056.64 || 1058.82 ||
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| || 16 || 1127.08 || 1129.41 ||
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| || 17 || 1197.53 || 1200.00 ||
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| || 18 || 1267.97 || 1270.59 ||
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| || 19 || 1338.41 || 1341.18 ||
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| || 20 || 1408.86 || 1411.76 ||
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| || 21 || 1479.30 || 1482.35 ||
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| || 22 || 1549.74 || 1551.94 ||
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| || 23 || 1620.18 || 1623.53 ||
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| || 24 || 1690.63 || 1694.12 ||
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| || 25 || 1761.07 || 1764.71 ||
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| || 26 || 1831.51 || 1835.29 ||
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| || 27 || 1901.96 || 1905.88 ||</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>27edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the tritave (3/1) into 27 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:4:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Division of the tritave (3/1) into 12 equal parts&quot; title=&quot;Anchor: Division of the tritave (3/1) into 12 equal parts&quot;/&gt; --><a name="Division of the tritave (3/1) into 12 equal parts"></a><!-- ws:end:WikiTextAnchorRule:4 -->Division of the tritave (3/1) into 27 equal parts</h1>
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| <br />
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| Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 <a class="wiki_link" href="/cent">cent</a>s, corresponding to 17.035 edo, which is nearly identical to one step of <a class="wiki_link" href="/17edo">17edo</a> (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a <a class="wiki_link" href="/prime%20number">prime number</a>.<br />
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| <br />
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| 27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.<br />
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| See, e.g., <a class="wiki_link_ext" href="http://launch.dir.groups.yahoo.com/group/tuning/message/86909" rel="nofollow">http://launch.dir.groups.yahoo.com/group/tuning/message/86909</a> and <a class="wiki_link_ext" href="http://www.klingon.org/smboard/index.php?topic=1810.0" rel="nofollow">http://www.klingon.org/smboard/index.php?topic=1810.0</a>.<br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Division of the tritave (3/1) into 27 equal parts-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
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| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>degrees of 27edt<br />
| | ! | degrees of 27edt |
| </th>
| | ! | cents value |
| <th>cents value<br />
| | ! | approximation in 17edo |
| </th>
| | |- |
| <th>approximation in 17edo<br />
| | | | 0 |
| </th>
| | | | 0.00 |
| </tr>
| | | | 0.00 |
| <tr>
| | |- |
| <td>0<br />
| | | | 1 |
| </td>
| | | | 70.44 |
| <td>0.00<br />
| | | | 70.59 |
| </td>
| | |- |
| <td>0.00<br />
| | | | 2 |
| </td>
| | | | 140.89 |
| </tr>
| | | | 141.18 |
| <tr>
| | |- |
| <td>1<br />
| | | | 3 |
| </td>
| | | | 211.33 |
| <td>70.44<br />
| | | | 211.76 |
| </td>
| | |- |
| <td>70.59<br />
| | | | 4 |
| </td>
| | | | 281.77 |
| </tr>
| | | | 282.35 |
| <tr>
| | |- |
| <td>2<br />
| | | | 5 |
| </td>
| | | | 352.21 |
| <td>140.89<br />
| | | | 352.94 |
| </td>
| | |- |
| <td>141.18<br />
| | | | 6 |
| </td>
| | | | 422.66 |
| </tr>
| | | | 423.53 |
| <tr>
| | |- |
| <td>3<br />
| | | | 7 |
| </td>
| | | | 493.10 |
| <td>211.33<br />
| | | | 494.12 |
| </td>
| | |- |
| <td>211.76<br />
| | | | 8 |
| </td>
| | | | 563.54 |
| </tr>
| | | | 564.71 |
| <tr>
| | |- |
| <td>4<br />
| | | | 9 |
| </td>
| | | | 633.99 |
| <td>281.77<br />
| | | | 635.29 |
| </td>
| | |- |
| <td>282.35<br />
| | | | 10 |
| </td>
| | | | 704.43 |
| </tr>
| | | | 705.88 |
| <tr>
| | |- |
| <td>5<br />
| | | | 11 |
| </td>
| | | | 774.87 |
| <td>352.21<br />
| | | | 776.47 |
| </td>
| | |- |
| <td>352.94<br />
| | | | 12 |
| </td>
| | | | 845.31 |
| </tr>
| | | | 847.06 |
| <tr>
| | |- |
| <td>6<br />
| | | | 13 |
| </td>
| | | | 915.76 |
| <td>422.66<br />
| | | | 917.65 |
| </td>
| | |- |
| <td>423.53<br />
| | | | 14 |
| </td>
| | | | 986.20 |
| </tr>
| | | | 988.24 |
| <tr>
| | |- |
| <td>7<br />
| | | | 15 |
| </td>
| | | | 1056.64 |
| <td>493.10<br />
| | | | 1058.82 |
| </td>
| | |- |
| <td>494.12<br />
| | | | 16 |
| </td>
| | | | 1127.08 |
| </tr>
| | | | 1129.41 |
| <tr>
| | |- |
| <td>8<br />
| | | | 17 |
| </td>
| | | | 1197.53 |
| <td>563.54<br />
| | | | 1200.00 |
| </td>
| | |- |
| <td>564.71<br />
| | | | 18 |
| </td>
| | | | 1267.97 |
| </tr>
| | | | 1270.59 |
| <tr>
| | |- |
| <td>9<br />
| | | | 19 |
| </td>
| | | | 1338.41 |
| <td>633.99<br />
| | | | 1341.18 |
| </td>
| | |- |
| <td>635.29<br />
| | | | 20 |
| </td>
| | | | 1408.86 |
| </tr>
| | | | 1411.76 |
| <tr>
| | |- |
| <td>10<br />
| | | | 21 |
| </td>
| | | | 1479.30 |
| <td>704.43<br />
| | | | 1482.35 |
| </td>
| | |- |
| <td>705.88<br />
| | | | 22 |
| </td>
| | | | 1549.74 |
| </tr>
| | | | 1551.94 |
| <tr>
| | |- |
| <td>11<br />
| | | | 23 |
| </td>
| | | | 1620.18 |
| <td>774.87<br />
| | | | 1623.53 |
| </td>
| | |- |
| <td>776.47<br />
| | | | 24 |
| </td>
| | | | 1690.63 |
| </tr>
| | | | 1694.12 |
| <tr>
| | |- |
| <td>12<br />
| | | | 25 |
| </td>
| | | | 1761.07 |
| <td>845.31<br />
| | | | 1764.71 |
| </td>
| | |- |
| <td>847.06<br />
| | | | 26 |
| </td>
| | | | 1831.51 |
| </tr>
| | | | 1835.29 |
| <tr>
| | |- |
| <td>13<br />
| | | | 27 |
| </td>
| | | | 1901.96 |
| <td>915.76<br />
| | | | 1905.88 |
| </td>
| | |} |
| <td>917.65<br />
| | [[Category:27edt]] |
| </td>
| | [[Category:edonoi]] |
| </tr>
| | [[Category:edt]] |
| <tr>
| | [[Category:equal]] |
| <td>14<br />
| | [[Category:nonoctave]] |
| </td>
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| <td>986.20<br />
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| </td>
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| <td>988.24<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>1056.64<br />
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| </td>
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| <td>1058.82<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>1127.08<br />
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| </td>
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| <td>1129.41<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>1197.53<br />
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| </td>
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| <td>1200.00<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>1267.97<br />
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| </td>
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| <td>1270.59<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>1338.41<br />
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| </td>
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| <td>1341.18<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>1408.86<br />
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| </td>
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| <td>1411.76<br />
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| </td>
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| </tr>
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| <tr>
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| <td>21<br />
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| </td>
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| <td>1479.30<br />
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| </td>
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| <td>1482.35<br />
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| </td>
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| </tr>
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| <tr>
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| <td>22<br />
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| </td>
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| <td>1549.74<br />
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| </td>
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| <td>1551.94<br />
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| </td>
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| </tr>
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| <tr>
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| <td>23<br />
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| </td>
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| <td>1620.18<br />
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| </td>
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| <td>1623.53<br />
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| </td>
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| </tr>
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| <tr>
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| <td>24<br />
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| </td>
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| <td>1690.63<br />
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| </td>
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| <td>1694.12<br />
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| </td>
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| </tr>
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| <tr>
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| <td>25<br />
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| </td>
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| <td>1761.07<br />
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| </td>
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| <td>1764.71<br />
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| </td>
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| </tr>
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| <tr>
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| <td>26<br />
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| </td>
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| <td>1831.51<br />
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| </td>
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| <td>1835.29<br />
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| </td>
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| </tr>
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| <tr>
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| <td>27<br />
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| </td>
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| <td>1901.96<br />
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| </td>
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| <td>1905.88<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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