Gentle region (extended version): Difference between revisions

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<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:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:05:38 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:06:49 UTC</tt>.<br>

: The original revision id was <tt>~~602894908~~</tt>.<br>

: The original revision id was <tt>602894936</tt>.<br>

: The revision comment was: <tt>~~extract of current version~~</tt><br>

: The revision comment was: <tt></tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

<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">// this is an externde version of the **[[Gentle region]] article. **//

----

[[@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) ||||~ <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span> ||~ 8/7+7/6 ||~ ||

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225+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"><html><head><title>Gentle region (extended version)</title></head><body><a class="wiki_link" href="/Margo%20Schulter" target="_blank">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow" target="_blank">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" target="_blank">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" target="_blank">29edo</a>, <a class="wiki_link" href="/46edo" target="_blank">46edo</a>, <a class="wiki_link" href="/75edo" target="_blank">75edo</a>, <a class="wiki_link" href="/104edo" target="_blank">104edo</a>, <a class="wiki_link" href="/109edo" target="_blank">109edo</a>, <a class="wiki_link" href="/121edo" target="_blank">121edo</a>, <a class="wiki_link" href="/145edo" target="_blank">133edo</a>, <a class="wiki_link" href="/155edo" target="_blank">155edo</a>, <a class="wiki_link" href="/162edo" target="_blank">162edo</a>, <a class="wiki_link" href="/167edo" target="_blank">167edo</a>, <a class="wiki_link" href="/179edo" target="_blank">179edo</a>, <a class="wiki_link" href="/191edo" target="_blank">191edo</a>, <a class="wiki_link" href="/201edo" target="_blank">201edo</a>, <a class="wiki_link" href="/213edo" target="_blank">213edo</a>, <a class="wiki_link" href="/225edo" target="_blank">225edo</a> and <a class="wiki_link" href="/237edo" target="_blank">237edo</a>, plus <a class="wiki_link" href="/63edo" target="_blank">63edo</a> and <a class="wiki_link" href="/80edo" target="_blank">80edo</a> in the extended region.<br />

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gentle region (extended version)</title></head><body><em> this is an externde version of the <strong><a class="wiki_link" href="/Gentle%20region">Gentle region</a> article. </strong></em><br />

<hr />

<a class="wiki_link" href="/Margo%20Schulter" target="_blank">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow" target="_blank">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" target="_blank">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" target="_blank">29edo</a>, <a class="wiki_link" href="/46edo" target="_blank">46edo</a>, <a class="wiki_link" href="/75edo" target="_blank">75edo</a>, <a class="wiki_link" href="/104edo" target="_blank">104edo</a>, <a class="wiki_link" href="/109edo" target="_blank">109edo</a>, <a class="wiki_link" href="/121edo" target="_blank">121edo</a>, <a class="wiki_link" href="/145edo" target="_blank">133edo</a>, <a class="wiki_link" href="/155edo" target="_blank">155edo</a>, <a class="wiki_link" href="/162edo" target="_blank">162edo</a>, <a class="wiki_link" href="/167edo" target="_blank">167edo</a>, <a class="wiki_link" href="/179edo" target="_blank">179edo</a>, <a class="wiki_link" href="/191edo" target="_blank">191edo</a>, <a class="wiki_link" href="/201edo" target="_blank">201edo</a>, <a class="wiki_link" href="/213edo" target="_blank">213edo</a>, <a class="wiki_link" href="/225edo" target="_blank">225edo</a> and <a class="wiki_link" href="/237edo" target="_blank">237edo</a>, plus <a class="wiki_link" href="/63edo" target="_blank">63edo</a> and <a class="wiki_link" href="/80edo" target="_blank">80edo</a> in the extended region.<br />

<br />

@@ 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:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:05:38 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:06:49 UTC</tt>.<br>
-: The original revision id was <tt>602894908</tt>.<br>
+: The original revision id was <tt>602894936</tt>.<br>
-: The revision comment was: <tt>extract of current version</tt><br>
+: The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <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">// this is an externde version of the **[[Gentle region]] article. **//
+----
+[[@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 ||~   ||
@@ Line 114: / Line 116: @@
 +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 (extended version)&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 (extended version)&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt; this is an externde version of the &lt;strong&gt;&lt;a class="wiki_link" href="/Gentle%20region"&gt;Gentle region&lt;/a&gt; article. &lt;/strong&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;hr /&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;
 &lt;br /&gt;