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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The ''80 equal temperament'', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent|cent]]s. 80et is the first equal temperament that represents the [[19-limit|19-limit]] [[Tonality_diamond|tonality diamond]] [[consistent|consistent]]ly (it barely manages to do so). |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:guest|guest]] and made on <tt>2012-08-30 19:51:04 UTC</tt>.<br>
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| : The original revision id was <tt>361115194</tt>.<br>
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| : The revision comment was: <tt>scala says otherwise</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">The //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[xenharmonic/cent|cent]]s. 80et is the first equal temperament that represents the [[xenharmonic/19-limit|19-limit]] [[xenharmonic/tonality diamond|tonality diamond]] [[xenharmonic/consistent|consistent]]ly (it barely manages to do so).
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| 80 et [[xenharmonic/tempering out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125. | | 80 et [[tempering_out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125. |
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| 80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention: | | 80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention: |
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| 31&80 <<7 6 15 27 -24 -23 -20 ... || | | 31&80 <<7 6 15 27 -24 -23 -20 ... || |
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| 72&80 <<24 30 40 24 32 24 0 ... || | | 72&80 <<24 30 40 24 32 24 0 ... || |
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| 34&80 <<2 -4 -50 22 16 2 -40 ... || | | 34&80 <<2 -4 -50 22 16 2 -40 ... || |
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| 46&80 <<2 -4 30 22 16 2 40 ... || | | 46&80 <<2 -4 30 22 16 2 40 ... || |
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| 29&80 <<3 34 45 33 24 -37 20 ... || | | 29&80 <<3 34 45 33 24 -37 20 ... || |
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| 12&80 <<4 -8 -20 -36 32 4 0 ... || | | 12&80 <<4 -8 -20 -36 32 4 0 ... || |
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| 22&80 <<6 -10 12 -14 -32 6 -40 ... || | | 22&80 <<6 -10 12 -14 -32 6 -40 ... || |
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| 58&80 <<6 -10 12 -14 -32 6 40 ... || | | 58&80 <<6 -10 12 -14 -32 6 40 ... || |
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| 41&80 <<7 26 25 -3 -24 -33 20 ... || | | 41&80 <<7 26 25 -3 -24 -33 20 ... || |
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| In each case, the numbers joined by an ampersand represent 19-limit [[xenharmonic/Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given. | | In each case, the numbers joined by an ampersand represent 19-limit [[Patent_val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given. |
| | |
| =Intervals of 80edo=
| |
| ||~ degrees ||~ cents ||~ ratios* ||
| |
| || 0 || 0 || 1/1 ||
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| || 1 || 15 || 64/63 ||
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| || 2 || 30 || 81/80 ||
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| || 3 || 45 || 34/33, 36/35 ||
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| || 4 || 60 || 26/25, 28/27, 33/32, 35/34 ||
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| || 5 || 75 || 22/21, 25/24, 27/26 ||
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| || 6 || 90 || 19/18, 20/19, 21/20 ||
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| || 7 || 105 || 16/15, 17/16, 18/17 ||
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| || 8 || 120 || 14/13, 15/14 ||
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| || 9 || 135 || 13/12 ||
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| || 10 || 150 || 12/11 ||
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| || 11 || 165 || 11/10 ||
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| || 12 || 180 || 10/9, 21/19 ||
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| || 13 || 195 || 19/17 ||
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| || 14 || 210 || 9/8, 17/15 ||
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| || 15 || 225 || 8/7 ||
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| || 16 || 240 || ||
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| || 17 || 255 || 15/13, 22/19 ||
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| || 18 || 270 || 7/6 ||
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| || 19 || 285 || 13/11, 20/17 ||
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| || 20 || 300 || 19/16, 25/21 ||
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| || 21 || 315 || 6/5 ||
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| || 22 || 330 || 17/14 ||
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| || 23 || 345 || 11/9 ||
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| || 24 || 360 || 16/13, 21/17 ||
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| || 25 || 375 || ||
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| || 26 || 390 || 5/4 ||
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| || 27 || 405 || 19/15, 24/19 ||
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| || 28 || 420 || 14/11 ||
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| || 29 || 435 || 9/7 ||
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| || 30 || 450 || 13/10, 22/17 ||
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| || 31 || 465 || 17/13 ||
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| || 32 || 480 || 21/16, 25/19 ||
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| || 33 || 495 || 4/3 ||
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| || 34 || 510 || ||
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| || 35 || 525 || 19/14 ||
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| || 36 || 540 || 26/19 ||
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| || 37 || 555 || 11/8 ||
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| || 38 || 570 || 18/13 ||
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| || 39 || 585 || 7/5 ||
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| || 40 || 600 || 17/12, 24/17 ||
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| *based on treating 80edo as a [[19-limit]] temperament; other approaches are possible.</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>80edo</title></head><body>The <em>80 equal temperament</em>, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. 80et is the first equal temperament that represents the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19-limit">19-limit</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tonality%20diamond">tonality diamond</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a>ly (it barely manages to do so).<br />
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| <br />
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| 80 et <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.<br />
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| <br />
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| 80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:<br />
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| <br />
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| 31&amp;80 &lt;&lt;7 6 15 27 -24 -23 -20 ... ||<br />
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| 72&amp;80 &lt;&lt;24 30 40 24 32 24 0 ... ||<br />
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| 34&amp;80 &lt;&lt;2 -4 -50 22 16 2 -40 ... ||<br />
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| 46&amp;80 &lt;&lt;2 -4 30 22 16 2 40 ... ||<br />
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| 29&amp;80 &lt;&lt;3 34 45 33 24 -37 20 ... ||<br />
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| 12&amp;80 &lt;&lt;4 -8 -20 -36 32 4 0 ... ||<br />
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| 22&amp;80 &lt;&lt;6 -10 12 -14 -32 6 -40 ... ||<br />
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| 58&amp;80 &lt;&lt;6 -10 12 -14 -32 6 40 ... ||<br />
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| 41&amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||<br />
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| <br />
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| In each case, the numbers joined by an ampersand represent 19-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Patent%20val">patent vals</a> (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals of 80edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals of 80edo</h1>
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| <table class="wiki_table">
| | =Intervals of 80edo= |
| <tr>
| |
| <th>degrees<br />
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| </th>
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| <th>cents<br />
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| </th>
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| <th>ratios*<br />
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| </th>
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| </tr>
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| <tr>
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| <td>0<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| </tr>
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| <tr>
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| <td>1<br />
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| </td>
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| <td>15<br />
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| </td>
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| <td>64/63<br />
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| </td>
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| </tr>
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| <tr>
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| <td>2<br />
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| </td>
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| <td>30<br />
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| </td>
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| <td>81/80<br />
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| </td>
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| </tr>
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| <tr>
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| <td>3<br />
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| </td>
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| <td>45<br />
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| </td>
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| <td>34/33, 36/35<br />
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| </td>
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| </tr>
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| <tr>
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| <td>4<br />
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| </td>
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| <td>60<br />
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| </td>
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| <td>26/25, 28/27, 33/32, 35/34<br />
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| </td>
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| </tr>
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| <tr>
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| <td>5<br />
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| </td>
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| <td>75<br />
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| </td>
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| <td>22/21, 25/24, 27/26<br />
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| </td>
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| </tr>
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| <tr>
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| <td>6<br />
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| </td>
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| <td>90<br />
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| </td>
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| <td>19/18, 20/19, 21/20<br />
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| </td>
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| </tr>
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| <tr>
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| <td>7<br />
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| </td>
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| <td>105<br />
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| </td>
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| <td>16/15, 17/16, 18/17<br />
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| </td>
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| </tr>
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| <tr>
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| <td>8<br />
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| </td>
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| <td>120<br />
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| </td>
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| <td>14/13, 15/14<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9<br />
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| </td>
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| <td>135<br />
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| </td>
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| <td>13/12<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10<br />
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| </td>
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| <td>150<br />
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| </td>
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| <td>12/11<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>165<br />
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| </td>
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| <td>11/10<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>180<br />
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| </td>
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| <td>10/9, 21/19<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>195<br />
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| </td>
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| <td>19/17<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>210<br />
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| </td>
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| <td>9/8, 17/15<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>225<br />
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| </td>
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| <td>8/7<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>240<br />
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| </td>
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| <td><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>255<br />
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| </td>
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| <td>15/13, 22/19<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>270<br />
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| </td>
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| <td>7/6<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>285<br />
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| </td>
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| <td>13/11, 20/17<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>300<br />
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| </td>
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| <td>19/16, 25/21<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>315<br />
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| </td>
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| <td>6/5<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>330<br />
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| </td>
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| <td>17/14<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>345<br />
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| </td>
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| <td>11/9<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>360<br />
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| </td>
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| <td>16/13, 21/17<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>375<br />
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| </td>
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| <td><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>390<br />
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| </td>
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| <td>5/4<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>405<br />
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| </td>
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| <td>19/15, 24/19<br />
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| </td>
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| </tr>
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| <tr>
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| <td>28<br />
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| </td>
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| <td>420<br />
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| </td>
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| <td>14/11<br />
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| </td>
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| </tr>
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| <tr>
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| <td>29<br />
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| </td>
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| <td>435<br />
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| </td>
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| <td>9/7<br />
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| </td>
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| </tr>
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| <tr>
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| <td>30<br />
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| </td>
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| <td>450<br />
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| </td>
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| <td>13/10, 22/17<br />
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| </td>
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| </tr>
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| <tr>
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| <td>31<br />
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| </td>
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| <td>465<br />
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| </td>
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| <td>17/13<br />
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| </td>
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| </tr>
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| <tr>
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| <td>32<br />
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| </td>
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| <td>480<br />
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| </td>
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| <td>21/16, 25/19<br />
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| </td>
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| </tr>
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| <tr>
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| <td>33<br />
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| </td>
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| <td>495<br />
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| </td>
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| <td>4/3<br />
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| </td>
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| </tr>
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| <tr>
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| <td>34<br />
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| </td>
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| <td>510<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>35<br />
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| </td>
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| <td>525<br />
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| </td>
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| <td>19/14<br />
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| </td>
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| </tr>
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| <tr>
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| <td>36<br />
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| </td>
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| <td>540<br />
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| </td>
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| <td>26/19<br />
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| </td>
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| </tr>
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| <tr>
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| <td>37<br />
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| </td>
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| <td>555<br />
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| </td>
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| <td>11/8<br />
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| </td>
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| </tr>
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| <tr>
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| <td>38<br />
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| </td>
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| <td>570<br />
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| </td>
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| <td>18/13<br />
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| </td>
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| </tr>
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| <tr>
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| <td>39<br />
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| </td>
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| <td>585<br />
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| </td>
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| <td>7/5<br />
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| </td>
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| </tr>
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| <tr>
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| <td>40<br />
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| </td>
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| <td>600<br />
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| </td>
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| <td>17/12, 24/17<br />
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| </td>
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| </tr>
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| </table>
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|
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|
| *based on treating 80edo as a <a class="wiki_link" href="/19-limit">19-limit</a> temperament; other approaches are possible.</body></html></pre></div> | | {| class="wikitable" |
| | |- |
| | ! | degrees |
| | ! | cents |
| | ! | ratios* |
| | |- |
| | | | 0 |
| | | | 0 |
| | | | 1/1 |
| | |- |
| | | | 1 |
| | | | 15 |
| | | | 64/63 |
| | |- |
| | | | 2 |
| | | | 30 |
| | | | 81/80 |
| | |- |
| | | | 3 |
| | | | 45 |
| | | | 34/33, 36/35 |
| | |- |
| | | | 4 |
| | | | 60 |
| | | | 26/25, 28/27, 33/32, 35/34 |
| | |- |
| | | | 5 |
| | | | 75 |
| | | | 22/21, 25/24, 27/26 |
| | |- |
| | | | 6 |
| | | | 90 |
| | | | 19/18, 20/19, 21/20 |
| | |- |
| | | | 7 |
| | | | 105 |
| | | | 16/15, 17/16, 18/17 |
| | |- |
| | | | 8 |
| | | | 120 |
| | | | 14/13, 15/14 |
| | |- |
| | | | 9 |
| | | | 135 |
| | | | 13/12 |
| | |- |
| | | | 10 |
| | | | 150 |
| | | | 12/11 |
| | |- |
| | | | 11 |
| | | | 165 |
| | | | 11/10 |
| | |- |
| | | | 12 |
| | | | 180 |
| | | | 10/9, 21/19 |
| | |- |
| | | | 13 |
| | | | 195 |
| | | | 19/17 |
| | |- |
| | | | 14 |
| | | | 210 |
| | | | 9/8, 17/15 |
| | |- |
| | | | 15 |
| | | | 225 |
| | | | 8/7 |
| | |- |
| | | | 16 |
| | | | 240 |
| | | | |
| | |- |
| | | | 17 |
| | | | 255 |
| | | | 15/13, 22/19 |
| | |- |
| | | | 18 |
| | | | 270 |
| | | | 7/6 |
| | |- |
| | | | 19 |
| | | | 285 |
| | | | 13/11, 20/17 |
| | |- |
| | | | 20 |
| | | | 300 |
| | | | 19/16, 25/21 |
| | |- |
| | | | 21 |
| | | | 315 |
| | | | 6/5 |
| | |- |
| | | | 22 |
| | | | 330 |
| | | | 17/14 |
| | |- |
| | | | 23 |
| | | | 345 |
| | | | 11/9 |
| | |- |
| | | | 24 |
| | | | 360 |
| | | | 16/13, 21/17 |
| | |- |
| | | | 25 |
| | | | 375 |
| | | | |
| | |- |
| | | | 26 |
| | | | 390 |
| | | | 5/4 |
| | |- |
| | | | 27 |
| | | | 405 |
| | | | 19/15, 24/19 |
| | |- |
| | | | 28 |
| | | | 420 |
| | | | 14/11 |
| | |- |
| | | | 29 |
| | | | 435 |
| | | | 9/7 |
| | |- |
| | | | 30 |
| | | | 450 |
| | | | 13/10, 22/17 |
| | |- |
| | | | 31 |
| | | | 465 |
| | | | 17/13 |
| | |- |
| | | | 32 |
| | | | 480 |
| | | | 21/16, 25/19 |
| | |- |
| | | | 33 |
| | | | 495 |
| | | | 4/3 |
| | |- |
| | | | 34 |
| | | | 510 |
| | | | |
| | |- |
| | | | 35 |
| | | | 525 |
| | | | 19/14 |
| | |- |
| | | | 36 |
| | | | 540 |
| | | | 26/19 |
| | |- |
| | | | 37 |
| | | | 555 |
| | | | 11/8 |
| | |- |
| | | | 38 |
| | | | 570 |
| | | | 18/13 |
| | |- |
| | | | 39 |
| | | | 585 |
| | | | 7/5 |
| | |- |
| | | | 40 |
| | | | 600 |
| | | | 17/12, 24/17 |
| | |} |
| | *based on treating 80edo as a [[19-limit|19-limit]] temperament; other approaches are possible. |
| | [[Category:19-limit]] |
| | [[Category:21-limit]] |
| | [[Category:edo]] |