Small comma: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 541492912 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 555535495 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-02-19 16:15:49 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-07-20 15:54:12 UTC</tt>.<br>
: The original revision id was <tt>541492912</tt>.<br>
: The original revision id was <tt>555535495</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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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">=Definition=  
<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">=Definition=  


A **comma** is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is //[[tempering out|tempered out]]//, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s.
A **comma** is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is //[[tempering out|tempered out]]//, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s.


=List of commas, by prime limit=  
=List of commas, by prime limit=  
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|| ditonma || [[tel/1220703125|1220703125]] / [[tel/1207959552|1207959552]] || | -27 -2 13 &gt; || 18.168 ||
|| ditonma || [[tel/1220703125|1220703125]] / [[tel/1207959552|1207959552]] || | -27 -2 13 &gt; || 18.168 ||
|| [[misty comma]] || 67108864 / 66430125 || | 26 -12 -3 &gt; || 17.599 ||
|| [[misty comma]] || 67108864 / 66430125 || | 26 -12 -3 &gt; || 17.599 ||
|| [[graviton]], [[Gravity family|gravity]] comma || 129140163 / 128000000 || | -13 17 -6 &gt; || 15.353 ||
|| [[Pental family|pental comma]] || 847288609443 / 838860800000 || |-28 25 -5&gt; || 17.306 ||
|| quartonic || 390625000 / 387420489 || | 3 -18 11 &gt; || 14.261 ||
|| [[graviton]], [[Gravity family|gravity]] comma || 129140163 / 128000000 || | -13 17 -6 &gt; || 15.353 ||  
|| quartonic || 390625000 / 387420489 || | 3 -18 11 &gt; || 14.261 ||  
|| medium semicomma, [[sensipent comma]] || 78732 / 78125 || | 2 9 -7 &gt; || 13.399 ||
|| medium semicomma, [[sensipent comma]] || 78732 / 78125 || | 2 9 -7 &gt; || 13.399 ||
|| [[Würschmidt comma]] || 393216 / 390625 || | 17 1 -8 &gt; || 11.445 ||
|| [[Würschmidt comma]] || 393216 / 390625 || | 17 1 -8 &gt; || 11.445 ||
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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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Definition&lt;/h1&gt;
<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;Comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Definition&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
A &lt;strong&gt;comma&lt;/strong&gt; is a small interval that occurs in &lt;a class="wiki_link" href="/just%20intonation"&gt;just intonation&lt;/a&gt;, between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, generally in a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;low prime limit&lt;/a&gt;. The word is often used in reference to &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;regular tempering&lt;/a&gt; when the comma is &lt;em&gt;&lt;a class="wiki_link" href="/tempering%20out"&gt;tempered out&lt;/a&gt;&lt;/em&gt;, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by &lt;a class="wiki_link" href="/Meantone"&gt;meantone temperament&lt;/a&gt;. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
A &lt;strong&gt;comma&lt;/strong&gt; is a small interval that occurs in &lt;a class="wiki_link" href="/just%20intonation"&gt;just intonation&lt;/a&gt;, between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, and generally in a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;low prime limit&lt;/a&gt;. The word is often used in reference to &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;regular tempering&lt;/a&gt; when the comma is &lt;em&gt;&lt;a class="wiki_link" href="/tempering%20out"&gt;tempered out&lt;/a&gt;&lt;/em&gt;, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by &lt;a class="wiki_link" href="/Meantone"&gt;meantone temperament&lt;/a&gt;. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="List of commas, by prime limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;List of commas, by prime limit&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="List of commas, by prime limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;List of commas, by prime limit&lt;/h1&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17.599&lt;br /&gt;
         &lt;td&gt;17.599&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Pental%20family"&gt;pental comma&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;847288609443 / 838860800000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-28 25 -5&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17.306&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;15.353&lt;br /&gt;
         &lt;td&gt;15.353&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
    &lt;/tr&gt;
        &lt;td&gt;&lt;br /&gt;
    &lt;tr&gt;
&lt;/td&gt;
         &lt;td&gt;quartonic&lt;br /&gt;
         &lt;td&gt;quartonic&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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         &lt;td&gt;14.261&lt;br /&gt;
         &lt;td&gt;14.261&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
    &lt;/tr&gt;
        &lt;td&gt;&lt;br /&gt;
    &lt;tr&gt;
&lt;/td&gt;
         &lt;td&gt;medium semicomma, &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;medium semicomma, &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;