Magic comma: Difference between revisions

The magic comma or small diesis is the interval 3125/3072. It is the amount by which five major thirds (5/4) exceeds the twelfth, or tritave; in other words (5/4)⁵/3, the amount by which two chromatic semitones of 25/24 exceed a diatonic semitone of 16/15, and the amount by which 25/24 exceeds the lesser diesis of 128/125.

In 12edo, instead of being tempered out, it is inflated to a whole semitone—five 5/4s make a minor thirteenth (20 steps), while 3/1 is a perfect twelfth (19 steps). Similarly, 25/24 and 16/15 are both mapped to one semitone, making a stack of two 25/24s one semitone larger than 16/15, and 25/24 is mapped to one step while 128/125 is tempered out.

Temperaments

Tempering it out leads to 5-limit magic temperament.

@@ Line 1: / Line 1: @@
-<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 = 3125/3072
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-24 15:31:48 UTC</tt>.<br>
+| Name = magic comma, small diesis
-: The original revision id was <tt>268058106</tt>.<br>
+| Color name = Ly<sup>5</sup>-2, Laquinyo comma
-: The revision comment was: <tt></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>
-<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">The magic comma or small diesis is the interval 3125/3072 of 29.614 cents. It is the amount by which five major thirds exceeds the twelfth, or "tritave"; in other words (5/4)^5/3. Tempering it out leads to 5-limit [[Magic family|magic temperament]], also known as astrology.</pre></div>
+The '''magic comma''' or '''small diesis''' is the interval '''3125/3072'''. It is the amount by which five major thirds ([[5/4]]) exceeds the twelfth, or ''[[tritave]]''; in other words (5/4)<sup>5</sup>/3, the amount by which two chromatic semitones of 25/24 exceed a diatonic semitone of 16/15, and the amount by which 25/24 exceeds the lesser diesis of [[128/125]].
-<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;magic comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The magic comma or small diesis is the interval 3125/3072 of 29.614 cents. It is the amount by which five major thirds exceeds the twelfth, or &amp;quot;tritave&amp;quot;; in other words (5/4)^5/3. Tempering it out leads to 5-limit &lt;a class="wiki_link" href="/Magic%20family"&gt;magic temperament&lt;/a&gt;, also known as astrology.&lt;/body&gt;&lt;/html&gt;</pre></div>
+In 12edo, instead of being tempered out, it is inflated to a whole semitone—five 5/4s make a minor thirteenth (20 steps), while 3/1 is a perfect twelfth (19 steps). Similarly, 25/24 and 16/15 are both mapped to one semitone, making a stack of two 25/24s one semitone larger than 16/15, and 25/24 is mapped to one step while 128/125 is tempered out.
+== Temperaments ==
+Tempering it out leads to [[Magic family #Five-limit magic|5-limit magic temperament]].
+== See also ==
+* [[Magic family]], where it is tempered out
+* [[Small comma]]
+[[Category:Magic]]
+[[Category:Commas named for their regular temperament properties]]

Magic comma: Difference between revisions

Latest revision as of 22:24, 19 March 2025

Temperaments

See also

Navigation menu

Search