Small comma

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2010-06-22 20:22:00 UTC.

The original revision id was 150090503.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

A **comma** is a small just interval, 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 //tempered out//, which is to say reduced to a unison, by the temperament. For example the Didymos comma of 81/80 is tempered out by [[Meantone|meantone temperament]]. 

==3-limit commas==

256 / 243 = |8 -5>: limma or Pythagorean minor second (90.225 [[cent]]s)
2187 / 2048 = |-11 7>: apotome (113.685 cents)
531441 / 524288 = |-19 12>: Pythagorean comma (23.460 cents)
134217728 / 129140163 = |27 -17>: 17-comma (66.765 cents)
70368744177664 / 68630377364883 = |46 -29>: 29-comma (43.305 cents)
36893488147419103232 / 36472996377170786403 = |65 -41>: 41-comma (19.845 cents)
19383245667680019896796723 / 19342813113834066795298816 = |-84 53>: Mercator's comma, 53-comma (3.615 cents)

==5-limit commas==

135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 [[cent]]s)
648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents)
16875 / 16384 = |-14 3 4>: negri comma, double augmentation diesis (51.120 cents)
250 / 243 = |1 -5 3>: maximal diesis, porcupine comma (49.166 cents)
128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents)
34171875 / 33554432 = |-25 7 6>: ampersand, Ampersand's comma (31.567 cents)
3125 / 3072 = |-10 -1 5> small diesis, magic comma (29.614 cents)
20000 / 19683 = |5 -9 4>: minimal diesis, tetracot comma (27.660 cents)
81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents)
2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents)
67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents)
78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents)
393216 / 390625 = |17 1 -8>: Wuerschmidt comma (11.445 cents)
2109375 / 2097152 = |-21 3 7>: semicomma, Fokker comma (10.061 cents)
15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)
1600000 / 1594323 = |9 -13 5>: amity comma (6.154 cents)
|8 14 -13>: parakleisma (5.292 cents)
|24 -21 4>: vulture (4.200 cents)
6115295232 / 6103515625 = |23 6 -14>: vishnuzma (3.338 cents)
|-14 -19 19>: enneadeca, 19-tone-comma (2.816 cents)
|39 -29 3>: tricot comma (2.246 cents)
32805 / 32768 = |-15 8 1>: schisma (1.954 cents)
274877906944 / 274658203125 = |38 -2 -15>: hemithirds comma (1.384 cents)
|-16 35 -17>: minortone comma (1.092 cents)
7629394531250 / 7625597484987 = |1 -27 18>: ennealimma (0.862 cents)
|-53 10 16>: kwazy comma (0.569 cents)
|54 -37 2>: monzisma (0.292 cents)

==7-limit commas==

1029 / 1000 = |-3 1 -3 3>: keega (49.492 [[cent]]s)
36 / 35 = |2 2 -1 -1>: septimal quarter tone (48.770 cents)
49 / 48 = |-4 -1 0 2>: slendro diesis (35.597 cents)
50 / 49 = |1 0 2 -2>: tritonic diesis (34.976 cents)
686 / 675 = |1 -3 -2 3>: senga (27.985 cents)
64 / 63 = |6 -2 0 -1>: septimal comma, Archytas' comma ([[http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma|"Leipziger Komma"]]) (27.264 cents)
875 / 864 = |-5 -3 3 1>: keemic (21.902 cents)
3125 / 3087 = |0 -2 5 -3>: gariboh (21.181 cents)
2430 / 2401 = |1 5 1 -4>: nuwell (20.785 cents)
245 / 243 = |0 -5 1 2>: sensamagic (14.191 cents)
126 / 125 = |1 2 -3 1>: septimal semicomma, starling comma (13.795 cents)
4000 / 3969 = |5 -4 3 -2>: octagar (13.469 cents)
1728 /1715 = |6 3 -1 -3>: orwellisma, orwell comma (13.074 cents)
1029 / 1024 = |-10 1 0 3>: gamelisma (8.433 cents)
19683 / 19600 = |-4 9 -2 -2>: cataharry (7.316 cents)
225 / 224 = |-5 2 2 -1>: septimal kleisma, marvel comma (7.712 cents)
16875 / 16807 = |0 3 4 -5>: mirkwai (6.990 cents)
10976 / 10935 = |5 -7 -1 3>: hemimage (6.479 cents)
3136 / 3125 = |6 0 -5 2>: hemimean (6.083 cents)
5120 / 5103 = |10 -6 1 -1>: hemifamity (5.758 cents)
6144 / 6125 = |11 1 -3 -2>: porwell (5.362 cents)
33554432 / 33480743 = |25 -14 0 -1> garischisma (3.804 cents)
65625 / 65536 = |-16 1 5 1>: horwell (2.349 cents)
703125 / 702464 = |-11 2 7 -3>: meter (1.628 cents)
420175 / 419904 = |-6 -8 2 5>: wizma (1.117 cents)
2401 / 2400 = |-5 -1 -2 4>: breedsma (0.721 cents)
4375 / 4374 = |-1 -7 4 1>: ragisma (0.396 cents)
250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents)

==11-limit commas==

99 / 98 = |-1 2 0 2 1>: mothwellsma (17.576 cents)
100 / 99 = |2 -2 2 0 -1>: ptolemisma (17.399 cents)
121 / 120 = |-3 -1 -1 0 2>: biyatisma (14.367 cents)
176 / 175 = |4 0 -2 -1 1>: valinorsma (9.865 cents)
896 / 891 = |7 -4 0 1 -1>: pentacircle (9.688 cents)
243 / 242 = |-1 5 0 0 -2>: rastma (7.139 cents)
385 / 384 = |-7 -1 1 1 1>:  unidecma (4.503 cents)
441 / 440 = |-3 2 -1 2 -1>: werckisma (3.930 cents)
540 / 539 = |2 3 1 -2 -1>: swetisma (3.209 cents)
3025 / 3024 = |-4 -3 2 -1 2>: lehmerisma (0.572 cents)
9801 / 9800 = |-3 4 -2 -2 2>: kalisma, Gauss' comma (0.177 cents)

Original HTML content:

<html><head><title>Comma</title></head><body>A <strong>comma</strong> is a small just interval, 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>tempered out</em>, which is to say reduced to a unison, by the temperament. For example the Didymos comma of 81/80 is tempered out by <a class="wiki_link" href="/Meantone">meantone temperament</a>. <br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->3-limit commas</h2>
<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 />
531441 / 524288 = |-19 12&gt;: Pythagorean comma (23.460 cents)<br />
134217728 / 129140163 = |27 -17&gt;: 17-comma (66.765 cents)<br />
70368744177664 / 68630377364883 = |46 -29&gt;: 29-comma (43.305 cents)<br />
36893488147419103232 / 36472996377170786403 = |65 -41&gt;: 41-comma (19.845 cents)<br />
19383245667680019896796723 / 19342813113834066795298816 = |-84 53&gt;: Mercator's comma, 53-comma (3.615 cents)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->5-limit commas</h2>
<br />
135 / 128 = |-7 3 1&gt;: major chroma, major limma, pelogic comma (92.179 <a class="wiki_link" href="/cent">cent</a>s)<br />
648 / 625 = |3 4 -4&gt;: major diesis, diminished comma (62.565 cents)<br />
16875 / 16384 = |-14 3 4&gt;: negri comma, double augmentation diesis (51.120 cents)<br />
250 / 243 = |1 -5 3&gt;: maximal diesis, porcupine comma (49.166 cents)<br />
128 / 125 = |7 0 -3&gt;: diesis, augmented comma (41.059 cents)<br />
34171875 / 33554432 = |-25 7 6&gt;: ampersand, Ampersand's comma (31.567 cents)<br />
3125 / 3072 = |-10 -1 5&gt; small diesis, magic comma (29.614 cents)<br />
20000 / 19683 = |5 -9 4&gt;: minimal diesis, tetracot comma (27.660 cents)<br />
81 / 80 = |-4 4 -1&gt;: syntonic comma, Didymos comma, meantone comma (21.506 cents)<br />
2048 / 2025 = |11 -4 -2&gt;: diaschisma (19.553 cents)<br />
67108864 / 66430125 = |26 -12 -3&gt;: misty comma (17.599 cents)<br />
78732 / 78125 = |2 9 -7&gt;: medium semicomma, sensipent comma (13.399 cents)<br />
393216 / 390625 = |17 1 -8&gt;: Wuerschmidt comma (11.445 cents)<br />
2109375 / 2097152 = |-21 3 7&gt;: semicomma, Fokker comma (10.061 cents)<br />
15625 / 15552 = |-6 -5 6&gt;: kleisma, semicomma majeur (8.107 cents)<br />
1600000 / 1594323 = |9 -13 5&gt;: amity comma (6.154 cents)<br />
|8 14 -13&gt;: parakleisma (5.292 cents)<br />
|24 -21 4&gt;: vulture (4.200 cents)<br />
6115295232 / 6103515625 = |23 6 -14&gt;: vishnuzma (3.338 cents)<br />
|-14 -19 19&gt;: enneadeca, 19-tone-comma (2.816 cents)<br />
|39 -29 3&gt;: tricot comma (2.246 cents)<br />
32805 / 32768 = |-15 8 1&gt;: schisma (1.954 cents)<br />
274877906944 / 274658203125 = |38 -2 -15&gt;: hemithirds comma (1.384 cents)<br />
|-16 35 -17&gt;: minortone comma (1.092 cents)<br />
7629394531250 / 7625597484987 = |1 -27 18&gt;: ennealimma (0.862 cents)<br />
|-53 10 16&gt;: kwazy comma (0.569 cents)<br />
|54 -37 2&gt;: monzisma (0.292 cents)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-7-limit commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->7-limit commas</h2>
<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 />
49 / 48 = |-4 -1 0 2&gt;: slendro diesis (35.597 cents)<br />
50 / 49 = |1 0 2 -2&gt;: tritonic diesis (34.976 cents)<br />
686 / 675 = |1 -3 -2 3&gt;: senga (27.985 cents)<br />
64 / 63 = |6 -2 0 -1&gt;: septimal comma, Archytas' comma (<a class="wiki_link_ext" href="http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma" rel="nofollow">&quot;Leipziger Komma&quot;</a>) (27.264 cents)<br />
875 / 864 = |-5 -3 3 1&gt;: keemic (21.902 cents)<br />
3125 / 3087 = |0 -2 5 -3&gt;: gariboh (21.181 cents)<br />
2430 / 2401 = |1 5 1 -4&gt;: nuwell (20.785 cents)<br />
245 / 243 = |0 -5 1 2&gt;: sensamagic (14.191 cents)<br />
126 / 125 = |1 2 -3 1&gt;: septimal semicomma, starling comma (13.795 cents)<br />
4000 / 3969 = |5 -4 3 -2&gt;: octagar (13.469 cents)<br />
1728 /1715 = |6 3 -1 -3&gt;: orwellisma, orwell comma (13.074 cents)<br />
1029 / 1024 = |-10 1 0 3&gt;: gamelisma (8.433 cents)<br />
19683 / 19600 = |-4 9 -2 -2&gt;: cataharry (7.316 cents)<br />
225 / 224 = |-5 2 2 -1&gt;: septimal kleisma, marvel comma (7.712 cents)<br />
16875 / 16807 = |0 3 4 -5&gt;: mirkwai (6.990 cents)<br />
10976 / 10935 = |5 -7 -1 3&gt;: hemimage (6.479 cents)<br />
3136 / 3125 = |6 0 -5 2&gt;: hemimean (6.083 cents)<br />
5120 / 5103 = |10 -6 1 -1&gt;: hemifamity (5.758 cents)<br />
6144 / 6125 = |11 1 -3 -2&gt;: porwell (5.362 cents)<br />
33554432 / 33480743 = |25 -14 0 -1&gt; garischisma (3.804 cents)<br />
65625 / 65536 = |-16 1 5 1&gt;: horwell (2.349 cents)<br />
703125 / 702464 = |-11 2 7 -3&gt;: meter (1.628 cents)<br />
420175 / 419904 = |-6 -8 2 5&gt;: wizma (1.117 cents)<br />
2401 / 2400 = |-5 -1 -2 4&gt;: breedsma (0.721 cents)<br />
4375 / 4374 = |-1 -7 4 1&gt;: ragisma (0.396 cents)<br />
250047 / 250000 = |-4 6 -6 3&gt;: landscape comma (0.325 cents)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit commas</h2>
<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 />
121 / 120 = |-3 -1 -1 0 2&gt;: biyatisma (14.367 cents)<br />
176 / 175 = |4 0 -2 -1 1&gt;: valinorsma (9.865 cents)<br />
896 / 891 = |7 -4 0 1 -1&gt;: pentacircle (9.688 cents)<br />
243 / 242 = |-1 5 0 0 -2&gt;: rastma (7.139 cents)<br />
385 / 384 = |-7 -1 1 1 1&gt;:  unidecma (4.503 cents)<br />
441 / 440 = |-3 2 -1 2 -1&gt;: werckisma (3.930 cents)<br />
540 / 539 = |2 3 1 -2 -1&gt;: swetisma (3.209 cents)<br />
3025 / 3024 = |-4 -3 2 -1 2&gt;: lehmerisma (0.572 cents)<br />
9801 / 9800 = |-3 4 -2 -2 2&gt;: kalisma, Gauss' comma (0.177 cents)</body></html>