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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 = 3125/3072 |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-24 15:41:58 UTC</tt>.<br>
| | | Name = magic comma, small diesis |
| : The original revision id was <tt>268062098</tt>.<br>
| | | Color name = Ly<sup>5</sup>-2, Laquinyo comma |
| : The revision comment was: <tt>Reverted to Aug 26, 2011 11:06 am</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>
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| <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]].</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>
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| <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"><html><head><title>magic comma</title></head><body>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 &quot;tritave&quot;; in other words (5/4)^5/3. Tempering it out leads to 5-limit <a class="wiki_link" href="/Magic%20family">magic temperament</a>.</body></html></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]] |