Small comma: Difference between revisions
Wikispaces>genewardsmith **Imported revision 556966951 - Original comment: ** |
Wikispaces>hstraub **Imported revision 557014151 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-20 02:18:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>557014151</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;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"><span style="display: block; text-align: right;">[[xenharmonie/Komma|Deutsch]] | ||
</span> | |||
=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, 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. | 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. | ||
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=List of commas, by prime limit= | =List of commas, by prime limit= | ||
==3-limit commas== | ==3-limit commas== | ||
||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||
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==5-limit commas== | ==5-limit commas== | ||
||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||
|| Twenty-two thirds limma | || Twenty-two thirds limma || || | -51 0 22 > || 98.902 || | ||
|| sibbolet || || | -58 0 25 > || 57.843 || | || sibbolet || || | -58 0 25 > || 57.843 || | ||
|| Hunt 5-cycle comma || || | -65 0 28 > || 16.784 || | || Hunt 5-cycle comma || || | -65 0 28 > || 16.784 || | ||
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|| titania || || | [[tel/2746 -521 -827|2746 -521 -827]] > || 0.003183 || | || titania || || | [[tel/2746 -521 -827|2746 -521 -827]] > || 0.003183 || | ||
|| quark || || | -537 237 85 > || 0.000884 || | || quark || || | -537 237 85 > || 0.000884 || | ||
|| scamp || | || scamp || || |-5836 4293 -417> || 0.000033 || | ||
|| rover || || | 1634 1502 -1729 > || 0.000028 || | || rover || || | 1634 1502 -1729 > || 0.000028 || | ||
|| rascal || || | -7470 2791 1312 > || 0.000006 || | || rascal || || | -7470 2791 1312 > || 0.000006 || | ||
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|| termite || 37252902984619140625000000000 / 37252879910233655318543787489 || | 9 -28 37 -18 > || 0.001072 || | || termite || 37252902984619140625000000000 / 37252879910233655318543787489 || | 9 -28 37 -18 > || 0.001072 || | ||
|| neutrino || || | 1889 -2145 138 424 > || 1.636 * 10^-10 || | || neutrino || || | 1889 -2145 138 424 > || 1.636 * 10^-10 || | ||
==11-limit commas== | ==11-limit commas== | ||
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|| animist || 105 / 104 || | -3 1 1 1 0 1 > || 16.567 || | || animist || 105 / 104 || | -3 1 1 1 0 1 > || 16.567 || | ||
|| secorian || 28672 / 28431 || | [[tel/12 -7 0 1 0 -1|12 -7 0 1 0 -1]] > || 14.613 || | || secorian || 28672 / 28431 || | [[tel/12 -7 0 1 0 -1|12 -7 0 1 0 -1]] > || 14.613 || | ||
|| mosaic || 3159 / 3136 || | || mosaic || 3159 / 3136 || |-6 5 0 -2 0 1> || 12.651 || | ||
|| gassorma || 275 / 273 || | 0 -1 2 -1 1 -1 > || 12.637 || | || gassorma || 275 / 273 || | 0 -1 2 -1 1 -1 > || 12.637 || | ||
|| [[grossma]] || 144 / 143 || | 4 2 0 0 -1 -1 > || 12.064 || | || [[grossma]] || 144 / 143 || | 4 2 0 0 -1 -1 > || 12.064 || | ||
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[[media type="custom" key="25699772"]]</pre></div> | [[media type="custom" key="25699772"]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>Comma</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definition</h1> | <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>Comma</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Komma">Deutsch</a><br /> | ||
</span><br /> | |||
A <strong>comma</strong> is a small interval that occurs in <a class="wiki_link" href="/just%20intonation">just intonation</a>, 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 <a class="wiki_link" href="/Harmonic%20Limit">low prime limit</a>. The word is often used in reference to <a class="wiki_link" href="/Regular%20Temperaments">regular tempering</a> when the comma is <em><a class="wiki_link" href="/tempering%20out">tempered out</a></em>, 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 <a class="wiki_link" href="/Meantone">meantone temperament</a>. 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 <a class="wiki_link" href="/cent">cent</a>s.<br /> | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definition</h1> | ||
A <strong>comma</strong> is a small interval that occurs in <a class="wiki_link" href="/just%20intonation">just intonation</a>, 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 <a class="wiki_link" href="/Harmonic%20Limit">low prime limit</a>. The word is often used in reference to <a class="wiki_link" href="/Regular%20Temperaments">regular tempering</a> when the comma is <em><a class="wiki_link" href="/tempering%20out">tempered out</a></em>, 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 <a class="wiki_link" href="/Meantone">meantone temperament</a>. 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 <a class="wiki_link" href="/cent">cent</a>s.<br /> | |||
<br /> | <br /> | ||
For commas over 100 cents in size, see <a class="wiki_link" href="/Large%20commas">Large commas</a><br /> | For commas over 100 cents in size, see <a class="wiki_link" href="/Large%20commas">Large commas</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="List of commas, by prime limit"></a><!-- ws:end:WikiTextHeadingRule:3 -->List of commas, by prime limit</h1> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="List of commas, by prime limit"></a><!-- ws:end:WikiTextHeadingRule:3 -->List of commas, by prime limit</h1> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="List of commas, by prime limit-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:5 -->3-limit commas</h2> | |||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="List of commas, by prime limit-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:5 -->3-limit commas</h2> | |||
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</table> | </table> | ||
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<!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="List of commas, by prime limit-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->11-limit commas</h2> | <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="List of commas, by prime limit-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->11-limit commas</h2> | ||