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Wikispaces>keenanpepper **Imported revision 248977817 - Original comment: ** |
Wikispaces>guest **Imported revision 249047555 - 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 03:50:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>249047555</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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||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || | ||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || | ||
|| 1\6 || || || || || || || || || || || 200 || || | || 1\6 || || || || || || || || || || || 200 ||= || | ||
|| || || || || || 6\34 || || || || || || 211.76 || || | || || || || || || 6\34 || || || || || || 211.76 ||= || | ||
|| || || || || 5\28 || || || || || || || 214.29 || Antikythera is around here || | || || || || || 5\28 || || || || || || || 214.29 ||= Antikythera is around here || | ||
|| || || || 4\22 || || || || || || || || 218.18 || || | || || || || 4\22 || || || || || || || || 218.18 ||= || | ||
|| || || 3\16 || || || || || || || || || 225 || | || || || 3\16 || || || || || || || || || 225 ||= Optimum rank range (L/s=3/2) || | ||
|| || || || || 8\42 || || || || || || || 228.57 || || | || || || || || 8\42 || || || || || || || 228.57 ||= || | ||
|| || || || || || || 21\110 || || || || || 229.09 || Golden lemba || | || || || || || || || 21\110 || || || || || 229.09 ||= Golden lemba || | ||
|| || || || || || 13\68 || || || || || || 229.41 || || | || || || || || || 13\68 || || || || || || 229.41 ||= || | ||
|| || || || 5\26 || || || || || || || || 230.77 || || | || || || || 5\26 || || || || || || || || 230.77 ||= || | ||
|| || || || || 7\36 || || || || || || || 233.33 || Lemba is around here || | || || || || || 7\36 || || || || || || || 233.33 ||= Lemba is around here || | ||
|| || 2\10 || || || || || || || || || || 240 || Boundary of propriety for near-MOS || | || || 2\10 || || || || || || || || || || 240 ||= Boundary of propriety for near-MOS || | ||
|| || || || 5\24 || || || || || || || || 250 || Decimal is around here || | || || || || 5\24 || || || || || || || || 250 ||= Decimal is around here || | ||
|| || || 3\14 || || || || || || || || || 257.14 || || | || || || 3\14 || || || || || || || || || 257.14 ||= || | ||
|| || || || 4\18 || || || || || || || || 266.67 || || | || || || || 4\18 || || || || || || || || 266.67 ||= || | ||
|| || || || || 5\22 || || || || || || || 272.73 || || | || || || || || 5\22 || || || || || || || 272.73 ||= || | ||
|| || || || || || 6\26 || || || || || || 276.92 || || | || || || || || || 6\26 || || || || || || 276.92 ||= || | ||
|| || || || || || || 7\30 || || || || || 280 || || | || || || || || || || 7\30 || || || || || 280 ||= || | ||
|| || || || || || || || 8\34 || || || || 282.35 || || | || || || || || || || || 8\34 || || || || 282.35 ||= || | ||
|| || || || || || || || || 9\38 || || || 284.21 || || | || || || || || || || || || 9\38 || || || 284.21 ||= || | ||
|| || || || || || || || || || 10\42 || || 285.71 || || | || || || || || || || || || || 10\42 || || 285.71 ||= || | ||
|| || || || || || || || || || || 11\46 || 286.96 || Doublewide is around here || | || || || || || || || || || || || 11\46 || 286.96 ||= Doublewide is around here || | ||
|| 1\4 || || || || || || || || || || || 300 || ||</pre></div> | || 1\4 || || || || || || || || || || || 300 ||= ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>4L 2s</title></head><body>There are three scales with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern that are significant minima of harmonic entropy.<br /> | <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>4L 2s</title></head><body>There are three scales with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern that are significant minima of harmonic entropy.<br /> | ||
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<td>200<br /> | <td>200<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>211.76<br /> | <td>211.76<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>214.29<br /> | <td>214.29<br /> | ||
</td> | </td> | ||
<td>Antikythera is around here<br /> | <td style="text-align: center;">Antikythera is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>218.18<br /> | <td>218.18<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>225<br /> | <td>225<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;">Optimum rank range (L/s=3/2)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>228.57<br /> | <td>228.57<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>229.09<br /> | <td>229.09<br /> | ||
</td> | </td> | ||
<td>Golden lemba<br /> | <td style="text-align: center;">Golden lemba<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>229.41<br /> | <td>229.41<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>230.77<br /> | <td>230.77<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>233.33<br /> | <td>233.33<br /> | ||
</td> | </td> | ||
<td>Lemba is around here<br /> | <td style="text-align: center;">Lemba is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>240<br /> | <td>240<br /> | ||
</td> | </td> | ||
<td>Boundary of propriety for near-MOS<br /> | <td style="text-align: center;">Boundary of propriety for near-MOS<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>250<br /> | <td>250<br /> | ||
</td> | </td> | ||
<td>Decimal is around here<br /> | <td style="text-align: center;">Decimal is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>257.14<br /> | <td>257.14<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>266.67<br /> | <td>266.67<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>272.73<br /> | <td>272.73<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>276.92<br /> | <td>276.92<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>280<br /> | <td>280<br /> | ||
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<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>282.35<br /> | <td>282.35<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>284.21<br /> | <td>284.21<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>285.71<br /> | <td>285.71<br /> | ||
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<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>286.96<br /> | <td>286.96<br /> | ||
</td> | </td> | ||
<td>Doublewide is around here<br /> | <td style="text-align: center;">Doublewide is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>300<br /> | <td>300<br /> | ||
</td> | </td> | ||
<td><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> |
Revision as of 03:50, 29 August 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author guest and made on 2011-08-29 03:50:23 UTC.
- The original revision id was 249047555.
- 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:
There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy. The first is "[[antikythera]]", or no-3's [[Diaschismic family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7. The second is [[Dicot family|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic clan|Doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5. In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents). ||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || || 1\6 || || || || || || || || || || || 200 ||= || || || || || || || 6\34 || || || || || || 211.76 ||= || || || || || || 5\28 || || || || || || || 214.29 ||= Antikythera is around here || || || || || 4\22 || || || || || || || || 218.18 ||= || || || || 3\16 || || || || || || || || || 225 ||= Optimum rank range (L/s=3/2) || || || || || || 8\42 || || || || || || || 228.57 ||= || || || || || || || || 21\110 || || || || || 229.09 ||= Golden lemba || || || || || || || 13\68 || || || || || || 229.41 ||= || || || || || 5\26 || || || || || || || || 230.77 ||= || || || || || || 7\36 || || || || || || || 233.33 ||= Lemba is around here || || || 2\10 || || || || || || || || || || 240 ||= Boundary of propriety for near-MOS || || || || || 5\24 || || || || || || || || 250 ||= Decimal is around here || || || || 3\14 || || || || || || || || || 257.14 ||= || || || || || 4\18 || || || || || || || || 266.67 ||= || || || || || || 5\22 || || || || || || || 272.73 ||= || || || || || || || 6\26 || || || || || || 276.92 ||= || || || || || || || || 7\30 || || || || || 280 ||= || || || || || || || || || 8\34 || || || || 282.35 ||= || || || || || || || || || || 9\38 || || || 284.21 ||= || || || || || || || || || || || 10\42 || || 285.71 ||= || || || || || || || || || || || || 11\46 || 286.96 ||= Doublewide is around here || || 1\4 || || || || || || || || || || || 300 ||= ||
Original HTML content:
<html><head><title>4L 2s</title></head><body>There are three scales with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern that are significant minima of harmonic entropy.<br /> <br /> The first is "<a class="wiki_link" href="/antikythera">antikythera</a>", or no-3's <a class="wiki_link" href="/Diaschismic%20family">srutal/pajara</a>, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.<br /> <br /> The second is <a class="wiki_link" href="/Dicot%20family">decimal</a>, in which two generators make a 4/3, and the third is <a class="wiki_link" href="/Jubilismic%20clan">Doublewide</a>, in which the generator is 7/6 so the period minus the generator is 6/5.<br /> <br /> In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).<br /> <br /> <table class="wiki_table"> <tr> <th colspan="11">Generator<br /> </th> <th>Cents<br /> </th> <th>Comments<br /> </th> </tr> <tr> <td>1\6<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>200<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>6\34<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>211.76<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>5\28<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>214.29<br /> </td> <td style="text-align: center;">Antikythera is around here<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>4\22<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>218.18<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>3\16<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>225<br /> </td> <td style="text-align: center;">Optimum rank range (L/s=3/2)<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>8\42<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>228.57<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>21\110<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>229.09<br /> </td> <td style="text-align: center;">Golden lemba<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>13\68<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>229.41<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>5\26<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>230.77<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>7\36<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>233.33<br /> </td> <td style="text-align: center;">Lemba is around here<br /> </td> </tr> <tr> <td><br /> </td> <td>2\10<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;">Boundary of propriety for near-MOS<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;">Decimal is around here<br /> </td> </tr> <tr> <td><br /> </td> <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>257.14<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>4\18<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>266.67<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>5\22<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>272.73<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>6\26<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>276.92<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>7\30<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>280<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>8\34<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>282.35<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>9\38<br /> </td> <td><br /> </td> <td><br /> </td> <td>284.21<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>10\42<br /> </td> <td><br /> </td> <td>285.71<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>11\46<br /> </td> <td>286.96<br /> </td> <td style="text-align: center;">Doublewide is around here<br /> </td> </tr> <tr> <td>1\4<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>300<br /> </td> <td style="text-align: center;"><br /> </td> </tr> </table> </body></html>