Definition[edit]
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 (0 cents) and not a power such as a square or cube of any other interval, and 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.
For commas over 100 cents in size, see Large commas; and for commas under 3.5 cents in size, see Unnoticeable commas
Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as stated by the conventions of this wiki. This is usually a bannable offense, as Mike Battaglia would say.
List of commas, by prime limit[edit]
3-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| limma, Pythagorean minor second
|
256 / 243
|
| 8 -5 >
|
90.225
|
| 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
|
| Pythagorean integer cents comma
|
|
| 317 -200 >
|
8.9998
|
| Mercator's comma, 53-comma
|
19383245667680019896796723/19342813113834066795298816
|
| -84 53 >
|
3.6150
|
| 70-comma
|
|
| 111 -70 >
|
63.150
|
5-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| Twenty-two thirds limma
|
|
| -51 0 22 >
|
98.902
|
| sibbolet
|
|
| -58 0 25 >
|
57.843
|
| Hunt 5-cycle comma
|
|
| -65 0 28 >
|
16.784
|
| acute thirds comma
|
|
| 72 0 -31 >
|
24.275
|
| 34-5-comma
|
|
| 79 0 -34 >
|
65.334
|
| Schismic thirds chromatic semitone
|
|
| -123 0 53 >
|
74.627
|
| 10-15-comma
|
|
| -39 10 10 >
|
82.687
|
| 11-15-comma
|
|
| 43 -11 -11 >
|
29.044
|
| 21-15-comma
|
|
| -82 21 21 >
|
53.643
|
| 32-15-comma
|
|
| -125 32 32 >
|
24.599
|
| Huntian 15-cycle comma
|
|
| 168 -43 -43 >
|
4.4453
|
| 56-syntonic comma
|
|
| -225 224 -56 >
|
4.3522
|
| 53-15-comma
|
|
| -207 53 53 >
|
78.242
|
| 54-15-comma
|
|
| 211 -54 -54 >
|
33.489
|
| 76-15-comma
|
|
| 297 -76 -76 >
|
91.578
|
| 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
|
|
| -3 -23 17 >
|
22.368
|
| syntonic comma, Didymos comma, meantone comma
|
81 / 80
|
| -4 4 -1 >
|
21.506
|
| maquila comma
|
|
| 49 -6 -17 >
|
20.937
|
| 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
|
| pental comma
|
|
| -28 25 -5 >
|
17.306
|
| 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
|
| Würschmidt comma
|
393216 / 390625
|
| 17 1 -8 >
|
11.445
|
| semicomma, Fokker comma
|
2109375 / 2097152
|
| -21 3 7 >
|
10.061
|
| escapade comma
|
4294967296 / 4271484375
|
| 32 -7 -9 >
|
9.4916
|
| kleisma, semicomma majeur
|
15625 / 15552
|
| -6 -5 6 >
|
8.1073
|
| unidecma
|
31381059609 / 31250000000
|
| -7 22 -12 >
|
7.2455
|
| mutt comma
|
|
| -44 -3 21 >
|
6.7230
|
| amity comma
|
1600000 / 1594323
|
| 9 -13 5 >
|
6.1536
|
| parakleisma
|
1224440064 / 1220703125
|
| 8 14 -13 >
|
5.2917
|
| gammic comma
|
|
| -29 -11 20 >
|
4.7693
|
| vulture comma
|
10485760000 / 10460353203
|
| 24 -21 4 >
|
4.1998
|
| 23-3/5-comma
|
|
| 17 23 -23 >
|
59.750
|
| 34-3/5-comma
|
|
| -25 -34 34 >
|
68.196
|
| 53-3/5-comma
|
|
| -39 -53 53 >
|
71.012
|
7-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| hexadecatone comma, 16-7-comma
|
|
| 45 0 0 -16 >
|
98.785
|
| 21-7-comma
|
|
| 59 0 0 -21 >
|
54.656
|
| Hunt 7-cycle comma
|
|
| 73 0 0 -26 >
|
10.526
|
| German sixth comma
|
|
| -87 0 0 31 >
|
33.603
|
| large deep red comma
|
6561 / 6272
|
| -7, 8, 0 -2 >
|
77.988
|
| 36-7-comma
|
|
| -101 0 0 36 >
|
77.736
|
| 47-7-comma
|
|
| 132 0 0 -47 >
|
65.182
|
slendro integer cents comma
|
|
| 1123 0 0 -400 >
|
69.637
|
| 29-7/5-comma
|
|
| -14 0 -29 29 >
|
92.854
|
| 31-7/5-comma
|
|
| -15 0 -31 31 >
|
57.878
|
| 33-7/5-comma
|
|
| -16 0 -33 33 >
|
22.902
|
| 35-7/5-comma
|
|
| 17 0 35 -35 >
|
12.073
|
| 37-7/5-comma
|
|
| 18 0 37 -37 >
|
47.049
|
| 39-7/5-comma
|
|
| 19 0 39 -39 >
|
82.024
|
| 5-21-comma
|
4194304 / 4084101
|
| 22 -5 0 -5 >
|
46.095
|
| 18-21-comma
|
|
| -79 18 0 18 >
|
74.056
|
| 23-21-comma
|
|
| -101 23 0 23 >
|
27.961
|
| Huntian 21-cycle comma
|
|
| 123 -28 0 -28 >
|
18.135
|
| 33-21-comma
|
|
| 145 -33 0 -33 >
|
64.230
|
| 8-35-comma
|
|
| -41 0 8 8 >
|
41.117
|
| 15-35-comma
|
|
| 77 0 -15 -15 >
|
72.906
|
| 23-35-comma
|
|
| 118 0 -23 -23 >
|
31.789
|
| 31-35-comma
|
|
| -159 0 31 31 >
|
9.3282
|
| 39-35-comma
|
|
| -200 0 39 39 >
|
50.445
|
| 47-35-comma
|
|
| -241 0 47 47 >
|
91.562
|
| Huntian 35-cycle comma
|
|
| 277 0 -54 -54 >
|
22.461
|
| 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
|
| quarter tone comma
|
|
| 49 50 -25 -25 >
|
19.260
|
| cloudy
|
16807 / 16384
|
| -14 0 0 5 >
|
44.130
|
| Avicenna, Avicenna's enharmonic diesis
|
525 / 512
|
| -9 1 2 1 >
|
43.408
|
| slendro diesis
|
49 / 48
|
| -4 -1 0 2 >
|
35.697
|
| slendro 34-comma
|
|
| -137 -34 0 68 >
|
13.692
|
| 34-jubilismic comma
|
|
| -33 0 -68 68 >
|
10.829
|
| 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 >
|
9.1539
|
| gamelisma
|
1029 / 1024
|
| -10 1 0 3 >
|
8.4327
|
| varunisma
|
321489 / 320000
|
| -9 8 -4 2 >
|
8.0370
|
| septimal kleisma, marvel comma
|
225 / 224
|
| -5 2 2 -1 >
|
7.7115
|
| dimcomp
|
390625 / 388962
|
| -1 -4 8 -4 >
|
7.3861
|
| cataharry
|
19683 / 19600
|
| -4 9 -2 -2 >
|
7.3158
|
| mirkwai
|
16875 / 16807
|
| 0 3 4 -5 >
|
6.9903
|
| stearnsma
|
118098 / 117649
|
| 1 10 0 -6 >
|
6.5946
|
| hemimage
|
10976 / 10935
|
| 5 -7 -1 3 >
|
6.4790
|
| hemimean
|
3136 / 3125
|
| 6 0 -5 2 >
|
6.0832
|
| hemifamity
|
5120 / 5103
|
| 10 -6 1 -1 >
|
5.7578
|
| linus
|
|
| 11 -10 -10 10 >
|
5.5719
|
| porwell
|
6144 / 6125
|
| 11 1 -3 -2 >
|
5.3620
|
| garischisma
|
33554432 / 33480783
|
| 25 -14 0 -1 >
|
3.8041
|
| wadisma
|
201768035 / 201326592
|
| -26 -1 1 9 >
|
3.7919
|
| quasiorwellisma
|
29360128 / 29296875
|
| 22 -1 -10 1 >
|
3.7338
|
| 218edo (stacked 7/4 and 10/9) comma
|
|
| 22 -32 16 -3 >
|
11.982
|
| bapbo
|
256 / 245
|
| 8 0 -1 -2 >
|
76.034
|
11-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| 11-cycle chroma, 11-11-comma
|
|
| -38 0 0 0 11 >
|
64.497
|
| 11-cycle major seventh prote, 35-11-comma
|
|
| -121 0 0 0 35 >
|
96.128
|
| Hunt 11-cycle comma
|
|
| -83 0 0 0 24 >
|
31.631
|
| Hunt flat 5 comma
|
8192 / 8019
|
| 13 -6 0 0 -1 >
|
36.952
|
| sterno
|
352 / 343
|
| 5 0 0 -3 1 >
|
44.840
|
| the Igs boson, 13-11-comma
|
|
| 45 0 0 0 -13 >
|
32.867
|
| telepathma
|
55 / 54
|
| -1 -3 1 0 1 >
|
31.767
|
| 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 >
|
9.8646
|
| pentacircle
|
896 / 891
|
| 7 -4 0 1 -1 >
|
9.6880
|
| orgonisma
|
65536 / 65219
|
| 16 0 0 -2 -3 >
|
8.3944
|
| rastma
|
243 / 242
|
| -1 5 0 0 -2 >
|
7.1391
|
| myhemiwell
|
3388 / 3375
|
| 2 -3 -3 1 2 >
|
6.6556
|
| keenanisma
|
385 / 384
|
| -7 -1 1 1 1 >
|
4.5026
|
| werckisma
|
441 / 440
|
| -3 2 -1 2 -1 >
|
3.9302
|
| moctdel
|
1375 / 1372
|
| -2 0 3 -3 1 >
|
3.7814
|
13-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| Sinbadma
|
1001 / 1000
|
| -3 0 -3 1 1 1 >
|
1.7304
|
| Hunt 13-cycle comma
|
|
| -37 0 0 0 0 10 >
|
5.2766
|
silver half cents comma
|
|
| -8881 0 0 0 0 2400 >
|
66.389
|
| Hunt minor submediant comma
|
1053 / 1024
|
| -10 4 0 0 0 1 >
|
48.348
|
| astburyp
|
4826809 / 4718592
|
| -19 -2 0 0 0 6 >
|
39.255
|
| wilsorma
|
65 / 64
|
| -6 0 1 0 0 1 >
|
26.841
|
| winmeanma
|
66 / 65
|
| 1 1 -1 0 1 -1 >
|
26.432
|
| negustma
|
78 / 77
|
| 1 1 0 -1 -1 1 >
|
22.339
|
| 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
|
| mosaic
|
3159 / 3136
|
| -6 5 0 -2 0 1>
|
12.651
|
| 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 >
|
9.4419
|
| mynucuma
|
196 / 195
|
| 2 -1 -1 2 0 -1 >
|
8.8554
|
| huntma
|
640 / 637
|
| 7 0 1 -2 0 -1 >
|
8.1342
|
| threedie
|
2197 / 2187
|
| 0 -7 0 0 0 3 >
|
7.8980
|
| kestrel comma
|
1188 / 1183
|
| 2 3 0 -1 1 -2 >
|
7.3017
|
| marveltwin
|
325 / 324
|
| -2 -4 2 0 0 1 >
|
5.3351
|
| ratwolfsma
|
351 / 350
|
| -1 3 -2 -1 0 1 >
|
4.9393
|
| minthma
|
352 / 351
|
| 5 -3 0 0 1 -1 >
|
4.9253
|
|
|
364 / 363
|
| 2 -1 0 1 -2 1 >
|
4.7627
|
| cuthbert
|
847 / 845
|
| 0 0 -1 1 2 -2 >
|
4.0928
|
17-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| 11 semitone comma
|
|
| 45 0 0 0 0 0 -11 >
|
45.490
|
| 12 semitone comma
|
|
| -49 0 0 0 0 0 12 >
|
59.465
|
| 23 semitone comma
|
|
| -94 0 0 0 0 0 23 >
|
13.974
|
| Hunt 17-cycle comma
|
|
| 139 0 0 0 0 0 -34 >
|
31.516
|
17-ripple integer cents comma
|
|
| 327 0 0 0 0 0 -80 >
|
3.5672
|
| Hunt flat 2 comma
|
4131 / 4096
|
| -12 5 0 0 0 0 1 >
|
14.730
|
| Blume comma
|
2057 / 2048
|
| -11 0 0 0 2 0 1 >
|
7.5913
|
| Septendecimal integer cents comma
|
289 / 288
|
| -5 -2 0 0 0 0 2 >
|
6.0008
|
| Tannisma
|
273/272
|
| -4 1 0 1 0 1 -1>
|
6.3532
|
19-limit commas[edit]
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| Hunt 19-cycle comma
|
131072 / 130321
|
| 17 0 0 0 0 0 0 -4 >
|
9.9479
|
| spleen comma
|
210 / 209
|
| 1 1 1 1 -1 0 0 -1 >
|
8.2637
|
| go comma
|
361 / 360
|
| -3 -2 -1 0 0 0 0 2 >
|
4.8023
|
de:Komma