118edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
''118edo'' divides the octave into 118 equal parts, each of 10.17 cents. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1&gt; and the parakleisma, |8 14 -13&gt;, as well as the vishnuzma, |23 6 -14&gt;, the hemithirds comma, |38 -2 -15&gt; and the kwazy, |-53 10 16&gt;. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-04 18:08:36 UTC</tt>.<br>
: The original revision id was <tt>342593762</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">//118edo// divides the octave into 118 equal parts, each of 10.17 cents. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1&gt; and the parakleisma, |8 14 -13&gt;, as well as the vishnuzma, |23 6 -14&gt;, the hemithirds comma, |38 -2 -15&gt; and the kwazy, |-53 10 16&gt;. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.


In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo]] does better with that.
In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo|99edo]] does better with that.


In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.</pre></div>
In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.
<h4>Original HTML content:</h4>
[[Category:edo]]
<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;118edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;118edo&lt;/em&gt; divides the octave into 118 equal parts, each of 10.17 cents. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1&amp;gt; and the parakleisma, |8 14 -13&amp;gt;, as well as the vishnuzma, |23 6 -14&amp;gt;, the hemithirds comma, |38 -2 -15&amp;gt; and the kwazy, |-53 10 16&amp;gt;. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.&lt;br /&gt;
[[Category:gamelisma]]
&lt;br /&gt;
[[Category:guiron]]
In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; does better with that.&lt;br /&gt;
[[Category:parakleismic]]
&lt;br /&gt;
[[Category:portent]]
In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:schismic]]

Revision as of 00:00, 17 July 2018

118edo divides the octave into 118 equal parts, each of 10.17 cents. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1> and the parakleisma, |8 14 -13>, as well as the vishnuzma, |23 6 -14>, the hemithirds comma, |38 -2 -15> and the kwazy, |-53 10 16>. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.

In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but 99edo does better with that.

In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.

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