Small comma: Difference between revisions
Wikispaces>genewardsmith **Imported revision 241222871 - Original comment: ** |
Wikispaces>igliashon **Imported revision 241605851 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:igliashon|igliashon]] and made on <tt>2011-07-16 17:28:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>241605851</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"> | <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. | |||
==List of commas, by prime limit== | |||
===3-limit commas=== | |||
256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 [[cent]]s) | 256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 [[cent]]s) | ||
2187 / 2048 = |-11 7>: apotome (113.685 cents) | 2187 / 2048 = |-11 7>: apotome (113.685 cents) | ||
| Line 20: | Line 22: | ||
|-1054 665>: Satanic comma (0.076 cents) | |-1054 665>: Satanic comma (0.076 cents) | ||
==5-limit commas== | ===5-limit commas=== | ||
[[135_128|135 / 128]] = |-7 3 1>: [[major chroma]], [[major limma]], [[pelogic comma]] (92.179 [[cent]]s) | [[135_128|135 / 128]] = |-7 3 1>: [[major chroma]], [[major limma]], [[pelogic comma]] (92.179 [[cent]]s) | ||
5000000 / 4782969 = |6 -14 7>: sevond (76.826 cents) | 5000000 / 4782969 = |6 -14 7>: sevond (76.826 cents) | ||
| Line 74: | Line 75: | ||
|161 -84 -12>: atom (0.015 cents) | |161 -84 -12>: atom (0.015 cents) | ||
==7-limit commas== | ===7-limit commas=== | ||
1029 / 1000 = |-3 1 -3 3>: keega (49.492 [[cent]]s) | 1029 / 1000 = |-3 1 -3 3>: keega (49.492 [[cent]]s) | ||
36 / 35 = |2 2 -1 -1>: septimal quarter tone (48.770 cents) | 36 / 35 = |2 2 -1 -1>: septimal quarter tone (48.770 cents) | ||
| Line 113: | Line 113: | ||
250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents) | 250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents) | ||
==11-limit commas== | ===11-limit commas=== | ||
99 / 98 = |-1 2 0 -2 1>: mothwellsma (17.576 cents) | 99 / 98 = |-1 2 0 -2 1>: mothwellsma (17.576 cents) | ||
100 / 99 = |2 -2 2 0 -1>: ptolemisma (17.399 cents) | 100 / 99 = |2 -2 2 0 -1>: ptolemisma (17.399 cents) | ||
| Line 135: | Line 134: | ||
3294225 / 3294172 = |-2 2 2 -7 4>: ultimo (0.028 cents) | 3294225 / 3294172 = |-2 2 2 -7 4>: ultimo (0.028 cents) | ||
==13-limit commas== | ===13-limit commas=== | ||
78 / 77 = |1 1 0 -1 -1 1>: negustma (22.229 cents) | 78 / 77 = |1 1 0 -1 -1 1>: negustma (22.229 cents) | ||
91 / 90 = |-1 -2 -1 1 0 1>: superleap (19.130 cents) | 91 / 90 = |-1 -2 -1 1 0 1>: superleap (19.130 cents) | ||
| Line 145: | Line 143: | ||
676 / 675 = |2 -3 -2 0 0 2>: [[The Archipelago|parizeksma]] (2.563 cents)</pre></div> | 676 / 675 = |2 -3 -2 0 0 2>: [[The Archipelago|parizeksma]] (2.563 cents)</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>A <strong>comma</strong> is a small | <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:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Definition"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition</h2> | ||
<br /> | |||
A <strong>comma</strong> 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 <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.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-List of commas, by prime limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->List of commas, by prime limit</h2> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-List of commas, by prime limit-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->3-limit commas</h3> | |||
256 / 243 = |8 -5&gt;: limma or Pythagorean minor second (90.225 <a class="wiki_link" href="/cent">cent</a>s)<br /> | 256 / 243 = |8 -5&gt;: limma or Pythagorean minor second (90.225 <a class="wiki_link" href="/cent">cent</a>s)<br /> | ||
2187 / 2048 = |-11 7&gt;: apotome (113.685 cents)<br /> | 2187 / 2048 = |-11 7&gt;: apotome (113.685 cents)<br /> | ||
531441 / 524288 = |-19 12&gt;: Pythagorean comma (23.460 cents)<br /> | 531441 / 524288 = |-19 12&gt;: Pythagorean comma (23.460 cents)<br /> | ||
| Line 159: | Line 159: | ||
|-1054 665&gt;: Satanic comma (0.076 cents)<br /> | |-1054 665&gt;: Satanic comma (0.076 cents)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-List of commas, by prime limit-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->5-limit commas</h3> | ||
<a class="wiki_link" href="/135_128">135 / 128</a> = |-7 3 1&gt;: <a class="wiki_link" href="/major%20chroma">major chroma</a>, <a class="wiki_link" href="/major%20limma">major limma</a>, <a class="wiki_link" href="/pelogic%20comma">pelogic comma</a> (92.179 <a class="wiki_link" href="/cent">cent</a>s)<br /> | |||
<a class="wiki_link" href="/135_128">135 / 128</a> = |-7 3 1&gt;: <a class="wiki_link" href="/major%20chroma">major chroma</a>, <a class="wiki_link" href="/major%20limma">major limma</a>, <a class="wiki_link" href="/pelogic%20comma">pelogic comma</a> (92.179 <a class="wiki_link" href="/cent">cent</a>s)<br /> | |||
5000000 / 4782969 = |6 -14 7&gt;: sevond (76.826 cents)<br /> | 5000000 / 4782969 = |6 -14 7&gt;: sevond (76.826 cents)<br /> | ||
25 /24 = |-3 -1 2&gt;: chromatic semitone (70.672 cents)<br /> | 25 /24 = |-3 -1 2&gt;: chromatic semitone (70.672 cents)<br /> | ||
| Line 213: | Line 212: | ||
|161 -84 -12&gt;: atom (0.015 cents)<br /> | |161 -84 -12&gt;: atom (0.015 cents)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-List of commas, by prime limit-7-limit commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->7-limit commas</h3> | ||
1029 / 1000 = |-3 1 -3 3&gt;: keega (49.492 <a class="wiki_link" href="/cent">cent</a>s)<br /> | |||
1029 / 1000 = |-3 1 -3 3&gt;: keega (49.492 <a class="wiki_link" href="/cent">cent</a>s)<br /> | |||
36 / 35 = |2 2 -1 -1&gt;: septimal quarter tone (48.770 cents)<br /> | 36 / 35 = |2 2 -1 -1&gt;: septimal quarter tone (48.770 cents)<br /> | ||
525 / 512 = |-9 1 2 1&gt;: avicennma, Avicenna's enharmonic diesis (43.408 cents)<br /> | 525 / 512 = |-9 1 2 1&gt;: avicennma, Avicenna's enharmonic diesis (43.408 cents)<br /> | ||
| Line 252: | Line 250: | ||
250047 / 250000 = |-4 6 -6 3&gt;: landscape comma (0.325 cents)<br /> | 250047 / 250000 = |-4 6 -6 3&gt;: landscape comma (0.325 cents)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-List of commas, by prime limit-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit commas</h3> | ||
99 / 98 = |-1 2 0 -2 1&gt;: mothwellsma (17.576 cents)<br /> | |||
99 / 98 = |-1 2 0 -2 1&gt;: mothwellsma (17.576 cents)<br /> | |||
100 / 99 = |2 -2 2 0 -1&gt;: ptolemisma (17.399 cents)<br /> | 100 / 99 = |2 -2 2 0 -1&gt;: ptolemisma (17.399 cents)<br /> | ||
121 / 120 = |-3 -1 -1 0 2&gt;: biyatisma (14.367 cents)<br /> | 121 / 120 = |-3 -1 -1 0 2&gt;: biyatisma (14.367 cents)<br /> | ||
| Line 274: | Line 271: | ||
3294225 / 3294172 = |-2 2 2 -7 4&gt;: ultimo (0.028 cents)<br /> | 3294225 / 3294172 = |-2 2 2 -7 4&gt;: ultimo (0.028 cents)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-List of commas, by prime limit-13-limit commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit commas</h3> | ||
78 / 77 = |1 1 0 -1 -1 1&gt;: negustma (22.229 cents)<br /> | |||
78 / 77 = |1 1 0 -1 -1 1&gt;: negustma (22.229 cents)<br /> | |||
91 / 90 = |-1 -2 -1 1 0 1&gt;: superleap (19.130 cents)<br /> | 91 / 90 = |-1 -2 -1 1 0 1&gt;: superleap (19.130 cents)<br /> | ||
105 / 104 = |-3 1 1 1 0 1&gt;: wintone (16.567 cents)<br /> | 105 / 104 = |-3 1 1 1 0 1&gt;: wintone (16.567 cents)<br /> | ||