Reversed meantone: Difference between revisions

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**Imported revision 336215312 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
=REVERSE MEANTONE!=
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-05-16 19:00:01 UTC</tt>.<br>
: The original revision id was <tt>336215312</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">=REVERSE MEANTONE!=  


As meantone is based on the syntonic comma, 81/80, tempering the fifth flat, tempering 82/81 instead results in a sharper fifth, and a major third equivalent to the 41st harmonic instead of the 5th, so it might as well be called reverse meantone. The 41st is very delicate however and mistuning by several cents destroys it, so if its use is intended as more than a joke exact quarter comma tempering is best, although 39edo does a fair job.
As meantone is based on the syntonic comma, 81/80, tempering the fifth flat, tempering 82/81 instead results in a sharper fifth, and a major third equivalent to the 41st harmonic instead of the 5th, so it might as well be called reverse meantone. The 41st is very delicate however and mistuning by several cents destroys it, so if its use is intended as more than a joke exact quarter comma tempering is best, although 39edo does a fair job.


Related to this idea, 162/161 is a 23-limit comma (specifically 161=7*23), and 163/162 being prime would indeed be ridiculous.</pre></div>
Related to this idea, 162/161 is a 23-limit comma (specifically 161=7*23), and 163/162 being prime would indeed be ridiculous.
<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;Reverse Meantone&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="REVERSE MEANTONE!"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;REVERSE MEANTONE!&lt;/h1&gt;
&lt;br /&gt;
As meantone is based on the syntonic comma, 81/80, tempering the fifth flat, tempering 82/81 instead results in a sharper fifth, and a major third equivalent to the 41st harmonic instead of the 5th, so it might as well be called reverse meantone. The 41st is very delicate however and mistuning by several cents destroys it, so if its use is intended as more than a joke exact quarter comma tempering is best, although 39edo does a fair job.&lt;br /&gt;
&lt;br /&gt;
Related to this idea, 162/161 is a 23-limit comma (specifically 161=7*23), and 163/162 being prime would indeed be ridiculous.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

REVERSE MEANTONE!

As meantone is based on the syntonic comma, 81/80, tempering the fifth flat, tempering 82/81 instead results in a sharper fifth, and a major third equivalent to the 41st harmonic instead of the 5th, so it might as well be called reverse meantone. The 41st is very delicate however and mistuning by several cents destroys it, so if its use is intended as more than a joke exact quarter comma tempering is best, although 39edo does a fair job.

Related to this idea, 162/161 is a 23-limit comma (specifically 161=7*23), and 163/162 being prime would indeed be ridiculous.

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