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Mystery comma: Difference between revisions

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**Imported revision 554926425 - Original comment: fixed - contained info copy/pasted from 41-comma**
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Ratio = 70368744177664/68630377364883
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2015-07-04 17:35:57 UTC</tt>.<br>
| Name = mystery comma, 29-comma, Pythagorean quadruple-diminished fourth, Pythagorean tridietic semilimma
: The original revision id was <tt>554926425</tt>.<br>
| Color name = Wa-29, s<sup>4</sup>w4
: The revision comment was: <tt>fixed - contained info copy/pasted from 41-comma</tt><br>
| Comma = yes
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>
'''{{monzo|46 -29}}''', the '''mystery comma''' or '''29-comma''' of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 2<sup>46</sup>/3<sup>29</sup>. When treated as an interval in its own right, there are actually two very good descriptive names for this interval.  Firstly, and most obviously, it can be called the '''Pythagorean quadruple-diminished fourth''', however, because it is also almost exactly half of the traditional [[Pythagorean limma]] (a stack of two mystery commas differing from the limma by [[Mercator's comma]]) in addition to being displaced from the unison's scale degree by three, one can also call this interval the '''Pythagorean tridietic semilimma'''.
<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">|46 -29&gt;, the 29-comma of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 2^46/3^29. It is tempered out by [[29edo]].</pre></div>
 
<h4>Original HTML content:</h4>
== Temperaments ==
<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;29-comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;|46 -29&amp;gt;, the 29-comma of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 2^46/3^29. It is tempered out by &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
Tempering out this comma splits the octave into 29 equal parts and maps the harmonic 3 to 17\29, leading to the 5-limit version of [[Mystery|mystery temperament]]. For EDOs up to 400, the 29-comma is tempered out if and only if 29 divides it, for example [[29edo]], [[58edo]] or [[87edo]].  
 
== See also ==
* [[Medium comma]]
* [[29th-octave temperaments]]
 
[[Category:29edo]]
[[Category:Mystery]]
[[Category:Commas with unknown etymology]]
Retrieved from "https://en.xen.wiki/w/Mystery_comma"