23-limit: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
In 23-limit [[Just_intonation|Just Intonation]], all ratios contain no prime factors higher than 23.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-01 18:33:38 UTC</tt>.<br>
: The original revision id was <tt>349425850</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">In 23-limit [[Just Intonation]], all ratios contain no prime factors higher than 23.


Ratios of 23 in the 23-odd limit include:
Ratios of 23 in the 23-odd limit include:


24/23 .. 73.681¢
24/23 .. 73.681¢
23/22 .. 76.956¢
23/22 .. 76.956¢
23/21 .. 157.493¢
23/21 .. 157.493¢
26/23 .. 212.253¢
26/23 .. 212.253¢
23/20 .. 241.961¢
23/20 .. 241.961¢
23/19 .. 330.761¢
23/19 .. 330.761¢
28/23 .. 340.552¢
28/23 .. 340.552¢
23/18 .. 424.364¢
23/18 .. 424.364¢
30/23 .. 459.994¢
30/23 .. 459.994¢
23/17 .. 523.319¢
23/17 .. 523.319¢
23/16 .. 628.274¢
23/16 .. 628.274¢
34/23 .. 676.681¢
34/23 .. 676.681¢
32/23 .. 571.726¢
32/23 .. 571.726¢
23/15 .. 740.006¢
23/15 .. 740.006¢
36/23 .. 775.636¢
36/23 .. 775.636¢
23/14 .. 859.448¢
23/14 .. 859.448¢
38/23 .. 869.239¢
38/23 .. 869.239¢
40/23 .. 958.039¢
40/23 .. 958.039¢
23/13 .. 987.747¢
23/13 .. 987.747¢
42/23 ..1042.507¢
42/23 ..1042.507¢
44/23 .. 1123.044¢
44/23 .. 1123.044¢
23/12 .. 1126.391¢
23/12 .. 1126.391¢


[[94edo]] is the first [[EDO]] to be consistent in the 23-limit. The smallest EDO where the 23-limit is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]].
[[94edo|94edo]] is the first [[EDO|EDO]] to be consistent in the 23-limit. The smallest EDO where the 23-limit is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo|282edo]].


See: [[Harmonic Limit]], [[19-limit]], [[17-limit]]</pre></div>
See: [[Harmonic_Limit|Harmonic Limit]], [[19-limit|19-limit]], [[17-limit|17-limit]]     [[Category:23-limit]]
<h4>Original HTML content:</h4>
[[Category:limit]]
<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;23-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In 23-limit &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, all ratios contain no prime factors higher than 23.&lt;br /&gt;
[[Category:prime_limit]]
&lt;br /&gt;
[[Category:rank_9]]
Ratios of 23 in the 23-odd limit include:&lt;br /&gt;
&lt;br /&gt;
24/23 .. 73.681¢&lt;br /&gt;
23/22 .. 76.956¢&lt;br /&gt;
23/21 .. 157.493¢&lt;br /&gt;
26/23 .. 212.253¢&lt;br /&gt;
23/20 .. 241.961¢&lt;br /&gt;
23/19 .. 330.761¢&lt;br /&gt;
28/23 .. 340.552¢&lt;br /&gt;
23/18 .. 424.364¢&lt;br /&gt;
30/23 .. 459.994¢&lt;br /&gt;
23/17 .. 523.319¢&lt;br /&gt;
23/16 .. 628.274¢&lt;br /&gt;
34/23 .. 676.681¢&lt;br /&gt;
32/23 .. 571.726¢&lt;br /&gt;
23/15 .. 740.006¢&lt;br /&gt;
36/23 .. 775.636¢&lt;br /&gt;
23/14 .. 859.448¢&lt;br /&gt;
38/23 .. 869.239¢&lt;br /&gt;
40/23 .. 958.039¢&lt;br /&gt;
23/13 .. 987.747¢&lt;br /&gt;
42/23 ..1042.507¢&lt;br /&gt;
44/23 .. 1123.044¢&lt;br /&gt;
23/12 .. 1126.391¢&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt; is the first &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; to be consistent in the 23-limit. The smallest EDO where the 23-limit is distinctly consistent, meaning each element of the tonality diamond is distinguished, is &lt;a class="wiki_link" href="/282edo"&gt;282edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;Harmonic Limit&lt;/a&gt;, &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

In 23-limit Just Intonation, all ratios contain no prime factors higher than 23.

Ratios of 23 in the 23-odd limit include:

24/23 .. 73.681¢

23/22 .. 76.956¢

23/21 .. 157.493¢

26/23 .. 212.253¢

23/20 .. 241.961¢

23/19 .. 330.761¢

28/23 .. 340.552¢

23/18 .. 424.364¢

30/23 .. 459.994¢

23/17 .. 523.319¢

23/16 .. 628.274¢

34/23 .. 676.681¢

32/23 .. 571.726¢

23/15 .. 740.006¢

36/23 .. 775.636¢

23/14 .. 859.448¢

38/23 .. 869.239¢

40/23 .. 958.039¢

23/13 .. 987.747¢

42/23 ..1042.507¢

44/23 .. 1123.044¢

23/12 .. 1126.391¢

94edo is the first EDO to be consistent in the 23-limit. The smallest EDO where the 23-limit is distinctly consistent, meaning each element of the tonality diamond is distinguished, is 282edo.

See: Harmonic Limit, 19-limit, 17-limit

Retrieved from "https://en.xen.wiki/index.php?title=23-limit&oldid=467"