5L 4s: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 540652428 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 540653732 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 15: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 15:23:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540653732</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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|| || || || || || 11\53 || || || || || || 249.057 ||= Semaphore is around here || | || || || || || || 11\53 || || || || || || 249.057 ||= Semaphore is around here || | ||
|| || || || 5\24 || || || || || || || || 250 ||= L/s = 4 || | || || || || 5\24 || || || || || || || || 250 ||= L/s = 4 || | ||
|| || || || || || 9\43 || || || || || || 251.163 || || | |||
|| || || || || || || || || || || || 252.540 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> || | || || || || || || || || || || || || 252.540 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> || | ||
|| || || 4\19 || || || || || || || || || 252.632 ||= Godzilla is around here | || || || 4\19 || || || || || || || || || 252.632 ||= Godzilla is around here | ||
L/s = 3 || | L/s = 3 || | ||
|| || || || || || || || || || || || 252.724 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> || | || || || || || || || || || || || || 252.724 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> || | ||
|| || || || || 11\52 || || || || || || || 253.813 || || | |||
|| || || || 7\33 || || || || || || || || 254.5455 || || | |||
|| || || || || 10\47 || || || || || || || 255.319 || || | |||
|| || || || || || 13\61 || || || || || || 255.734 || || | |||
|| || || || || || || 16\75 || || || || || 256.000 || || | |||
|| || 3\14 || || || || || || || || || || 257.143 ||= Boundary of propriety (generators | || || 3\14 || || || || || || || || || || 257.143 ||= Boundary of propriety (generators | ||
larger than this are proper) || | larger than this are proper) || | ||
|| || || || || 11\51 || || || || || || || 258.8235 || || | |||
|| || || || 8\37 || || || || || || || || 259.459 ||= || | || || || || 8\37 || || || || || || || || 259.459 ||= || | ||
|| || || || || || 21\97 || || || || || || 259.794 ||= || | || || || || || || 21\97 || || || || || || 259.794 ||= || | ||
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</td> | </td> | ||
<td style="text-align: center;">L/s = 4<br /> | <td style="text-align: center;">L/s = 4<br /> | ||
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<td><br /> | |||
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<td><br /> | |||
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<td><br /> | |||
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<td>9\43<br /> | |||
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</td> | |||
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<td><br /> | |||
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<td>251.163<br /> | |||
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</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br /> | <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>11\52<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
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<td><br /> | |||
</td> | |||
<td><br /> | |||
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<td>253.813<br /> | |||
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</tr> | |||
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<td><br /> | |||
</td> | |||
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</td> | |||
<td><br /> | |||
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<td>7\33<br /> | |||
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</td> | |||
<td><br /> | |||
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<td><br /> | |||
</td> | |||
<td><br /> | |||
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<td><br /> | |||
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<td>254.5455<br /> | |||
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</tr> | |||
<tr> | |||
<td><br /> | |||
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<td>10\47<br /> | |||
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<td>255.319<br /> | |||
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</td> | |||
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<td>13\61<br /> | |||
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<td>255.734<br /> | |||
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<td>16\75<br /> | |||
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<td>256.000<br /> | |||
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<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">Boundary of propriety (generators<br /> | <td style="text-align: center;">Boundary of propriety (generators<br /> | ||
larger than this are proper)<br /> | larger than this are proper)<br /> | ||
</td> | |||
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<td>11\51<br /> | |||
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<td>258.8235<br /> | |||
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</td> | </td> | ||
</tr> | </tr> |
Revision as of 15:23, 11 February 2015
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2015-02-11 15:23:11 UTC.
- The original revision id was 540653732.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
The familiar harmonic entropy minimum with this MOS pattern is [[meantone family#Godzilla|godzilla]], in which a generator is [[8_7|8/7]] or [[7_6|7/6]] (tempered to be the same interval, or even 37/32 if you like) so two of them make a [[4_3|4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[Chromatic pairs#semaphore|semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3_2|3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. ||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || || 1\5 || || || || || || || || || || || 240 ||= || || || || || || || || || || || || 12\59 || 244.068 ||= Pseudo-semaphore is around here || || || || || || || || || || || 11\54 || || 244.444 ||= || || || || || || || || || || 10\49 || || || 244.898 ||= || || || || || || || || || 9\44 || || || || 245.455 ||= || || || || || || || || 8\39 || || || || || 246.154 ||= || || || || || || || 7\34 || || || || || || 247.059 ||= || || || || || || 6\29 || || || || || || || 248.276 ||= || || || || || || || 11\53 || || || || || || 249.057 ||= Semaphore is around here || || || || || 5\24 || || || || || || || || 250 ||= L/s = 4 || || || || || || || 9\43 || || || || || || 251.163 || || || || || || || || || || || || || || 252.540 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> || || || || 4\19 || || || || || || || || || 252.632 ||= Godzilla is around here L/s = 3 || || || || || || || || || || || || || 252.724 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> || || || || || || 11\52 || || || || || || || 253.813 || || || || || || 7\33 || || || || || || || || 254.5455 || || || || || || || 10\47 || || || || || || || 255.319 || || || || || || || || 13\61 || || || || || || 255.734 || || || || || || || || || 16\75 || || || || || 256.000 || || || || 3\14 || || || || || || || || || || 257.143 ||= Boundary of propriety (generators larger than this are proper) || || || || || || 11\51 || || || || || || || 258.8235 || || || || || || 8\37 || || || || || || || || 259.459 ||= || || || || || || || 21\97 || || || || || || 259.794 ||= || || || || || || || || || 55\254 || || || || 259.843 ||= || || || || || || || || || || || 144\665 || || 259.850 ||= || || || || || || || || || || || || 233\1076 || 259.851 ||= Golden [[superpelog]] || || || || || || || || || || 89\411 || || || 259.854 ||= || || || || || || || || 34\157 || || || || || 259.873 ||= || || || || || || 13\60 || || || || || || || 260 ||= || || || || 5\23 || || || || || || || || || 260.870 ||= Optimum rank range (L/s=3/2) superpelog || || || || || 7\32 || || || || || || || || 262.5 ||= || || || || || || 9\41 || || || || || || || 263.415 ||= || || || || || || || 11\50 || || || || || || 264 ||= || || || || || || || || 13\59 || || || || || 264.407 ||= || || || || || || || || || 15\68 || || || || 264.706 ||= || || || || || || || || || || 17\77 || || || 264.935 ||= || || || || || || || || || || || 19\86 || || 265.116 ||= || || || || || || || || || || || || 21\95 || 265.263 ||= || || 2\9 || || || || || || || || || || || 266.667 ||= ||
Original HTML content:
<html><head><title>5L 4s</title></head><body>The familiar harmonic entropy minimum with this MOS pattern is <a class="wiki_link" href="/meantone%20family#Godzilla">godzilla</a>, in which a generator is <a class="wiki_link" href="/8_7">8/7</a> or <a class="wiki_link" href="/7_6">7/6</a> (tempered to be the same interval, or even 37/32 if you like) so two of them make a <a class="wiki_link" href="/4_3">4/3</a>. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament <a class="wiki_link" href="/Chromatic%20pairs#semaphore">semaphore</a>, there is also a weird scale called "<a class="wiki_link" href="/pseudo-semaphore">pseudo-semaphore</a>", in which two different flavors of <a class="wiki_link" href="/3_2">3/2</a> exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2.<br /> <table class="wiki_table"> <tr> <th colspan="11">Generator<br /> </th> <th>Cents<br /> </th> <th>Comments<br /> </th> </tr> <tr> <td>1\5<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>240<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>12\59<br /> </td> <td>244.068<br /> </td> <td style="text-align: center;">Pseudo-semaphore is around here<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>11\54<br /> </td> <td><br /> </td> <td>244.444<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>10\49<br /> </td> <td><br /> </td> <td><br /> </td> <td>244.898<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>9\44<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>245.455<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>8\39<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>246.154<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>7\34<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>247.059<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>6\29<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>248.276<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>11\53<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>249.057<br /> </td> <td style="text-align: center;">Semaphore is around here<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>5\24<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>250<br /> </td> <td style="text-align: center;">L/s = 4<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>9\43<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>251.163<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>252.540<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>4\19<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>252.632<br /> </td> <td style="text-align: center;">Godzilla is around here<br /> L/s = 3<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>252.724<br /> </td> <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>11\52<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>253.813<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>7\33<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>254.5455<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>10\47<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>255.319<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>13\61<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>255.734<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>16\75<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>256.000<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>3\14<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>257.143<br /> </td> <td style="text-align: center;">Boundary of propriety (generators<br /> larger than this are proper)<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>11\51<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>258.8235<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>8\37<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>259.459<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>21\97<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>259.794<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>55\254<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>259.843<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>144\665<br /> </td> <td><br /> </td> <td>259.850<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>233\1076<br /> </td> <td>259.851<br /> </td> <td style="text-align: center;">Golden <a class="wiki_link" href="/superpelog">superpelog</a><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>89\411<br /> </td> <td><br /> </td> <td><br /> </td> <td>259.854<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>34\157<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>259.873<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>13\60<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>260<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>5\23<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>260.870<br /> </td> <td style="text-align: center;">Optimum rank range (L/s=3/2) superpelog<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>7\32<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>262.5<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>9\41<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>263.415<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>11\50<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>264<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>13\59<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>264.407<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>15\68<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>264.706<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>17\77<br /> </td> <td><br /> </td> <td><br /> </td> <td>264.935<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>19\86<br /> </td> <td><br /> </td> <td>265.116<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>21\95<br /> </td> <td>265.263<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td>2\9<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>266.667<br /> </td> <td style="text-align: center;"><br /> </td> </tr> </table> </body></html>