1953 scale: Difference between revisions

Wikispaces>MasonGreen1
**Imported revision 567552629 - Original comment: **
Wikispaces>MasonGreen1
**Imported revision 567554093 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-23 19:38:32 UTC</tt>.<br>
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-23 19:57:49 UTC</tt>.<br>
: The original revision id was <tt>567552629</tt>.<br>
: The original revision id was <tt>567554093</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 50: Line 50:
Approximations using the alternate (non-patent) val for 7 are shown with an asterisk (*).
Approximations using the alternate (non-patent) val for 7 are shown with an asterisk (*).


The 1953 scale, like the diatonic scale, possesses [[https://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's property]]. It is also strictly proper (whereas the 12-equal-tempered diatonic scale is proper, but not strictly proper).</pre></div>
The 1953 scale, like the diatonic scale, possesses [[https://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's property]]. It is also strictly proper (whereas the 12-equal-tempered diatonic scale is proper, but not strictly proper).
 
==Modes==
 
The most interesting modes are the ones that have both a perfect fifth and fourth above the root (neither being a wolf). There are seven such modes. They are:
 
* 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3
 
* 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3
&gt;
* 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3
&gt;
* 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3,
&gt;
* 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3,
&gt;
* 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3
&gt;
* 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2</pre></div>
<h4>Original HTML content:</h4>
<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;1953 scale&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;1953 scale&lt;/strong&gt; is my (Mason Green's) name for a nineteen-note subset of &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; (a MOS). It is a 15L+4S scale (it has 15 long intervals 3 &lt;a class="wiki_link" href="/Holdrian%20comma"&gt;Holdrian commas&lt;/a&gt; wide, plus 4 short intervals 2 Holdrians wide).&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;1953 scale&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;1953 scale&lt;/strong&gt; is my (Mason Green's) name for a nineteen-note subset of &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; (a MOS). It is a 15L+4S scale (it has 15 long intervals 3 &lt;a class="wiki_link" href="/Holdrian%20comma"&gt;Holdrian commas&lt;/a&gt; wide, plus 4 short intervals 2 Holdrians wide).&lt;br /&gt;
Line 354: Line 372:
Approximations using the alternate (non-patent) val for 7 are shown with an asterisk (*).&lt;br /&gt;
Approximations using the alternate (non-patent) val for 7 are shown with an asterisk (*).&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The 1953 scale, like the diatonic scale, possesses &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow"&gt;Myhill's property&lt;/a&gt;. It is also strictly proper (whereas the 12-equal-tempered diatonic scale is proper, but not strictly proper).&lt;/body&gt;&lt;/html&gt;</pre></div>
The 1953 scale, like the diatonic scale, possesses &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow"&gt;Myhill's property&lt;/a&gt;. It is also strictly proper (whereas the 12-equal-tempered diatonic scale is proper, but not strictly proper).&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Modes&lt;/h2&gt;
&lt;br /&gt;
The most interesting modes are the ones that have both a perfect fifth and fourth above the root (neither being a wolf). There are seven such modes. They are:&lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3&lt;br /&gt;
&lt;br /&gt;
&lt;/li&gt;&lt;li&gt;3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3&lt;br /&gt;
&lt;br /&gt;
&lt;/li&gt;&lt;li&gt;3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3,&lt;br /&gt;
&lt;br /&gt;
&lt;/li&gt;&lt;li&gt;3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3,&lt;br /&gt;
&lt;br /&gt;
&lt;/li&gt;&lt;li&gt;3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3&lt;br /&gt;
&lt;br /&gt;
&lt;/li&gt;&lt;li&gt;3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>