Xenharmonic Wiki

250/243: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 248657161 - Original comment: **
 
→Approximation: 24edo itself does not qualify as a chromium tuning
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| de = 250/243
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-26 12:35:12 UTC</tt>.<br>
| en = 250/243
: The original revision id was <tt>248657161</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
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>
{{Infobox Interval
<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">250/243, known as the porcupine comma or maximal diesis, is an interval of size 49.166 cents. It is the amount by which three [[10_9|minor whole tones]] exceed a fourth, that is, (10/9)^3/(4/3). Tempering it out leads to 5-limit [[Porcupine family|porcupine temperament]].</pre></div>
| Name = porcupine comma, maximal diesis
<h4>Original HTML content:</h4>
| Color name = y<sup>3</sup>1, triyo 1sn,<br>y<sup>3</sup>M, triyoma
<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;250_243&lt;/title&gt;&lt;/head&gt;&lt;body&gt;250/243, known as the porcupine comma or  maximal diesis, is an interval of size 49.166 cents. It is the amount by which three &lt;a class="wiki_link" href="/10_9"&gt;minor whole tones&lt;/a&gt; exceed a fourth, that is, (10/9)^3/(4/3). Tempering it out leads to 5-limit &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine temperament&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
| Comma = yes
}}
'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). It is also the difference between [[25/24]] and [[81/80]], the two smallest [[5-limit]] [[superparticular]] ratios, and between three syntonic commas and the [[2187/2048|Pythagorean apotome]], putting it on the [[Syntonic&ndash;chromatic equivalence continuum]].
 
== Temperaments ==
Tempering it out leads to the [[5-limit]] [[porcupine]] temperament. See [[porcupine family]] for the family of rank-2 temperaments where it is tempered out.  
 
== Approximation ==
250/243 is very close to one step of [[24edo]], which is the quarter tone that is exactly the half of [[12edo]] semitone. Therefore, if 250/243 is not tempered and instead is treated as an identity where it is equated with 1/24th of the octave, it serves as the period in the [[chromium]] temperament. (However, note that 24edo itself maps 250/243 inconsistently, and so chromium temperament starts at [[72edo]].) Thus in the framework of this temperament and the tuning systems associated with it, [[Eliora]] proposes the name ''chromium quartertone''.  
 
[[Category:Porcupine]]
[[Category:Commas named after compositions]]
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