Gentle region

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This revision was by author JosephRuhf and made on 2015-02-14 17:11:11 UTC.
The original revision id was 540983612.
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; later [[http://launch.groups.yahoo.com/group/tuning/message/105172|amending that]] to from 1.49 to 3.04 cents sharp. We can consider the first 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 [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo|133edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.

|| 17\29 ||   ||   ||   ||   || 703.448 ||   ||
||   ||   ||   ||   || 61\104 || 703.846 ||   ||
||   ||   ||   || 44\75 ||   || 704 ||   ||
||   ||   ||   ||   || 71\121 || 704.132 ||   ||
||   ||   || 27\46 ||   ||   || 704.348 ||   ||
||   ||   ||   ||   || 118\201 || 704.478 ||   ||
||   ||   ||   || 91\155 ||   || 704.516 ||   ||
||   ||   ||   ||   || 155\264 || 704.5455 ||   ||
||   || 64\109 ||   ||   ||   || 704.587 || Boundary of smaller "gentle region" ||
||   ||   ||   ||   || 165\281 || 704.626 ||   ||
||   ||   ||   || 101\172 ||   || 704.651 ||   ||
||   ||   ||   ||   || 138\235 || 704.681 ||   ||
||   ||   ||   ||   ||   || 704.7535 ||   ||
||   ||   || 37\63 ||   ||   || 704.762 ||   ||
||   ||   ||   ||   ||   || 704.770 ||   ||
||   ||   ||   ||   || 121\206 || 704.854 ||   ||
||   ||   ||   || 84\143 ||   || 704.895 ||   ||
||   ||   ||   ||   || 131\223 || 704.933 ||   ||
|| 47\80 ||   ||   ||   ||   || 705 || Boundary of larger "gentle region" ||

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; later <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow">amending that</a> to from 1.49 to 3.04 cents sharp. We can consider the first 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 <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>, plus <a class="wiki_link" href="/63edo">63edo</a> and <a class="wiki_link" href="/80edo">80edo</a> in the extended region.<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>703.448<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>61\104<br />
</td>
        <td>703.846<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>44\75<br />
</td>
        <td><br />
</td>
        <td>704<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>71\121<br />
</td>
        <td>704.132<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>27\46<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.348<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>118\201<br />
</td>
        <td>704.478<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>91\155<br />
</td>
        <td><br />
</td>
        <td>704.516<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>155\264<br />
</td>
        <td>704.5455<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>64\109<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.587<br />
</td>
        <td>Boundary of smaller &quot;gentle region&quot;<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>165\281<br />
</td>
        <td>704.626<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>101\172<br />
</td>
        <td><br />
</td>
        <td>704.651<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>138\235<br />
</td>
        <td>704.681<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.7535<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>37\63<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.762<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.770<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>121\206<br />
</td>
        <td>704.854<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>84\143<br />
</td>
        <td><br />
</td>
        <td>704.895<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>131\223<br />
</td>
        <td>704.933<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47\80<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>705<br />
</td>
        <td>Boundary of larger &quot;gentle region&quot;<br />
</td>
    </tr>
</table>

</body></html>
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