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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = Gentle |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-10-02 18:59:15 UTC</tt>.<br>
| | | en = Gentle region |
| : The original revision id was <tt>369712382</tt>.<br>
| | | es = |
| : The revision comment was: <tt></tt><br>
| | | ja = |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | }} |
| <h4>Original Wikitext content:</h4>
| | ''For an alternative version of the page, see: [[Gentle region (extended version)]].'' |
| <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">[[Margo Schulter]], in a [[http://launch.groups.yahoo.com/group/tuning/message/38721|tuning list posting]], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp. We can consider this region to extend from fifths of size 17\29 to 64\109. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo|133edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]].
| |
|
| |
|
| || 17\29 || || || || || || || 703.44828 ||
| | The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of [[29edo]] (~703.4c) and [[17edo]] (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo. |
| || || || || || || || 112\191 || 703.66492 ||
| |
| || || || || || || 95\162 || || 703.__703__ ||
| |
| || || || || || || || 173\295 || 703.72881 ||
| |
| || || || || || 78\133 || || || 703.7594 ||
| |
| || || || || || || || 217\370 || 703.__783__ ||
| |
| || || || || || || 139\237 || || 703.79747 ||
| |
| || || || || || || || 200\341 || 703.81232 ||
| |
| || || || || 61\104 || || || || 703.84615 ||
| |
| || || || || || || || 227\387 || 703.87597 ||
| |
| || || || || || || 166\283 || || 703.88693 ||
| |
| || || || || || || || 271\462 || 703.8961 ||
| |
| || || || || || 105\179 || || || 703.91061 ||
| |
| || || || || || || || 254\433 || 703.9261 ||
| |
| || || || || || || 149\254 || || 703.93701 ||
| |
| || || || || || || || 193\329 || 703.95137 ||
| |
| || || || 44\75 || || || || || 704 ||
| |
| || || || || || || || 203\346 || 704.04624 ||
| |
| || || || || || || 159\271 || || 704.__05904__ ||
| |
| || || || || || || || 274\467 || 704.06852 ||
| |
| || || || || || 115\196 || || || 704.08163 ||
| |
| || || || || || || || 301\513 || 704.09357 ||
| |
| || || || || || || 186\317 || || 704.10095 ||
| |
| || || || || || || || 257\438 || 704.10959 ||
| |
| || || || || 71\121 || || || || 704.13223 ||
| |
| || || || || || || || 240\409 || 704.15648 ||
| |
| || || || || || || 169\288 || || 704.1__6__ ||
| |
| || || || || || || || 267\455 || 704.17582 ||
| |
| || || || || || 98\167 || || || 704.19162 ||
| |
| || || || || || || || 223\380 || 704.21053 ||
| |
| || || || || || || 125\213 || || 704.22535 ||
| |
| || || || || || || || 152\259 || 704.2471 ||
| |
| || || 27\46 || || || || || || 704.34783 ||
| |
| || || || || || || || 199\339 || 704.42478 ||
| |
| || || || || || || 172\293 || || 704.43686 ||
| |
| || || || || || || || 317\540 || 704.__4__ ||
| |
| || || || || || 145\247 || || || 704.45344 ||
| |
| || || || || || || || 408\695 || 704.46043 ||
| |
| || || || || || || 263\448 || || 704.46429 ||
| |
| || || || || || || || 381\649 || 704.46841 ||
| |
| || || || || 118\201 || || || || 704.47761 ||
| |
| || || || || || || || 445\758 || 704.48549 ||
| |
| || || || || || || 327\557 || || 704.48833 ||
| |
| || || || || || || || 536\913 || 704.49069 ||
| |
| || || || || || 209\356 || || || 704.49438 ||
| |
| || || || || || || || 509\867 || 704.49827 ||
| |
| || || || || || || 300\511 || || 704.50098 ||
| |
| || || || || || || || 391\666 || 704.__504__ ||
| |
| || || || 91\155 || || || || || 704.51613 ||
| |
| || || || || || || || 428\729 || 704.52675 ||
| |
| || || || || || || 337\574 || || 704.52962 ||
| |
| || || || || || || || 583\993 || 704.53172 ||
| |
| || || || || || 246\419 || || || 704.53461 ||
| |
| || || || || || || || 647\1102 || 704.537205 ||
| |
| || || || || || || 401\683 || || 704.5388 ||
| |
| || || || || || || || 556\947 || 704.540655 ||
| |
| || || || || 155\264 || || || || 704.__54__ ||
| |
| || || || || || || || 529\901 || 704.5505 ||
| |
| || || || || || || 374\637 || || 704.55259 ||
| |
| || || || || || || || 593\1010 || 704.__5544__ ||
| |
| || || || || || 219\373 || || || 704.55764 ||
| |
| || || || || || || || 502\855 || 704.5614 ||
| |
| || || || || || || 283\482 || || 704.564315 ||
| |
| || || || || || || || 347\591 || 704.56853 ||
| |
| || 64\109 || || || || || || || 704.58716 ||</pre></div>
| |
| <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>Gentle region</title></head><body><a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow">tuning list posting</a>, defined the &quot;gentle region&quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp. We can consider this region to extend from fifths of size 17\29 to 64\109. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the gentle region include multiples of <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/75edo">75edo</a>, <a class="wiki_link" href="/104edo">104edo</a>, <a class="wiki_link" href="/109edo">109edo</a>, <a class="wiki_link" href="/121edo">121edo</a>, <a class="wiki_link" href="/145edo">133edo</a>, <a class="wiki_link" href="/155edo">155edo</a>, <a class="wiki_link" href="/162edo">162edo</a>, <a class="wiki_link" href="/167edo">167edo</a>, <a class="wiki_link" href="/179edo">179edo</a>, <a class="wiki_link" href="/191edo">191edo</a>, <a class="wiki_link" href="/201edo">201edo</a>, <a class="wiki_link" href="/213edo">213edo</a>, <a class="wiki_link" href="/225edo">225edo</a> and <a class="wiki_link" href="/237edo">237edo</a>.<br />
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| <br />
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|
| |
|
| | Gentle tuning systems are thus "mild" (or, as the name says, "gentle") versions of tuning systems like [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for neogothic harmony systems; besides, they are possible temperament frameworks for [[Arabic music|Arabic]] and [[Turkish music|Turkish]] tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering. |
|
| |
|
| <table class="wiki_table">
| | When the tempering of the fifth is "very gentle"/near-just as in 29edo, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third (implying [[schismic]] temperament), as used in Turkish music; sharper tempering as in 17edo will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a pythagorean or neomajor third.) |
| <tr>
| |
| <td>17\29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>703.44828<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>112\191<br />
| |
| </td>
| |
| <td>703.66492<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>95\162<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>703.<u>703</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>173\295<br />
| |
| </td>
| |
| <td>703.72881<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>78\133<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>703.7594<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td>217\370<br />
| |
| </td>
| |
| <td>703.<u>783</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>139\237<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>703.79747<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td>200\341<br />
| |
| </td>
| |
| <td>703.81232<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>61\104<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
| |
| </td>
| |
| <td>703.84615<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>227\387<br />
| |
| </td>
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| <td>703.87597<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>166\283<br />
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| </td>
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| <td><br />
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| </td>
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| <td>703.88693<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>271\462<br />
| |
| </td>
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| <td>703.8961<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>105\179<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>703.91061<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>254\433<br />
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| </td>
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| <td>703.9261<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>149\254<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td>703.93701<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>193\329<br />
| |
| </td>
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| <td>703.95137<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
| |
| <td><br />
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| </td>
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| <td>44\75<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>704<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>203\346<br />
| |
| </td>
| |
| <td>704.04624<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>159\271<br />
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| </td>
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| <td><br />
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| </td>
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| <td>704.<u>05904</u><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>274\467<br />
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| </td>
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| <td>704.06852<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>115\196<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>704.08163<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>301\513<br />
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| </td>
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| <td>704.09357<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>186\317<br />
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| </td>
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| <td><br />
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| </td>
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| <td>704.10095<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>257\438<br />
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| </td>
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| <td>704.10959<br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| <td>71\121<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.13223<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>240\409<br />
| |
| </td>
| |
| <td>704.15648<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>169\288<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.1<u>6</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>267\455<br />
| |
| </td>
| |
| <td>704.17582<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>98\167<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.19162<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>223\380<br />
| |
| </td>
| |
| <td>704.21053<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>125\213<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.22535<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>152\259<br />
| |
| </td>
| |
| <td>704.2471<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>27\46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.34783<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>199\339<br />
| |
| </td>
| |
| <td>704.42478<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>172\293<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.43686<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>317\540<br />
| |
| </td>
| |
| <td>704.<u>4</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>145\247<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.45344<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>408\695<br />
| |
| </td>
| |
| <td>704.46043<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>263\448<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.46429<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>381\649<br />
| |
| </td>
| |
| <td>704.46841<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>118\201<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.47761<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>445\758<br />
| |
| </td>
| |
| <td>704.48549<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>327\557<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.48833<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>536\913<br />
| |
| </td>
| |
| <td>704.49069<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>209\356<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.49438<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>509\867<br />
| |
| </td>
| |
| <td>704.49827<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>300\511<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.50098<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>391\666<br />
| |
| </td>
| |
| <td>704.<u>504</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>91\155<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.51613<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>428\729<br />
| |
| </td>
| |
| <td>704.52675<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>337\574<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.52962<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>583\993<br />
| |
| </td>
| |
| <td>704.53172<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>246\419<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.53461<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>647\1102<br />
| |
| </td>
| |
| <td>704.537205<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>401\683<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.5388<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>556\947<br />
| |
| </td>
| |
| <td>704.540655<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>155\264<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.<u>54</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>529\901<br />
| |
| </td>
| |
| <td>704.5505<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>374\637<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.55259<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>593\1010<br />
| |
| </td>
| |
| <td>704.<u>5544</u><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>219\373<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.55764<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>502\855<br />
| |
| </td>
| |
| <td>704.5614<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>283\482<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.564315<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>347\591<br />
| |
| </td>
| |
| <td>704.56853<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>64\109<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>704.58716<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | We can consider the originally-defined gentle region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region. |
| | |
| | The extended gentle region is further divided into two subregions: |
| | * "Lower gentle": 703.4{{c}} (near 17\29) to 704.3{{c}} (near 27\46) |
| | * "Upper gentle": 704.3{{c}} to 705.0{{c}} (near 10\17, or more accurately 47\80). |
| | [[46edo]] is effectively the boundary between lower and upper neogothic. |
| | |
| | {| class="wikitable" |
| | |- |
| | ! colspan="4" | EDO Generator |
| | ! Fifth |
| | ! Dim 4th |
| | ! Comments |
| | |- |
| | | 17\29 |
| | | |
| | | |
| | | |
| | | 703.448 |
| | | 372.416 |
| | | |
| | |- |
| | | |
| | | |
| | | |
| | | |
| | |703.711 |
| | |370.312 |
| | |Margo Schulter's MET-24 fifth |
| | |- |
| | | |
| | | |
| | | |
| | | 61\104 |
| | | 703.846 |
| | | 369.231 |
| | | Neo-gothic theory of harmony |
| | |- |
| | | |
| | | |
| | | 44\75 |
| | | |
| | | 704.000 |
| | | 368.000 |
| | | |
| | |- |
| | | |
| | | |
| | | |
| | | 71\121 |
| | | 704.132 |
| | | 366.942 |
| | | |
| | |- |
| | | |
| | | 27\46 |
| | | |
| | | |
| | | 704.348 |
| | | 365.217 |
| | | |
| | |- |
| | | |
| | | |
| | | |
| | | 64\109 |
| | | 704.587 |
| | | 363.303 |
| | | Boundary of smaller "gentle region" |
| | |- |
| | | |
| | | |
| | | 37\63 |
| | | |
| | | 704.762 |
| | | 361.905 |
| | | |
| | |- |
| | | |
| | | |
| | | |
| | | 47\80 |
| | | 705.000 |
| | | 360.000 |
| | | Boundary of larger "gentle region" |
| | |- |
| | | 10\17 |
| | | |
| | | |
| | | |
| | | 705.882 |
| | | 352.941 |
| | | |
| | |} |
| | |
| | == See also == |
| | * [[Interseptimal]] |
| | |
| | [[Category:EDO theory pages]] |
| | [[Category:Fifth]] |
| | [[Category:Gentle]] |