Gentle region: Difference between revisions

Revision as of 12:08, 29 December 2016

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author xenwolf and made on 2016-12-29 12:08:41 UTC.

The original revision id was 602894982.

The revision comment was: Reverted to Oct 30, 2012 12:44 am: reset to "original" version, extended version moved to a new article

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 ||   ||
||   ||   ||   || 64\109 || 704.587 || Boundary of smaller "gentle region" ||
||   ||   || 37\63 ||   || 704.762 ||   ||
||   ||   ||       || 47\80 || 705 ||  Boundary of larger "gentle region" ||
|| 10\17 ||   ||   ||   || 705.882 ||   ||

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>703.448<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <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>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>71\121<br />
</td>
        <td>704.132<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <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>64\109<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>37\63<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>47\80<br />
</td>
        <td>705<br />
</td>
        <td>Boundary of larger &quot;gentle region&quot;<br />
</td>
    </tr>
    <tr>
        <td>10\17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>705.882<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-09-11 21:51:59 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:08:41 UTC</tt>.<br>
-: The original revision id was <tt>591632398</tt>.<br>
+: The original revision id was <tt>602894982</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>Reverted to Oct 30, 2012 12:44 am: reset to "original" version, extended version moved to a new article</tt><br>
 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>
-<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; 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.
+<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; 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.
-||||~ Geneator ||~ Cents ||~ 2-3-7(b)-11-13(b) ||||~ &lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;Half 8/7+ 1\3 7/6&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;1\3 8/7+ Half 7/6&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; ||~ 8/7+7/6 ||~   ||
+|| 17\29 ||   ||   ||   || 703.448 ||   ||
-|| (7+10)\29 ||   ||= 289.655+413.793 || &lt; [[@tel/29%2046%2081%20100%20107|29 46 81 100 107]]| ||||= 2\29+&lt;span style="line-height: 1.5;"&gt;3\29&lt;/span&gt;
+||   ||   ||   || 61\104 || 703.846 ||   ||
-.759+124.138 ||= 6\29+6\29
+||   ||   || 44\75 ||   || 704 ||   ||
-.276+248.276 ||   ||
+||   ||   ||   || 71\121 || 704.132 ||   ||
-|| (25+36)\104 ||   ||= 288.4615+415.385 || &lt; [[@tel/104%20165%20292%20360%20385|104 165 292 360 385]]| ||||= 10\104+23\312
+||   || 27\46 ||   ||   || 704.348 ||   ||
-.385+88.4615
+||   ||   ||   || 64\109 || 704.587 || Boundary of smaller "gentle region" ||
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;20\312+23\208&lt;/span&gt;
+||   ||   || 37\63 ||   || 704.762 ||   ||
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;76.923+132.692&lt;/span&gt; ||= 20\104+23\104
+||   ||   ||       || 47\80 || 705 ||  Boundary of larger "gentle region" ||
-.769+265.385 ||   ||
+|| 10\17 ||   ||   ||   || 705.882 ||   ||</pre></div>
-|| (18+26)\75 ||   ||= 288+416 || &lt; [[@tel/75%20119%20210;211%20259%20277|7]]&lt;span style="line-height: 1.5;"&gt;[[@tel/75%20119%20210;211%20259%20277|5 119 210~211 259 277]]|&lt;/span&gt; ||||= 7\75+17\225
-+90.667
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;14\225+17\150&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;74.667+136&lt;/span&gt; ||= 14\75+17\75
-+272 ||   ||
-||   || (47+68)\196 ||= 287.755+416.3265 || &lt;&lt;span style="line-height: 1.5;"&gt; [[@tel/196%20311%20551%20678%20725|196 311 549-551 678 725]]|&lt;/span&gt; ||||= 37\392+44\588
-.265+89.796
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;37/588+22/196&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;75.51+134.694&lt;/span&gt; ||= 37/196+44/196
-.531+269.388 ||   ||
-||   ||   ||= 287.713+416.382 || &lt; [[@tel/29%2046%2081%20100%20107|29 46 81 100 107]]|+&lt; &lt;span style="line-height: 1.5;"&gt;[[@tel/46%2073%20129%20159%20170|46 73 129 159 170]]|&lt;/span&gt;&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;"&gt;φ&lt;/span&gt; ||||= 119.283+85.7795
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;79.522+128.769&lt;/span&gt; ||= 238.566+257.3385 ||   ||
-||   || (29+42)\121 ||= 287.603+416.529 || &lt; [[@tel/121%20192%20340%20419%20448|121 192 339~340 419 448]]| ||||= 23\242+9\121
-.05+89.256
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;23\363+27\242&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.033+133.884&lt;/span&gt; ||= 23\121+27\121
-.099+267.769 ||   ||
-||   ||   ||= 287.267+416.978 || &lt; [[@tel/29%2046%2081%20100%20107|29 46 81 100 107]]|+&lt; [[@tel/109%20173%20306%20377%20403|109 173 306 377 403]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 116.8205+87.323
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;78.617+130.984&lt;/span&gt; ||= 235.85+261.969 ||   ||
-|| (11+16)\46 ||   ||= 286.9565+417.391 || &lt; [[@tel/46%2073%20129%20159%20170|46 73 129 159 170]]| ||||= 9\92+10\138
-.391+86.9565
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;3\46+5\46&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.261+130.435&lt;/span&gt; ||= 9\46+10\46
-.783+260.87 ||   ||
-||   ||   ||= 286.587+417.884 || &lt; [[@tel/29%2046%2081%20100%20107|29 46 81 100 107]]|+&lt;[[@tel/63%20100%20177%20218%20233|63 100 177 218 233]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 117.925+88.626
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.635+132.9395&lt;/span&gt; ||= 232.936+265.879 ||   ||
-||   || (48+70)\201 ||= 286.567+417.91 || &lt; [[@tel/201%20319%20564%20695%20703|201 319 564 695 703]]| ||||= 39\402+44\603
-.418+87.56
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;13\201+22\201&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.612+131.343&lt;/span&gt; ||= 39\201+44\201
-.836+262.687 ||   ||
-||   || (37+54)\155 ||= 286.452+418.0645 || &lt; [[@tel/155%20246%20435%20536%20573|155 246 435 536 573]]| ||||= 15\155+34\465
-.129+87.742
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;10\155+17\15&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.419+131.613&lt;/span&gt; ||= 30\155+34\155
-.258+263.226 ||   ||
-||   ||   ||= 286.387+418.151 || &lt; [[@tel/46%2073%20129%20159%20170|46 73 129 159 170]]|+&lt; [[@tel/109%20173%20306%20377%20403|109 173 306 377 403]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 115.968+87.842
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.312+131.7365&lt;/span&gt; ||= 231.935+263.527 ||   ||
-||   || (63+92)\264 ||= 286.364+418.182 || &lt; [[@tel/264%20419%20741%20913%20976|264 419 741 913 976]]| ||||= 51\528+58\792
-.909+87.87
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;17\264+29\264&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.273+131.818&lt;/span&gt; ||= 51\264+58\264
-.818+263.636 ||   ||
-|| (26+38)\109 ||   ||= 286.2385+418.349 || &lt; [[@tel/109%20173%20306%20377%20403|109 173 306 377 403]]| ||||= 21\218+8\109
-.596+88.07
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;7\109+12\10&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.064+132.11&lt;/span&gt; ||= 21\109+24\109
-.192+264.22 || Boundary of smaller "gentle region" ||
-||   || (67+98)\281 ||= 286.121+418.505 || &lt; [[@tel/281%20446%20789%20972|281 446 789 972]] 1039| ||||= 27\281+62\843
-.3025+88.256
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;18\281+31\28&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.868+132.384&lt;/span&gt; ||= 54\281+62\281
-.605+264.769 ||   ||
-||   ||   ||= 286.101+418.533 || &lt; [[@tel/46%2073%20129%20159%20170|46 73 129 159 170]]|+&lt; [[@tel/63%20100%20177%20218%20233|63 100 177 218 233]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 116.526+89.264
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.684+133.8965&lt;/span&gt; ||= 233.052+267.793 ||   ||
-||   || (41+60)\172 ||= 286.0465+418.605 || &lt; [[@tel/172%20273%20483%20595%20636|172 273 483 595 636]]| ||||= 33\344+38\516
-.116+88.372
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;11\172+19\17&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.744+132.558&lt;/span&gt; ||= 33\172+38\172
-.232+265.116 ||   ||
-||   || (56+82)\235 ||= 285.957+418.723 || &lt; [[@tel/235%20373%20660%20813%20869|235 373 660 813 869]]| ||||= 45\470+52\705
-.894+81.511
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;15\235+26\23&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.596+132.766&lt;/span&gt; ||= 45\235+52\235
-.787+265.532 ||   ||
-||   ||   ||= 285.852+418.864 || &lt; &lt;span style="line-height: 1.5;"&gt;[[@tel/109%20173%20306%20377%20403|109 173 306 377 403]]|+&lt;/span&gt;&lt; [[@tel/63%20100%20177%20218%20233|63 100 177 218 233]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 114.963+88.4675
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;76.642+132.701&lt;/span&gt; ||= 229.926+265.402 ||   ||
-|| &lt;span style="display: block; text-align: center;"&gt;(15+22)\63&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285.714+419.048&lt;/span&gt; || &lt; [[@tel/63%20100%20177%20218%20233|63 100 177 218 233]]| ||||= 6\63+14\189
-.286+88.88
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;4\63+7\63&lt;/span&gt;
-&lt;span style="text-align: start;"&gt;&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.1905+133.333&lt;/span&gt;&lt;/span&gt; ||= 12\63+14\63
-.571+266.667 ||   ||
-||   ||   ||= 285.513+419.316 || &lt; [[@tel/46%2073%20129%20159%20170|46 73 129 159 170]]|+&lt; [[@tel/80%20127%20225%20277%20296|80 127 225 277 296]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= &lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;113.7825+89.20&lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0);"&gt;75.855+133.80&lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;
-&lt;/span&gt; ||= 227.565+267.606 ||   ||
-||   || &lt;span style="display: block; text-align: center;"&gt;(49+72)\206&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;285.437+419.4175&lt;/span&gt; || &lt; [[@tel/206%20327%20579%20713%20762|206 327 578~579 713 762]]| ||||= 20\206+15\206
-.505+87.37
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;40\618+45\41&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.67+131.068&lt;/span&gt; ||= 40\206+45\206
-.01+262.136 ||   ||
-|| &lt;span style="display: block; text-align: center;"&gt;(34+50)\143&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285.315+419.58&lt;/span&gt; || &lt; [[@tel/143%20227%20401;402%20495%20529|143 227 401~402 495 529]]| ||||= 14\143+31\429
-.4825+86.71
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;28\429+31\28&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.322+130.07&lt;/span&gt; ||= 28\143+31\143
-.965+260.14 ||   ||
-||   ||   ||= 285.234+419.688 || &lt; [[@tel/63%20100%20177%20218%20233|63 100 177 218 233]]|+&lt; [[@tel/80%20127%20225%20277%20296|80 127 225 277 296]]|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 113.085+89.636
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;75.39+134.454&lt;/span&gt; ||= 226.169+268.909 ||   ||
-|| &lt;span style="display: block; text-align: center;"&gt;(54+78)\223&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285.202+419.731&lt;/span&gt; || &lt; [[@tel/223%20354%20626%20771%20825|223 354 626~627 771 825]]| ||||= 43\446+49\669
-.695+87.892
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;43\669+49\44&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.13+131.839&lt;/span&gt; ||= 43\223+49\223
-.39+263.677 ||   ||
-|| &lt;span style="display: block; text-align: center;"&gt;(19+28)\80&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285+420&lt;/span&gt; || &lt; [[@tel/80%20127%20225%20277%20296|80 127 225 277 296]]| ||||= 15\160+6\80
-.5+90
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;5\80+9\80&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;75+135&lt;/span&gt; ||= 15\80+18\80
-+270 || Boundary of larger "gentle region" ||</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gentle region&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Margo%20Schulter" target="_blank"&gt;Margo Schulter&lt;/a&gt;, in a &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow" target="_blank"&gt;tuning list posting&lt;/a&gt;, defined the &amp;quot;gentle region&amp;quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow" target="_blank"&gt;amending that&lt;/a&gt; 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 &lt;a class="wiki_link" href="/29edo" target="_blank"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo" target="_blank"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/75edo" target="_blank"&gt;75edo&lt;/a&gt;, &lt;a class="wiki_link" href="/104edo" target="_blank"&gt;104edo&lt;/a&gt;, &lt;a class="wiki_link" href="/109edo" target="_blank"&gt;109edo&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo" target="_blank"&gt;121edo&lt;/a&gt;, &lt;a class="wiki_link" href="/145edo" target="_blank"&gt;133edo&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo" target="_blank"&gt;155edo&lt;/a&gt;, &lt;a class="wiki_link" href="/162edo" target="_blank"&gt;162edo&lt;/a&gt;, &lt;a class="wiki_link" href="/167edo" target="_blank"&gt;167edo&lt;/a&gt;, &lt;a class="wiki_link" href="/179edo" target="_blank"&gt;179edo&lt;/a&gt;, &lt;a class="wiki_link" href="/191edo" target="_blank"&gt;191edo&lt;/a&gt;, &lt;a class="wiki_link" href="/201edo" target="_blank"&gt;201edo&lt;/a&gt;, &lt;a class="wiki_link" href="/213edo" target="_blank"&gt;213edo&lt;/a&gt;, &lt;a class="wiki_link" href="/225edo" target="_blank"&gt;225edo&lt;/a&gt; and &lt;a class="wiki_link" href="/237edo" target="_blank"&gt;237edo&lt;/a&gt;, plus &lt;a class="wiki_link" href="/63edo" target="_blank"&gt;63edo&lt;/a&gt; and &lt;a class="wiki_link" href="/80edo" target="_blank"&gt;80edo&lt;/a&gt; in the extended region.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gentle region&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;, in a &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow"&gt;tuning list posting&lt;/a&gt;, defined the &amp;quot;gentle region&amp;quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow"&gt;amending that&lt;/a&gt; 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 &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/75edo"&gt;75edo&lt;/a&gt;, &lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;, &lt;a class="wiki_link" href="/109edo"&gt;109edo&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121edo&lt;/a&gt;, &lt;a class="wiki_link" href="/145edo"&gt;133edo&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo"&gt;155edo&lt;/a&gt;, &lt;a class="wiki_link" href="/162edo"&gt;162edo&lt;/a&gt;, &lt;a class="wiki_link" href="/167edo"&gt;167edo&lt;/a&gt;, &lt;a class="wiki_link" href="/179edo"&gt;179edo&lt;/a&gt;, &lt;a class="wiki_link" href="/191edo"&gt;191edo&lt;/a&gt;, &lt;a class="wiki_link" href="/201edo"&gt;201edo&lt;/a&gt;, &lt;a class="wiki_link" href="/213edo"&gt;213edo&lt;/a&gt;, &lt;a class="wiki_link" href="/225edo"&gt;225edo&lt;/a&gt; and &lt;a class="wiki_link" href="/237edo"&gt;237edo&lt;/a&gt;, plus &lt;a class="wiki_link" href="/63edo"&gt;63edo&lt;/a&gt; and &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; in the extended region.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 120: / Line 24: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-        &lt;th colspan="2"&gt;Geneator&lt;br /&gt;
+         &lt;td&gt;17\29&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Cents&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;2-3-7(b)-11-13(b)&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th colspan="2"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;Half 8/7+ 1\3 7/6&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;1\3 8/7+ Half 7/6&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;8/7+7/6&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-         &lt;td&gt;(7+10)\29&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;289.655+413.793&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/29%252046%252081%2520100%2520107" target="_blank"&gt;29 46 81 100 107&lt;/a&gt;|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;2\29+&lt;span style="line-height: 1.5;"&gt;3\29&lt;/span&gt;&lt;br /&gt;
-.759+124.138&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;6\29+6\29&lt;br /&gt;
-.276+248.276&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;(25+36)\104&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;288.4615+415.385&lt;br /&gt;
+         &lt;td&gt;703.448&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/104%2520165%2520292%2520360%2520385" target="_blank"&gt;104 165 292 360 385&lt;/a&gt;|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;10\104+23\312&lt;br /&gt;
-.385+88.4615&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;20\312+23\208&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;76.923+132.692&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;20\104+23\104&lt;br /&gt;
-.769+265.385&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 172: / Line 38: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;(18+26)\75&lt;br /&gt;
-&lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;288+416&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/75%2520119%2520210%3B211%2520259%2520277" target="_blank"&gt;7&lt;/a&gt;&lt;span style="line-height: 1.5;"&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/75%2520119%2520210%3B211%2520259%2520277" target="_blank"&gt;5 119 210~211 259 277&lt;/a&gt;|&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;7\75+17\225&lt;br /&gt;
-+90.667&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;14\225+17\150&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;74.667+136&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;14\75+17\75&lt;br /&gt;
-+272&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(47+68)\196&lt;br /&gt;
+         &lt;td&gt;61\104&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;287.755+416.3265&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt;&lt;span style="line-height: 1.5;"&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/196%2520311%2520551%2520678%2520725" target="_blank"&gt;196 311 549-551 678 725&lt;/a&gt;|&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;37\392+44\588&lt;br /&gt;
-.265+89.796&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;37/588+22/196&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;75.51+134.694&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;37/196+44/196&lt;br /&gt;
+         &lt;td&gt;703.846&lt;br /&gt;
-.531+269.388&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 216: / Line 56: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;287.713+416.382&lt;br /&gt;
+         &lt;td&gt;44\75&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/29%252046%252081%2520100%2520107" target="_blank"&gt;29 46 81 100 107&lt;/a&gt;|+&amp;lt; &lt;span style="line-height: 1.5;"&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/46%252073%2520129%2520159%2520170" target="_blank"&gt;46 73 129 159 170&lt;/a&gt;|&lt;/span&gt;&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;"&gt;φ&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;119.283+85.7795&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;79.522+128.769&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;238.566+257.3385&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(29+42)\121&lt;br /&gt;
+         &lt;td&gt;704&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;287.603+416.529&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/121%2520192%2520340%2520419%2520448" target="_blank"&gt;121 192 339~340 419 448&lt;/a&gt;|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;23\242+9\121&lt;br /&gt;
-.05+89.256&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;23\363+27\242&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.033+133.884&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;23\121+27\121&lt;br /&gt;
-.099+267.769&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 252: / Line 69: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;287.267+416.978&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/29%252046%252081%2520100%2520107" target="_blank"&gt;29 46 81 100 107&lt;/a&gt;|+&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/109%2520173%2520306%2520377%2520403" target="_blank"&gt;109 173 306 377 403&lt;/a&gt;|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;116.8205+87.323&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;78.617+130.984&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;235.85+261.969&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;(11+16)\46&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;286.9565+417.391&lt;br /&gt;
+         &lt;td&gt;71\121&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/46%252073%2520129%2520159%2520170" target="_blank"&gt;46 73 129 159 170&lt;/a&gt;|&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2" style="text-align: center;"&gt;9\92+10\138&lt;br /&gt;
+         &lt;td&gt;704.132&lt;br /&gt;
-.391+86.9565&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;3\46+5\46&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.261+130.435&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;9\46+10\46&lt;br /&gt;
-.783+260.87&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 288: / Line 82: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;27\46&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;286.587+417.884&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/29%252046%252081%2520100%2520107" target="_blank"&gt;29 46 81 100 107&lt;/a&gt;|+&amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/63%2520100%2520177%2520218%2520233" target="_blank"&gt;63 100 177 218 233&lt;/a&gt;|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;117.925+88.626&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.635+132.9395&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;232.936+265.879&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(48+70)\201&lt;br /&gt;
+         &lt;td&gt;704.348&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;286.567+417.91&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/201%2520319%2520564%2520695%2520703" target="_blank"&gt;201 319 564 695 703&lt;/a&gt;|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;39\402+44\603&lt;br /&gt;
-.418+87.56&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;13\201+22\201&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.612+131.343&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;39\201+44\201&lt;br /&gt;
-.836+262.687&lt;br /&gt;
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-         &lt;td&gt;&lt;br /&gt;
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-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;(19+28)\80&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;285+420&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/80%2520127%2520225%2520277%2520296" target="_blank"&gt;80 127 225 277 296&lt;/a&gt;|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;15\160+6\80&lt;br /&gt;
-.5+90&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;5\80+9\80&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;75+135&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;15\80+18\80&lt;br /&gt;
-+270&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Boundary of larger &amp;quot;gentle region&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

Gentle region: Difference between revisions

Revision as of 12:08, 29 December 2016

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