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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, as well as the size in cents.

List of commas, by prime limit


3-limit commas

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

| 485 -306 >
1.770
Satanic comma

| -1054 665 >
0.076

5-limit commas

name(s)
ratio
monzo
cents
enipucrop
1125 / 1024
| -10 2 3 >
162.851
supersharp
800 / 729
| 5 -6 2 >
160.897
gorgo
2187 / 2000
| -4 7 -3 >
154.744
lemba
140625 / 131072
| -17 2 6 >
121.792
sixix
3125 / 2916
| -2 -6 5 >
119.839
diesma
10460353203 / 9765625000
| -3 21 -13 >
118.977
comic
5120000 / 4782969
| 13 -14 4 >
117.885
beatles
524288 / 492075
| 19 -9 -2 >
109.778
wronecki
531441 / 500000
| -5 12 -6 >
105.578
wesley
78125 / 73728
| -13 -2 7 >
100.286
major chroma, major limma, pelogic comma
135 / 128
| -7 3 1 >
92.179
ripple
6561 / 6250
| -1 8 -5 >
84.071
doublewide
390625 / 373248
| -9 -6 8 >
78.780
sevond
5000000 / 4782969
| 6 -14 7 >
76.826
nusecond
51018336 / 48828125
| 5 13 -11 >
75.964
sentinel
8968066875 / 8589934592
| -33 15 4 >
74.580
chromatic semitone
25 / 24
| -3 -1 2 >
70.672
superpyth, grave minor second
20480 / 19683
| 12 -9 1 >
68.719
major diesis, diminished comma
648 / 625
| 3 4 -4 >
62.565
passion
262144 / 253125
| 18 -4 -5 >
60.611
shibboleth
1953125 / 1889568
| -5 -10 9 >
57.273
mynic
10077696 / 9765625
| 9 9 -10 >
54.458
tritonic
553584375 / 536870912
| -29 11 5 >
53.074
negri comma, double augmentation diesis
16875 / 16384
| -14 3 4 >
51.120
maximal diesis, porcupine comma
250 / 243
| 1 -5 3 >
49.166
immunity
1638400 / 1594323
| 16 -13 2 >
47.212
diesis, augmented comma
128 / 125
| 7 0 -3 >
41.059
wizard
2197265625 / 2147483648
| -31 2 12 >
39.675
sycamore
48828125 / 47775744
| -16 -6 11 >
37.721
fifive
9765625 / 9565938
| -1 -14 10 >
35.767
unicorn
1594323 / 1562500
| -2 13 -8 >
34.905
valensixthtone
1990656 / 1953125
| 13 5 -9 >
32.952
ampersand, Ampersand's comma
34171875 / 33554432
| -25 7 6 >
31.567
small diesis, magic comma
3125 / 3072
| -10 -1 5 >
29.614
minimal diesis, tetracot comma
20000 / 19683
| 5 -9 4 >
27.660
roda
131072000 / 129140163
| 20 -17 3 >
25.706
maja
762939453125 / 753145430616
| -3 -23 17 >
22.368
syntonic comma, Didymos comma, meantone comma
81 / 80
| -4 4 -1 >
21.506
diaschisma
2048 / 2025
| 11 -4 -2 >
19.553
ditonma
1220703125 / 1207959552
| -27 -2 13 >
18.168
misty comma
67108864 / 66430125
| 26 -12 -3 >
17.599
graviton, 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
W├╝rschmidt comma
393216 / 390625
| 17 1 -8 >
11.445
semicomma, Fokker comma
2109375 / 2097152
| -21 3 7 >
10.061
escapade comma

| 32 -7 -9 >
9.492
kleisma, semicomma majeur
15625 / 15552
| -6 -5 6 >
8.107
unidecma
31381059609 / 31250000000
| -7 22 -12 >
7.245
mutt comma

| -44 -3 21 >
6.723
amity comma
1600000 / 1594323
| 9 -13 5 >
6.154
parakleisma

| 8 14 -13 >
5.292
gammic comma

| -29 -11 20 >
4.769
vulture comma

| 24 -21 4 >
4.200
vishnuzma, semisuper
6115295232 / 6103515625
| 23 6 -14 >
3.338
enneadeca, 19-tone-comma

| -14 -19 19 >
2.816
vavoom

| -68 18 17 >
2.523
tricot comma

| 39 -29 3 >
2.246
schisma
32805 / 32768
| -15 8 1 >
1.954
counterschisma

| -69 45 -1 >
1.661
septendecima

| -52 -17 34 >
1.431
hemithirds comma, lunama
274877906944 / 274658203125
| 38 -2 -15 >
1.384
minortone comma

| -16 35 -17 >
1.092
ennealimma
7629394531250 / 7625597484987
| 1 -27 18 >
0.862
astro

| 91 -12 -31 >
0.815
kwazy

| -53 10 16 >
0.569
whoosh

| 37 25 -33 >
0.522
egads

| -36 -52 51 >
0.339
monzisma

| 54 -37 2 >
0.292
fortune

| -107 47 14 >
0.277
gross

| 144 -22 -47 >
0.245
senior

| -17 62 -35 >
0.230
raider

| 71 -99 37 >
0.062
pirate

| -90 -15 49 >
0.047
atom

| 161 -84 -12 >
0.015

7-limit commas

name(s)
ratio
monzo
cents
greenwoodma
405 / 392
| -3 4 1 -2 >
56.482
Harrison's comma
59049 / 57344
| -13 10 0 -1 >
50.724
keega
1029 / 1000
| -3 1 -3 3 >
49.492
septimal quarter tone
36 / 35
| 2 2 -1 -1 >
48.770
cloudy
16807 / 16384
| -14 0 0 5 >
44.130
avicennma, Avicenna's enharmonic diesis
525 / 512
| -9 1 2 1 >
43.408
slendro diesis
49 / 48
| -4 -1 0 2 >
35.597
tritonic diesis, jubilisma
50 / 49
| 1 0 2 -2 >
34.976
eric
839808 / 823543
| 7 8 0 -7 >
33.859
senga
686 / 675
| 1 -3 -2 3 >
27.985
septimal comma, Archytas' comma, Leipziger Komma
64 / 63
| 6 -2 0 -1 >
27.264
blackjackisma
854296875 / 843308032
| -10 7 8 -7 >
22.413
squalentine
64827 / 64000
| -9 3 -3 4 >
22.227
keema
875 / 864
| -5 -3 3 1 >
21.902
gariboh
3125 / 3087
| 0 -2 5 -3 >
21.181
nuwell
2430 / 2401
| 1 5 1 -4 >
20.785
tolerma
179200 / 177147
| 10 -11 2 1 >
19.948
mirwomo
33075 / 32768
| -15 3 2 2 >
16.144
trimyna
50421 / 50000
| -4 1 -5 5 >
14.516
sensamagic
245 / 243
| 0 -5 1 2 >
14.191
septimal semicomma, starling comma
126 / 125
| 1 2 -3 1 >
13.795
octagar
4000 / 3969
| 5 -4 3 -2 >
13.469
orwellisma, orwell comma
1728 / 1715
| 6 3 -1 -3 >
13.074
quince
823543 / 819200
| -15 0 -2 7 >
9.154
gamelisma
1029 / 1024
| -10 1 0 3 >
8.433
varunisma
321489 / 320000
| -9 8 -4 2 >
8.037
septimal kleisma, marvel comma
225 / 224
| -5 2 2 -1 >
7.712
dimcomp
390625 / 388962
| -1 -4 8 -4 >
7.386
cataharry
19683 / 19600
| -4 9 -2 -2 >
7.316
mirkwai
16875 / 16807
| 0 3 4 -5 >
6.990
stearnsma
118098 / 117649
| 1 10 0 -6 >
6.595
hemimage
10976 / 10935
| 5 -7 -1 3 >
6.479
hemimean
3136 / 3125
| 6 0 -5 2 >
6.083
hemifamity
5120 / 5103
| 10 -6 1 -1 >
5.758
linus
578509309952 / 576650390625
| 11 -10 -10 10 >
5.572
porwell
6144 / 6125
| 11 1 -3 -2 >
5.362
garischisma
33554432 / 33480783
| 25 -14 0 -1 >
3.804
wadisma
201768035 / 201326592
| -26 -1 1 9 >
3.792
quasiorwellisma?
29360128 / 29296875
| 22 -1 -10 1 >
3.734
horwell
65625 / 65536
| -16 1 5 1 >
2.349
meter
703125 / 702464
| -11 2 7 -3 >
1.628
wizma
420175 / 419904
| -6 -8 2 5 >
1.117
breedsma
2401 / 2400
| -5 -1 -2 4 >
0.721
ragisma
4375 / 4374
| -1 -7 4 1 >
0.396
akjaysma, 5\7 octave comma
140737488355328 / 140710042265625
| 47 -7 -7 -7 >
0.338
landscape comma
250047 / 250000
| -4 6 -6 3 >
0.325
euzenius
78125000/78121827
| 3 -13 10 -2 >
0.070


11-limit commas

name(s)
ratio
monzo
cents
sterno
352 / 343
| 5 0 0 -3 1 >
44.840
the Igs boson
35184372088832 / 34522712143931
| 45 0 0 0 -13 >
32.867
thuja comma
163840 / 161051
| 15 0 1 0 -5 >
29.724
sensmus
1232 / 1215
| 4 -5 -1 1 1 >
24.055
sevnothrush
3168 / 3125
| 5 2 -5 0 1 >
23.659
cassacot
245 / 242
| -1 0 1 2 -2 >
21.330
mothwellsma
99 / 98
| -1 2 0 -2 1 >
17.576
ptolemisma
100 / 99
| 2 -2 2 0 -1 >
17.399
hemimin
1344 / 1331
| 6 1 0 1 -3 >
16.827
biyatisma
121 / 120
| -3 -1 -1 0 2 >
14.367
aphrowe
1331 / 1323
| 0 -3 0 -2 3 >
10.437
valinorsma
176 / 175
| 4 0 -2 -1 1 >
9.865
pentacircle
896 / 891
| 7 -4 0 1 -1 >
9.688
orgonisma
65536 / 65219
| 16 0 0 -2 -3 >
8.394
rastma
243 / 242
| -1 5 0 0 -2 >
7.139
myhemiwell
3388 / 3375
| 2 -3 -3 1 2 >
6.656
keenanisma
385 / 384
| -7 -1 1 1 1 >
4.503
werckisma
441 / 440
| -3 2 -1 2 -1 >
3.930
moctdel
1375 / 1372
| -2 0 3 -3 1 >
3.781
swetisma
540 / 539
| 2 3 1 -2 -1 >
3.209
wizardharry
4000 / 3993
| 5 -1 3 0 -3 >
3.032
vishdel
5632 / 5625
| 9 -2 -4 0 1 >
2.153
sesdecal
234375 / 234256
| -4 1 7 0 -4 >
0.879
hemigail
43923 / 43904
| -7 1 0 -3 4 >
0.749
lehmerisma
3025 / 3024
| -4 -3 2 -1 2 >
0.572
kalisma, Gauss' comma
9801 / 9800
| -3 4 -2 -2 2 >
0.177
odiheim
151263 / 151250
| -1 2 -4 5 -2 >
0.149
parimo
1771561 / 1771470
| -1 -11 -1 0 6 >
0.089
ultimo
3294225 / 3294172
| -2 2 2 -7 4 >
0.028

13-limit commas

name(s)
ratio
monzo
cents
astbury
4826809 / 4718592
| -19 -2 0 0 0 6 >
39.255
negustma
78 / 77
| 1 1 0 -1 -1 1 >
22.229
superleap
91 / 90
| -1 -2 -1 1 0 1 >
19.130
animist
105 / 104
| -3 1 1 1 0 1 >
16.567
secorian
28672 / 28431
| 12 -7 0 1 0 -1 >
14.613
gassorma
275 / 273
| 0 -1 2 -1 1 -1 >
12.637
grossma
144 / 143
| 4 2 0 0 -1 -1 >
12.064
buzurgisma, dhanvantarisma
169 / 168
| -3 -1 0 -1 0 2 >
10.274
catadictma
1287 / 1280
| -8 2 -1 0 1 1 >
9.442
mynucuma
196 / 195
| 2 -1 -1 2 0 -1 >
8.855
huntma
640 / 637
| 7 0 1 -2 0 -1 >
8.134
threedie
2197 / 2187
| 0 -7 0 0 0 3 >
7.897
kestrel comma
1188 / 1183
| 2 3 0 -1 1 -2 >
7.302
marveltwin
325 / 324
| -2 -4 2 0 0 1 >
5.335
ratwolfsma
351 / 350
| -1 3 -2 -1 0 1 >
4.939
minthma
352 / 351
| 5 -3 0 0 1 -1 >
4.925
gentle comma
364 / 363
| 2 -1 0 1 -2 1 >
4.763
cuthbert
847 / 845
| 0 0 -1 1 2 -2 >
4.093
tunbarsma
625 / 624
| -4 -1 4 0 0 -1 >
2.772
island comma
676 / 675
| 2 -3 -2 0 0 2 >
2.563
squbema
729 / 728
| -3 6 0 -1 0 -1 >
2.376
petrma
2200 / 2197
| 3 0 2 0 1 -3 >
2.362
nicola
1575 / 1573
| 0 2 2 1 -2 -1 >
2.200
sinbadma
1001 / 1000
| -3 0 -3 1 1 1 >
1.730
cantonisma
10985 / 10976
| -5 0 1 -3 0 3 >
1.419
lummic
1716 / 1715
| 2 1 -1 -3 1 1 >
1.009
ibnsinma
2080 / 2079
| 5 -3 1 -1 -1 1 >
0.833
schismina
4096 / 4095
| 12 -2 -1 -1 0 -1 >
0.423
leprechaun comma
4225 / 4224
| -7 -1 2 0 -1 2 >
0.410
jacobin
6656 / 6655
| 9 0 -1 0 -3 1 >
0.260
harmonisma
10648 / 10647
| 3 -2 0 -1 3 -2 >
0.163
chalmersima
123201 / 123200
| -6 6 -2 -1 -1 2 >
0.014

17-limit commas

name(s)
ratio
monzo
cents
xenisma
2058 / 2057
| 1 1 0 3 -2 0 -1 >
0.841
scintillisma
194481 / 194480
| -4 4 -1 4 -1 -1 -1 >
0.009

19-limit commas

name(s)
ratio
monzo
cents
spleen comma
210 / 209
| 1 1 1 1 -1 0 0 -1 >
8.264
go comma
361 / 360
| -6 -1 0 0 0 0 0 2 >
4.802