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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 low prime limit. The word is often used in reference to regular tempering when the comma is 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 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 cents)
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)
|485 -306>: Sasktel comma (1.770 cents)
|-1054 665>: Satanic comma (0.076 cents)

5-limit commas

1125 / 1024 = |-10 2 3>: enipucrop (162.851 cents)
800 / 729 = |5 -6 2>: supersharp (160.897 cents)
2187 / 2000 = |-4 7 -3>: gorgo (154.744 cents)
140625 / 131072 = |-17 2 6>: lemba (121.792 cents)
3125 / 2916 = |-2 -6 5>: sixix (119.839 cents)
10460353203 / 9765625000 = |-3 21 -13>: diesma (118.977 cents)
5120000 / 4782969 = |13 -14 4>: comic (117.885 cents)
524288 / 492075 = |19 -9 -2>: beatles (109.778 cents)
531441 / 500000 = |-5 12 -6>: wronecki (105.578 cents)
78125 / 73728 = |-13 -2 7>: wesley (100.286 cents)
135 / 128 = |-7 3 1>: major chroma, major limma, pelogic comma (92.179 cents)
6561 / 6250 = |-1 8 -5>: ripple (84.071 cents)
390625 / 373248 = |-9 -6 8>: doublewide (78.780 cents)
5000000 / 4782969 = |6 -14 7>: sevond (76.826 cents)
51018336 / 48828125 = |5 13 -11>: nusecond (75.964 cents)
8968066875 / 8589934592 = |-33 15 4>: sentinel (74.580 cents)
25 / 24 = |-3 -1 2>: chromatic semitone (70.672 cents)
20480 / 19683 = |12 -9 1>: superpyth, grave minor second (68.719 cents)
648 / 625 = |3 4 -4>: major diesis, diminished comma (62.565 cents)
262144 / 253125 = |18 -4 -5>: passion (60.611 cents)
1953125 / 1889568 = |-5 -10 9>: shibboleth (57.273 cents)
10077696 / 9765625 = |9 9 -10>: mynic (54.458)
553584375 / 536870912 = |-29 11 5> tritonic (53.074 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)
1638400 / 1594323 = |16 -13 2>: immunity (47.212 cents)
128 / 125 = |7 0 -3>: diesis, augmented comma (41.059 cents)
2197265625 / 2147483648 = |-31 2 12>: wizard (39.675 cents)
48828125 / 47775744 = |-16 -6 11>: sycamore (37.721 cents)
9765625 / 9565938 = |-1 -14 10>: fifive (35.767 cents)
1594323 / 1562500 = |-2 13 -8>: unicorn (34.905 cents)
1990656 / 1953125 = |13 5 -9>: valensixthtone (32.952 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)
131072000 / 129140163 = |20 -17 3> roda (25.706 cents)
762939453125/753145430616 = |-3 -23 17> maja (22.368 cents)
81 / 80 = |-4 4 -1>: syntonic comma, Didymos comma, meantone comma (21.506 cents)
2048 / 2025 = |11 -4 -2>: diaschisma (19.553 cents)
1220703125 / 1207959552 = |-27 -2 13>: ditonma (18.168 cents)
67108864 / 66430125 = |26 -12 -3>: misty comma (17.599 cents)
129140163 / 128000000 = |-13 17 -6>: graviton, the gravity comma (15.353 cents)
390625000 / 387420489 = |3 -18 11>: quartonic (14.261 cents)
78732 / 78125 = |2 9 -7>: medium semicomma, sensipent comma (13.399 cents)
393216 / 390625 = |17 1 -8>: W├╝rschmidt comma (11.445 cents)
2109375 / 2097152 = |-21 3 7>: semicomma, Fokker comma (10.061 cents)
|32 -7 -9>: escapade comma (9.492 cents)
15625 / 15552 = |-6 -5 6>: kleisma, semicomma majeur (8.107 cents)
31381059609 / 31250000000 = |-7 22 -12> unidecma (7.245 cents)
|-44 -3 21>: mutt comma (6.723 cents)
1600000 / 1594323 = |9 -13 5>: amity comma (6.154 cents)
|8 14 -13>: parakleisma (5.292 cents)
|-29 -11 20>: gammic comma (4.769 cents)
|24 -21 4>: vulture comma (4.200 cents)
6115295232 / 6103515625 = |23 6 -14>: vishnuzma, semisuper (3.338 cents)
|-14 -19 19>: enneadeca, 19-tone-comma (2.816 cents)
|-68 18 17>: vavoom (2.523 cents)
|39 -29 3>: tricot comma (2.246 cents)
32805 / 32768 = |-15 8 1>: schisma (1.954 cents)
|-69 45 -1>: counterschisma (1.661 cents)
|-52 -17 34>: septendecima (1.431 cents)
274877906944 / 274658203125 = |38 -2 -15>: hemithirds comma, lunama (1.384 cents)
|-16 35 -17>: minortone comma (1.092 cents)
7629394531250 / 7625597484987 = |1 -27 18>: ennealimma (0.862 cents)
|91 -12 -31>: astro (0.815 cents)
|-53 10 16>: kwazy (0.569 cents)
|37 25 -33>: whoosh (0.522 cents)
|-36 -52 51>: egads (0.339 cents)
|54 -37 2>: monzisma (0.292 cents)
|-107 47 14>: fortune (0.277 cents)
|144 -22 -47>: gross (0.245 cents)
|-17 62 -35>: senior (0.230 cents)
|71 -99 37>: raider (0.062 cents)
|-90 -15 49>: pirate (0.047 cents)
|161 -84 -12>: atom (0.015 cents)

7-limit commas

405 / 392 = |-3 4 1 -2>: greenwoodma (56.482 cents)
59049 / 57344 = |-13 10 0 -1>: Harrison's comma (50.724 cents)
1029 / 1000 = |-3 1 -3 3>: keega (49.492 cents)
36 / 35 = |2 2 -1 -1>: septimal quarter tone (48.770 cents)
16807 / 16384 = |-14 0 0 5>: cloudy (44.130 cents)
525 / 512 = |-9 1 2 1>: avicennma, Avicenna's enharmonic diesis (43.408 cents)
49 / 48 = |-4 -1 0 2>: slendro diesis (35.597 cents)
50 / 49 = |1 0 2 -2>: tritonic diesis, jubilisma (34.976 cents)
839808 / 823543 = |7 8 0 -7>: eric (33.859 cents)
686 / 675 = |1 -3 -2 3>: senga (27.985 cents)
64 / 63 = |6 -2 0 -1>: septimal comma, Archytas' comma ("Leipziger Komma") (27.264 cents)
854296875 / 843308032 = |-10 7 8 -7>: blackjackisma (22.413 cents)
64827 / 64000 = |-9 3 -3 4>: squalentine (22.227 cents)
875 / 864 = |-5 -3 3 1>: keema (21.902 cents)
3125 / 3087 = |0 -2 5 -3>: gariboh (21.181 cents)
2430 / 2401 = |1 5 1 -4>: nuwell (20.785 cents)
179200 / 177147 = |10 -11 2 1>: tolerma (19.948 cents)
33075 / 32768 = |-15 3 2 2>: mirwomo (16.144 cents)
50421 / 50000 = |-4 1 -5 5>: trimyna (14.516 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)
823543 / 819200 = |-15 0 -2 7>: quince (9.154 cents)
1029 / 1024 = |-10 1 0 3>: gamelisma (8.433 cents)
321489 / 320000 = |-9 8 -4 2>: varunisma (8.037 cents)
225 / 224 = |-5 2 2 -1>: septimal kleisma, marvel comma (7.712 cents)
390625 / 388962 = |-1 -4 8 -4>: dimcomp (7.386 cents)
19683 / 19600 = |-4 9 -2 -2>: cataharry (7.316 cents)
16875 / 16807 = |0 3 4 -5>: mirkwai (6.990 cents)
118098 / 117649 = |1 10 0 -6>: stearnsma (6.595 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)
578509309952 / 576650390625 = |11 -10 -10 10>: linus (5.572 cents)
6144 / 6125 = |11 1 -3 -2>: porwell (5.362 cents)
33554432 / 33480783 = |25 -14 0 -1>: garischisma (3.804 cents)
201768035 / 201326592 = |-26 -1 1 9>: wadisma (3.792 cents)
29360128/29296875 = |22 -1 -10 1>: [name?] (3.734 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)
140737488355328 / 140710042265625 = |47 -7 -7 -7>: akjaysma, 5\7 octave comma, (0.338 cents)
250047 / 250000 = |-4 6 -6 3>: landscape comma (0.325 cents)
78125000/78121827 = |3 -13 10 -2>: euzenius (0.070 cents)

11-limit commas

352 / 343 = |5 0 0 -3 1>: sterno (44.840 cents)
35184372088832 / 34522712143931 = |45 0 0 0 -13>: the Igs boson (32.867 cents)
163840 / 161051 = |15 0 1 0 -5>: thuja comma (29.724 cents)
1232 / 1215 = |4 -5 -1 1 1>: sensmus (24.055 cents)
3168 / 3125 = |5 2 -5 0 1>: sevnothrush (23.659 cents)
245 / 242 = |-1 0 1 2 -2>: cassacot (21.330 cents)
99 / 98 = |-1 2 0 -2 1>: mothwellsma (17.576 cents)
100 / 99 = |2 -2 2 0 -1>: ptolemisma (17.399 cents)
1344 / 1331 = |6 1 0 1 -3>: hemimin (16.827 cents)
121 / 120 = |-3 -1 -1 0 2>: biyatisma (14.367 cents)
1331 / 1323 = |0 -3 0 -2 3>: aphrowe (10.437 cents)
176 / 175 = |4 0 -2 -1 1>: valinorsma (9.865 cents)
896 / 891 = |7 -4 0 1 -1>: pentacircle (9.688 cents)
65536 / 65219 = |16 0 0 -2 -3>: orgonisma (8.394 cents)
243 / 242 = |-1 5 0 0 -2>: rastma (7.139 cents)
3388 / 3375 = |2 -3 -3 1 2>: myhemiwell (6.656 cents)
385 / 384 = |-7 -1 1 1 1>: keenanisma (4.503 cents)
441 / 440 = |-3 2 -1 2 -1>: werckisma (3.930 cents)
1375 / 1372 = |-2 0 3 -3 1>: moctdel (3.781 cents)
540 / 539 = |2 3 1 -2 -1>: swetisma (3.209 cents)
4000 / 3993 = |5 -1 3 0 -3>: wizardharry (3.032 cents)
5632 / 5625 = |9 -2 -4 0 1>: vishdel (2.153 cents)
234375 / 234256 = |-4 1 7 0 -4>: sesdecal (0.879 cents)
43923 / 43904 = |-7 1 0 -3 4>: hemigail (0.749 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)
151263 / 151250 = |-1 2 -4 5 -2>: odiheim (0.149 cents)
1771561 / 1771470 = |-1 -11 -1 0 6>: parimo (0.089 cents)
3294225 / 3294172 = |-2 2 2 -7 4>: ultimo (0.028 cents)

13-limit commas


4826809 / 4718592 = | -19 -2 0 0 0 6 >: astbury (39.255 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)
105 / 104 = |-3 1 1 1 0 1>: animist (16.567 cents)
28672 / 28431 = |12 -7 0 1 0 -1>: secorian (14.613 cents)
275 / 273 = |0 -1 2 -1 1 -1>: gassorma (12.637 cents)
144 / 143 = |4 2 0 0 -1 -1>: grossma (12.064 cents)
169 / 168 = |-3 -1 0 -1 0 2>: buzurgisma, dhanvantarisma (10.274 cents)
1287 / 1280 = |-8 2 -1 0 1 1>: catadictma (9.442 cents)
196 / 195 = |2 -1 -1 2 0 -1>: mynucuma (8.855 cents)
640 / 637 = |7 0 1 -2 0 -1>: huntma (8.134 cents)
2197 / 2187 = |0 -7 0 0 0 3>: threedie (7.897 cents)
1188 / 1183 = |2 3 0 -1 1 -2>: kestrel comma (7.302 cents)
325 / 324 = |-2 -4 2 0 0 1>: marveltwin (5.335 cents)
351 / 350 = |-1 3 -2 -1 0 1>: ratwolfsma (4.939 cents)
352 / 351 = |5 -3 0 0 1 -1>: minthma (4.925 cents)
364 / 363 = |2 -1 0 1 -2 1>: gentle comma (4.763 cents)
847 / 845 = |0 0 -1 1 2 -2>: cuthbert (4.093 cents)
625 / 624 = |-4 -1 4 0 0 -1>: tunbarsma (2.772 cents)
676 / 675 = |2 -3 -2 0 0 2>: island comma (2.563 cents)
729 / 728 = |-3 6 0 -1 0 -1>: squbema (2.376 cents)
1575 / 1573 = |0 2 2 1 -2 -1>: nicola (2.200 cents)
2200 / 2197 = |3 0 2 0 1 -3>: petrma (2.362 cents)
1001 / 1000 = |-3 0 -3 1 1 1>: sinbadma (1.730 cents)
10985 / 10976 = |-5 0 1 -3 0 3>: cantonisma (1.419 cents)
1716 /1715 = |2 1 -1 -3 1 1>: lummic (1.009 cents)
2080 /2079 = |5 -3 1 -1 -1 1>: ibnsinma (0.833 cents)
4096 / 4095 = |12 -2 -1 -1 0 -1>: schismina (0.423 cents)
4225 / 4224 = |-7 -1 2 0 -1 2>: leprechaun comma (0.410 cents)
6656 / 6655 = |9 0 -1 0 -3 1>: jacobin (0.260 cents)
10648 / 10647 = |3 -2 0 -1 3 -2>: harmonisma (0.163 cents)
123201 / 123200 = |-6 6 -2 -1 -1 2>: chalmersima (0.014 cents)

17-limit commas

2058 / 2057 = |1 1 0 3 -2 0 -1>: xenisma (0.841 cents)
194481 / 194480 = |-4 4 -1 4 -1 -1 -1>: scintillisma (0.009 cents)

19-limit commas

210 / 209 = |1 1 1 1 -1 0 0 -1>: spleen comma (8.264 cents)
361 / 360 = |-6 -1 0 0 0 0 0 2>: Go comma (4.802 cents; 19/12 * 19/15)