Xenharmonic Wiki

Semicomma: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 248728077 - Original comment: **
 
m Recategorize todo
 
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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 = 2109375/2097152
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-26 19:41:27 UTC</tt>.<br>
| Name = semicomma, orson comma, Fokker's comma
: The original revision id was <tt>248728077</tt>.<br>
| Color name = Ly<sup>7</sup>-3, Lasepyo 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>
{{Wikipedia}}
<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">2109375/2097152 = |-21 3 7&gt;, called the semicomma or Fokker comma, is an interval of 10.061 cents which is the amount by which three 75/64 intervals exceed 8/5. That means (75/64)^3/(8/5), which can also be written ((9/8)*(25/24))^3/(8/5). Tempering it out leads to [[Orson|orson temperament]].</pre></div>
The '''semicomma''' or '''Fokker's comma''' ([[ratio]]: 2109375/2097152, [[monzo]]: {{monzo| -21 3 7 }}), is a [[small comma|small]] [[5-limit]] [[comma]] of 10.061 [[cent]]s which is the amount by which three classic augmented second intervals of [[75/64]] exceed [[8/5]]. That means (75/64)<sup>3</sup>/(8/5), which can also be written ((9/8)(25/24))<sup>3</sup>/(8/5). In terms of commas, it factors into simpler commas as ([[15625/15552]])([[32805/32768]]), the kleisma and the schisma. It is also the difference between the [[31-comma]] ({{nowrap|3<sup>31</sup>/2<sup>49</sup>}}) and seven syntonic commas ([[81/80]]).
<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;semicomma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;2109375/2097152 = |-21 3 7&amp;gt;, called the semicomma or Fokker comma, is an interval of 10.061 cents which is the amount by which three 75/64 intervals exceed 8/5. That means (75/64)^3/(8/5), which can also be written ((9/8)*(25/24))^3/(8/5). Tempering it out leads to &lt;a class="wiki_link" href="/Orson"&gt;orson temperament&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
== Temperaments ==
[[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament.
 
== Etymology ==
Given the other intervals called "semicomma", it is likely that "semicomma" refers to the comma's size as about half the size of the syntonic comma. The name "semicomma" was given by [[Adriaan Fokker]], while the name "Fokker's comma" refers to him directly and was likely proposed later.
 
== See also ==
* [[126/125]] (aka starling comma or septimal semicomma)
* [[15625/15552]] (aka kleisma or semicomma majeur)
* [[Sensipent comma]] (78732/78125, aka medium semicomma)
 
== External links ==
* [http://tonalsoft.com/enc/s/semicomma.aspx Semicomma] on [[Tonalsoft Encyclopedia]]
 
[[Category:Orson]]
[[Category:Commas with unknown etymology]]
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]
{{Todo|research|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}
Retrieved from "https://en.xen.wiki/w/Semicomma"