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- | : 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> | : 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 > || 18.168 || | || ditonma || [[tel/1220703125|1220703125]] / [[tel/1207959552|1207959552]] || | -27 -2 13 > || 18.168 || | ||
|| [[misty comma]] || 67108864 / 66430125 || | 26 -12 -3 > || 17.599 || | || [[misty comma]] || 67108864 / 66430125 || | 26 -12 -3 > || 17.599 || | ||
|| [[graviton]], [[Gravity family|gravity]] comma || 129140163 / 128000000 || | -13 17 -6 > || 15.353 || | || [[Pental family|pental comma]] || 847288609443 / 838860800000 || |-28 25 -5> || 17.306 || | ||
|| quartonic || 390625000 / 387420489 || | 3 -18 11 > || 14.261 || | || [[graviton]], [[Gravity family|gravity]] comma || 129140163 / 128000000 || | -13 17 -6 > || 15.353 || | ||
|| quartonic || 390625000 / 387420489 || | 3 -18 11 > || 14.261 || | |||
|| medium semicomma, [[sensipent comma]] || 78732 / 78125 || | 2 9 -7 > || 13.399 || | || medium semicomma, [[sensipent comma]] || 78732 / 78125 || | 2 9 -7 > || 13.399 || | ||
|| [[Würschmidt comma]] || 393216 / 390625 || | 17 1 -8 > || 11.445 || | || [[Würschmidt comma]] || 393216 / 390625 || | 17 1 -8 > || 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"><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><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definition</h1> | ||
<br /> | <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, 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 /> | 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 /> | ||
<!-- 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> | ||
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</td> | </td> | ||
<td>17.599<br /> | <td>17.599<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/Pental%20family">pental comma</a><br /> | |||
</td> | |||
<td>847288609443 / 838860800000<br /> | |||
</td> | |||
<td>|-28 25 -5&gt;<br /> | |||
</td> | |||
<td>17.306<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>15.353<br /> | <td>15.353<br /> | ||
</td> | </td> | ||
<td><br /> | |||
</td> | |||
<td>quartonic<br /> | <td>quartonic<br /> | ||
</td> | </td> | ||
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<td>14.261<br /> | <td>14.261<br /> | ||
</td> | </td> | ||
<td><br /> | |||
</td> | |||
<td>medium semicomma, <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a><br /> | <td>medium semicomma, <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a><br /> | ||
</td> | </td> | ||