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: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2013-12-03 19:33:58 UTC</tt>.<br>

: The original revision id was <tt>474442426</tt>.<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==  

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==

===5-limit commas===  

1125 / 1024 = |-10 2 3&gt;: enipucrop (162.851 cents)

800 / 729 = |5 -6 2&gt;: supersharp (160.897 cents)

2187 / 2000 = |-4 7 -3&gt;: gorgo (154.744 cents)

140625 / 131072 = |-17 2 6&gt;: lemba (121.792 cents)

3125 / 2916 = |-2 -6 5&gt;: sixix (119.839 cents)

10460353203 / 9765625000 = |-3 21 -13&gt;: diesma (118.977 cents)

5120000 / 4782969 = |13 -14 4&gt;: comic (117.885 cents)

524288 / 492075 = |19 -9 -2&gt;: beatles (109.778 cents)

531441 / 500000 = |-5 12 -6&gt;: wronecki (105.578 cents)

78125 / 73728 = |-13 -2 7&gt;: wesley (100.286 cents)

[[135_128|135 / 128]] = |-7 3 1&gt;: [[major chroma]], [[major limma]], [[pelogic comma]] (92.179 [[cent]]s)

6561 / 6250 = |-1 8 -5&gt;: ripple (84.071 cents)

390625 / 373248 = |-9 -6 8&gt;: doublewide (78.780 cents)

5000000 / 4782969 = |6 -14 7&gt;: sevond (76.826 cents)

51018336 / 48828125 = |5 13 -11&gt;: nusecond (75.964 cents)

8968066875 / 8589934592 = |-33 15 4&gt;: sentinel (74.580 cents)

[[25_24|25 / 24]] = |-3 -1 2&gt;: chromatic semitone (70.672 cents)

20480 / 19683 = |12 -9 1&gt;: superpyth, grave minor second (68.719 cents)

[[648_625|648 / 625]] = |3 4 -4&gt;: major diesis, diminished comma (62.565 cents)

262144 / 253125 = |18 -4 -5&gt;: passion (60.611 cents)

1953125 / 1889568 = |-5 -10 9&gt;: shibboleth (57.273 cents)

10077696 / 9765625 = |9 9 -10&gt;: mynic (54.458)

553584375 / 536870912 = |-29 11 5&gt; tritonic (53.074 cents)

16875 / 16384 = |-14 3 4&gt;: [[negri comma]], double augmentation diesis (51.120 cents)

[[250_243|250 / 243]] = |1 -5 3&gt;: maximal diesis, porcupine comma (49.166 cents)

1638400 / 1594323 = |16 -13 2&gt;: immunity (47.212 cents)

[[128_125|128 / 125]] = |7 0 -3&gt;: diesis, augmented comma (41.059 cents)

2197265625 / 2147483648 = |-31 2 12&gt;: wizard (39.675 cents)

&lt;span style="background-color: #ffffff;"&gt;48828125 / 47775744 = |-16 -6 11&gt;: sycamore (37.721 cents)&lt;/span&gt;

9765625 / 9565938 = |-1 -14 10&gt;: fifive (35.767 cents)

1594323 / 1562500 = |-2 13 -8&gt;: unicorn (34.905 cents)

1990656 / 1953125 = |13 5 -9&gt;: valensixthtone (32.952 cents)

34171875 / 33554432 = |-25 7 6&gt;: [[ampersand]], Ampersand's comma (31.567 cents)

3125 / 3072 = |-10 -1 5&gt; small diesis, [[magic comma]] (29.614 cents)

20000 / 19683 = |5 -9 4&gt;: minimal diesis, [[tetracot comma]] (27.660 cents)

131072000 / 129140163 = |20 -17 3&gt; roda (25.706 cents)

762939453125/753145430616 = |-3 -23 17&gt; maja (22.368 cents)

[[81_80|81 / 80]] = |-4 4 -1&gt;: syntonic comma, Didymos comma, meantone comma (21.506 cents)

2048 / 2025 = |11 -4 -2&gt;: [[diaschisma]] (19.553 cents)

1220703125 / 1207959552 = |-27 -2 13&gt;: ditonma (18.168 cents)

67108864 / 66430125 = |26 -12 -3&gt;: [[misty comma]] (17.599 cents)

129140163 / 128000000 = |-13 17 -6&gt;: [[graviton]], the [[Gravity family|gravity]] comma (15.353 cents)

390625000 / 387420489 = |3 -18 11&gt;: quartonic (14.261 cents)

78732 / 78125 = |2 9 -7&gt;: medium semicomma, [[sensipent comma]] (13.399 cents)

393216 / 390625 = |17 1 -8&gt;: [[Würschmidt comma]] (11.445 cents)

2109375 / 2097152 = |-21 3 7&gt;: [[semicomma]], Fokker comma (10.061 cents)

|32 -7 -9&gt;: [[escapade comma]] (9.492 cents)

15625 / 15552 = |-6 -5 6&gt;: [[kleisma]], semicomma majeur (8.107 cents)

31381059609 / 31250000000 = |-7 22 -12&gt; unidecma (7.245 cents)

|-44 -3 21&gt;: [[mutt comma]] (6.723 cents)

1600000 / 1594323 = |9 -13 5&gt;: [[amity comma]] (6.154 cents)

|8 14 -13&gt;: [[parakleisma]] (5.292 cents)

|-29 -11 20&gt;: gammic comma (4.769 cents)

|24 -21 4&gt;: [[vulture  comma|vulture comma]] (4.200 cents)

6115295232 / 6103515625 = |23 6 -14&gt;: [[vishnuzma]], semisuper (3.338 cents)

|-14 -19 19&gt;: [[enneadeca]], 19-tone-comma (2.816 cents)

|-68 18 17&gt;: vavoom (2.523 cents)

|39 -29 3&gt;: tricot comma (2.246 cents)

[[32805_32768|32805 / 32768]] = |-15 8 1&gt;: schisma (1.954 cents)

|-69 45 -1&gt;: counterschisma (1.661 cents)

|-52 -17 34&gt;: septendecima (1.431 cents)

274877906944 / 274658203125 = |38 -2 -15&gt;: hemithirds comma, lunama (1.384 cents)

|-16 35 -17&gt;: minortone comma (1.092 cents)

7629394531250 / 7625597484987 = |1 -27 18&gt;: [[Ennealimmal|ennealimma]] (0.862 cents)

|91 -12 -31&gt;: astro (0.815 cents)

|-53 10 16&gt;: kwazy (0.569 cents)

|37 25 -33&gt;: whoosh (0.522 cents)

|-36 -52 51&gt;: egads (0.339 cents)

|54 -37 2&gt;: monzisma (0.292 cents)

|-17 62 -35&gt;: senior (0.230 cents)

|71 -99 37&gt;: raider (0.062 cents)

|-90 -15 49&gt;: pirate (0.047 cents)

|161 -84 -12&gt;: atom (0.015 cents)

===7-limit commas===

405 / 392 = |-3 4 1 -2&gt;: greenwoodma (56.482 [[cent]]s)

59049 / 57344 = |-13 10 0 -1&gt;: Harrison's comma (50.724 cents)

1029 / 1000 = |-3 1 -3 3&gt;: keega (49.492 cents)

[[36_35|36 / 35]] = |2 2 -1 -1&gt;: septimal quarter tone (48.770 cents)

16807 / 16384 = |-14 0 0 5&gt;: cloudy (44.130 cents)

525 / 512 = |-9 1 2 1&gt;: avicennma, Avicenna's enharmonic diesis (43.408 cents)

[[49_48|49 / 48]] = |-4 -1 0 2&gt;: slendro diesis (35.597 cents)

[[50_49|50 / 49]] = |1 0 2 -2&gt;: tritonic diesis, jubilisma (34.976 cents)

839808 / 823543 = |7 8 0 -7&gt;: eric (33.859 cents)

686 / 675 = |1 -3 -2 3&gt;: senga (27.985 cents)

[[64_63|64 / 63]] = |6 -2 0 -1&gt;: septimal comma, Archytas' comma ([[http://de.wikipedia.org/wiki/Komma_%28Musik%29#Leipziger_Komma|"Leipziger Komma"]]) (27.264 cents)

854296875 / 843308032 = |-10 7 8 -7&gt;: blackjackisma (22.413 cents)

64827 / 64000 = |-9 3 -3 4&gt;: squalentine (22.227 cents)

875 / 864 = |-5 -3 3 1&gt;: keema (21.902 cents)

3125 / 3087 = |0 -2 5 -3&gt;: gariboh (21.181 cents)

2430 / 2401 = |1 5 1 -4&gt;: nuwell (20.785 cents)

179200 / 177147 = |10 -11 2 1&gt;: tolerma (19.948 cents)

33075 / 32768 = |-15 3 2 2&gt;: mirwomo (16.144 cents)

50421 / 50000 = |-4 1 -5 5&gt;: trimyna (14.516 cents)

245 / 243 = |0 -5 1 2&gt;: sensamagic (14.191 cents)

[[126_125|126 / 125]] = |1 2 -3 1&gt;: septimal semicomma, starling comma (13.795 cents)

4000 / 3969 = |5 -4 3 -2&gt;: octagar (13.469 cents)

1728 /1715 = |6 3 -1 -3&gt;: orwellisma, orwell comma (13.074 cents)

823543 / 819200 = |-15 0 -2 7&gt;: quince (9.154 cents)

1029 / 1024 = |-10 1 0 3&gt;: gamelisma (8.433 cents)

321489 / 320000 = |-9 8 -4 2&gt;: varunisma (8.037 cents)

[[225_224|225 / 224]] = |-5 2 2 -1&gt;: septimal kleisma, marvel comma (7.712 cents)

390625 / 388962 = |-1 -4 8 -4&gt;: dimcomp (7.386 cents)

19683 / 19600 = |-4 9 -2 -2&gt;: cataharry (7.316 cents)

16875 / 16807 = |0 3 4 -5&gt;: mirkwai (6.990 cents)

118098 / 117649 = |1 10 0 -6&gt;: stearnsma (6.595 cents)

10976 / 10935 = |5 -7 -1 3&gt;: hemimage (6.479 cents)

3136 / 3125 = |6 0 -5 2&gt;: hemimean (6.083 cents)

5120 / 5103 = |10 -6 1 -1&gt;: hemifamity (5.758 cents)

578509309952 / 576650390625 = |11 -10 -10 10&gt;: linus (5.572 cents)

6144 / 6125 = |11 1 -3 -2&gt;: porwell (5.362 cents)

33554432 / 33480783 = |25 -14 0 -1&gt;: garischisma (3.804 cents)

201768035 / 201326592 = |-26 -1 1 9&gt;: wadisma (3.792 cents)

&lt;span style="background-color: #ffffff;"&gt;29360128/29296875 = |22 -1 -10 1&gt;: [name?] (3.734 cents)&lt;/span&gt;

65625 / 65536 = |-16 1 5 1&gt;: horwell (2.349 cents)

703125 / 702464 = |-11 2 7 -3&gt;: meter (1.628 cents)

420175 / 419904 = |-6 -8 2 5&gt;: wizma (1.117 cents)

[[2401_2400|2401 / 2400]] = |-5 -1 -2 4&gt;: breedsma (0.721 cents)

4375 / 4374 = |-1 -7 4 1&gt;: ragisma (0.396 cents)

140737488355328 / 140710042265625 = |47 -7 -7 -7&gt;: akjaysma, 5\7 octave comma, (0.338 cents)

250047 / 250000 = |-4 6 -6 3&gt;: landscape comma (0.325 cents)

78125000/78121827 = |3 -13 10 -2&gt;: euzenius (0.070 cents)

===11-limit commas===

352 / 343 = |5 0 0 -3 1&gt;: sterno (44.840 cents)

35184372088832 / 34522712143931 = |45 0 0 0 -13&gt;: the Igs boson (32.867 cents)

163840 / 161051 = |15 0 1 0 -5&gt;: thuja comma (29.724 cents)

1232 / 1215 = |4 -5 -1 1 1&gt;: sensmus (24.055 cents)

3168 / 3125 = |5 2 -5 0 1&gt;: sevnothrush (23.659 cents)

245 / 242 = |-1 0 1 2 -2&gt;: cassacot (21.330 cents)

99 / 98 = |-1 2 0 -2 1&gt;: [[mothwellsmic triad|mothwellsma]] (17.576 cents)

[[100_99|100 / 99]] = |2 -2 2 0 -1&gt;: [[ptolemismic triad|ptolemisma]] (17.399 cents)

1344 / 1331 = |6 1 0 1 -3&gt;: hemimin (16.827 cents)

121 / 120 = |-3 -1 -1 0 2&gt;: biyatisma (14.367 cents)

1331 / 1323 = |0 -3 0 -2 3&gt;: aphrowe (10.437 cents)

176 / 175 = |4 0 -2 -1 1&gt;: [[valinorsmic chords|valinorsma]] (9.865 cents)

896 / 891 = |7 -4 0 1 -1&gt;: [[pentacircle comma|pentacircle]] (9.688 cents)

65536 / 65219 = |16 0 0 -2 -3&gt;: orgonisma (8.394 cents)

243 / 242 = |-1 5 0 0 -2&gt;: [[rastmic chords|rastma]] (7.139 cents)

3388 / 3375 = |2 -3 -3 1 2&gt;: myhemiwell (6.656 cents)

[[385_384|385 / 384]] = |-7 -1 1 1 1&gt;: [[keenanismic chords|keenanisma]] (4.503 cents)

441 / 440 = |-3 2 -1 2 -1&gt;: [[werckismic chords|werckisma]] (3.930 cents)

1375 / 1372 = |-2 0 3 -3 1&gt;: moctdel (3.781 cents)

540 / 539 = |2 3 1 -2 -1&gt;: [[swetismic chords|swetisma]] (3.209 cents)

4000 / 3993 = |5 -1 3 0 -3&gt;: wizardharry (3.032 cents)

5632 / 5625 = |9 -2 -4 0 1&gt;: vishdel (2.153 cents)

234375 / 234256 = |-4 1 7 0 -4&gt;: sesdecal (0.879 cents)

43923 / 43904 = |-7 1 0 -3 4&gt;: hemigail (0.749 cents)

3025 / 3024 = |-4 -3 2 -1 2&gt;: lehmerisma (0.572 cents)

9801 / 9800 = |-3 4 -2 -2 2&gt;: kalisma, Gauss' comma (0.177 cents)

151263 / 151250 = |-1 2 -4 5 -2&gt;: odiheim (0.149 cents)

1771561 / 1771470 = |-1 -11 -1 0 6&gt;: parimo (0.089 cents)

3294225 / 3294172 = |-2 2 2 -7 4&gt;: ultimo (0.028 cents)

4826809 / 4718592 = | -19 -2 0 0 0 6 &gt;: astbury (39.255 cents)

78 / 77 = |1 1 0 -1 -1 1&gt;: negustma (22.229 cents)

91 / 90 = |-1 -2 -1 1 0 1&gt;: superleap (19.130 cents)

105 / 104 = |-3 1 1 1 0 1&gt;: animist (16.567 cents)

28672 / 28431 = |12 -7 0 1 0 -1&gt;: secorian (14.613 cents)

275 / 273 = |0 -1 2 -1 1 -1&gt;: gassorma (12.637 cents)

144 / 143 = |4 2 0 0 -1 -1&gt;: grossma (12.064 cents)

169 / 168 = |-3 -1 0 -1 0 2&gt;: buzurgisma, dhanvantarisma (10.274 cents)

1287 / 1280 = |-8 2 -1 0 1 1&gt;: catadictma (9.442 cents)

196 / 195 = |2 -1 -1 2 0 -1&gt;: [[mynucumic chords|mynucuma]] (8.855 cents)

640 / 637 = |7 0 1 -2 0 -1&gt;: [[huntmic chords|huntma]] (8.134 cents)

2197 / 2187 = |0 -7 0 0 0 3&gt;: [[threedie]] (7.897 cents)

1188 / 1183 = |2 3 0 -1 1 -2&gt;: [[kestrel chords|kestrel comma]] (7.302 cents)

325 / 324 = |-2 -4 2 0 0 1&gt;: [[Marveltwin|marveltwin]] (5.335 cents)

351 / 350 = |-1 3 -2 -1 0 1&gt;: [[ratwolf triad|ratwolfsma]] (4.939 cents)

352 / 351 = |5 -3 0 0 1 -1&gt;: [[minthmic chords|minthma]] (4.925 cents)

364 / 363 = |2 -1 0 1 -2 1&gt;: [[gentle chords|gentle comma]] (4.763 cents)

847 / 845 = |0 0 -1 1 2 -2&gt;: [[cuthbert triad|cuthbert]] (4.093 cents)

625 / 624 = |-4 -1 4 0 0 -1&gt;: tunbarsma (2.772 cents)

676 / 675 = |2 -3 -2 0 0 2&gt;: [[The Archipelago|island comma]] (2.563 cents)

729 / 728 = |-3 6 0 -1 0 -1&gt;: [[squbemic chords|squbema]] (2.376 cents)

1575 / 1573 = |0 2 2 1 -2 -1&gt;: [[nicolic tetrad|nicola]] (2.200 cents)

2200 / 2197 = |3 0 2 0 1 -3&gt;: [[petrmic triad|petrma]] (2.362 cents)

1001 / 1000 = |-3 0 -3 1 1 1&gt;: [[sinbadmic tetrad|sinbadma]] (1.730 cents)

10985 / 10976 = |-5 0 1 -3 0 3&gt;: cantonisma (1.419 cents)

1716 /1715 = |2 1 -1 -3 1 1&gt;: lummic (1.009 cents)

2080 /2079 = |5 -3 1 -1 -1 1&gt;: ibnsinma (0.833 cents)

4096 / 4095 = |12 -2 -1 -1 0 -1&gt;: schismina (0.423 cents)

4225 / 4224 = |-7 -1 2 0 -1 2&gt;: leprechaun comma (0.410 cents)

6656 / 6655 = |9 0 -1 0 -3 1&gt;: jacobin (0.260 cents)

10648 / 10647 = |3 -2 0 -1 3 -2&gt;: harmonisma (0.163 cents)

123201 / 123200 = |-6 6 -2 -1 -1 2&gt;: chalmersima (0.014 cents)

===17-limit commas===

2058 / 2057 = |1 1 0 3 -2 0 -1&gt;: xenisma (0.841 cents)

194481 / 194480 = |-4 4 -1 4 -1 -1 -1&gt;: scintillisma (0.009 cents)

===19-limit commas===

210 / 209 = |1 1 1 1 -1 0 0 -1&gt;: spleen comma (8.264 cents)

361 / 360 = |-6 -1 0 0 0 0 0 2&gt;: Go comma (4.802 cents; [[19_12|19/12]] * [[19_15|19/15]])</pre></div>

<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:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Definition&lt;/h2&gt;

A &lt;strong&gt;comma&lt;/strong&gt; 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 &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.&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-List of commas, by prime limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;List of commas, by prime limit&lt;/h2&gt;

  &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-List of commas, by prime limit-3-limit commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;3-limit commas&lt;/h3&gt;

&lt;a class="wiki_link" href="/256_243"&gt;256 / 243&lt;/a&gt; = |8 -5&amp;gt;: limma or Pythagorean minor second (90.225 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s)&lt;br /&gt;

&lt;a class="wiki_link" href="/2187_2048"&gt;2187 / 2048&lt;/a&gt; = |-11 7&amp;gt;: apotome (113.685 cents)&lt;br /&gt;

&lt;a class="wiki_link" href="/531441_524288"&gt;531441 / 524288&lt;/a&gt; = |-19 12&amp;gt;: &lt;a class="wiki_link" href="/Pythagorean%20comma"&gt;Pythagorean comma&lt;/a&gt; (23.460 cents)&lt;br /&gt;

134217728 / 129140163 = |27 -17&amp;gt;: &lt;a class="wiki_link" href="/17-comma"&gt;17-comma&lt;/a&gt; (66.765 cents)&lt;br /&gt;

70368744177664 / 68630377364883 = |46 -29&amp;gt;: &lt;a class="wiki_link" href="/29-comma"&gt;29-comma&lt;/a&gt; (43.305 cents)&lt;br /&gt;

36893488147419103232 / 36472996377170786403 = |65 -41&amp;gt;: &lt;a class="wiki_link" href="/41-comma"&gt;41-comma&lt;/a&gt; (19.845 cents)&lt;br /&gt;

19383245667680019896796723 / 19342813113834066795298816 = |-84 53&amp;gt;: &lt;a class="wiki_link" href="/Mercator%27s%20comma"&gt;Mercator's comma&lt;/a&gt;, 53-comma (3.615 cents)&lt;br /&gt;

|485 -306&amp;gt;: &lt;a class="wiki_link" href="/Sasktel%20comma"&gt;Sasktel comma&lt;/a&gt; (1.770 cents)&lt;br /&gt;

|-1054 665&amp;gt;: &lt;a class="wiki_link" href="/Satanic%20comma"&gt;Satanic comma&lt;/a&gt; (0.076 cents)&lt;br /&gt;