Semicomma: Difference between revisions

The semicomma or Fokker's comma (ratio: 2109375/2097152, monzo: [-21 3 7⟩), is a small 5-limit comma of 10.061 cents which is the amount by which three classic augmented second intervals of 75/64 exceed 8/5. That means (75/64)³/(8/5), which can also be written ((9/8)(25/24))³/(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 (3³¹/2⁴⁹) and seven syntonic commas (81/80).

Temperaments

Tempering out this comma in the 5-limit leads to the orson temperament.

Name

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 "Fokker's comma" comes from Adriaan Fokker.

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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, <br>orson comma, <br>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>
+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]]).
-<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>
-<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;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>
+[[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament.
+== Name ==
+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 "Fokker's comma" comes from [[Adriaan Fokker]].
+== See also ==
+Intervals with the word "semicomma" in the name:
+* Medium semicomma, aka [[sensipent comma]]
+* Septimal semicomma, aka [[126/125|starling comma]]
+* Semicomma majeur, aka [[15625/15552|kleisma]]
+[[Category:Orson]]
+[[Category:Commas with unknown etymology]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]
+{{Todo|add etymology|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}

Semicomma: Difference between revisions

Latest revision as of 06:41, 25 June 2025

Temperaments

Name

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