Gentle region: Difference between revisions

Revision as of 20:44, 11 September 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2012-09-11 20:44:11 UTC.

The original revision id was 363947692.

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:

[[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 [[29edo]], [[46edo]], [[58edo]], [[87edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[208edo]] and [[232edo]].

|| 17\29 ||   ||   ||   ||   ||   ||   || 703.44828 ||
||   ||   ||   ||   ||   ||   || 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 ||

Original HTML content:

<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 <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/87edo">87edo</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">145edo</a>, <a class="wiki_link" href="/208edo">208edo</a> and <a class="wiki_link" href="/232edo">232edo</a>.<br />
<br />


<table class="wiki_table">
    <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 />
</td>
        <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 />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>200\341<br />
</td>
        <td>703.81232<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>61\104<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>703.84615<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>227\387<br />
</td>
        <td>703.87597<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>166\283<br />
</td>
        <td><br />
</td>
        <td>703.88693<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>271\462<br />
</td>
        <td>703.8961<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>105\179<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>703.91061<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>254\433<br />
</td>
        <td>703.9261<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>149\254<br />
</td>
        <td><br />
</td>
        <td>703.93701<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>193\329<br />
</td>
        <td>703.95137<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>44\75<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>203\346<br />
</td>
        <td>704.04624<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>159\271<br />
</td>
        <td><br />
</td>
        <td>704.<u>05904</u><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>274\467<br />
</td>
        <td>704.06852<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>115\196<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.08163<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>301\513<br />
</td>
        <td>704.09357<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>186\317<br />
</td>
        <td><br />
</td>
        <td>704.10095<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>257\438<br />
</td>
        <td>704.10959<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</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>

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