1953 scale: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 567552629 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 567554093 - Original comment: ** |
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<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: | : 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> | : 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> | ||
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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 | |||
> | |||
* 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3 | |||
> | |||
* 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, | |||
> | |||
* 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, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3 | |||
> | |||
* 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"><html><head><title>1953 scale</title></head><body>The <strong>1953 scale</strong> is my (Mason Green's) name for a nineteen-note subset of <a class="wiki_link" href="/53edo">53edo</a> (a MOS). It is a 15L+4S scale (it has 15 long intervals 3 <a class="wiki_link" href="/Holdrian%20comma">Holdrian commas</a> wide, plus 4 short intervals 2 Holdrians wide).<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>1953 scale</title></head><body>The <strong>1953 scale</strong> is my (Mason Green's) name for a nineteen-note subset of <a class="wiki_link" href="/53edo">53edo</a> (a MOS). It is a 15L+4S scale (it has 15 long intervals 3 <a class="wiki_link" href="/Holdrian%20comma">Holdrian commas</a> wide, plus 4 short intervals 2 Holdrians wide).<br /> | ||
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Approximations using the alternate (non-patent) val for 7 are shown with an asterisk (*).<br /> | Approximations using the alternate (non-patent) val for 7 are shown with an asterisk (*).<br /> | ||
<br /> | <br /> | ||
The 1953 scale, like the diatonic scale, possesses <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's property</a>. It is also strictly proper (whereas the 12-equal-tempered diatonic scale is proper, but not strictly proper).</body></html></pre></div> | The 1953 scale, like the diatonic scale, possesses <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's property</a>. It is also strictly proper (whereas the 12-equal-tempered diatonic scale is proper, but not strictly proper).<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Modes"></a><!-- ws:end:WikiTextHeadingRule:0 -->Modes</h2> | |||
<br /> | |||
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:<br /> | |||
<br /> | |||
<ul><li>3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3</li></ul><br /> | |||
<ul><li>3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3<br /> | |||
<br /> | |||
</li><li>3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3<br /> | |||
<br /> | |||
</li><li>3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3,<br /> | |||
<br /> | |||
</li><li>3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3,<br /> | |||
<br /> | |||
</li><li>3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3<br /> | |||
<br /> | |||
</li><li>3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2</li></ul></body></html></pre></div> | |||