Comma

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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 (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 is the convention elsewhere on the wiki.

List of commas, by prime limit

3-limit commas

Name(s) Color Name Ratio Monzo Cents
limma, Pythagorean minor second small wa 2nd sw2 256 / 243 | 8 -5 > 90.225
Pythagorean comma wa comma LLw-2 531441 / 524288 | -19 12 > 23.460
17-comma wa-17 comma ssw3 134217728 / 129140163 | 27 -17 > 66.765
29-comma wa-29 comma s4w4 70368744177664 / 68630377364883 | 46 -29 > 43.305
41-comma wa-41 comma s6w5 36893488147419103232 /
36472996377170786403
| 65 -41 > 19.845
Mercator's comma, 53-comma wa-53 comma L8w-6 19383245667680019896796723 /
19342813113834066795298816
| -84 53 > 3.6150
70-comma wa-70 comma s10w8 | 111 -70 > 63.150
77-comma wa-77 comma L11w-8 | -122 77 > 50.535
200-comma, Pythagorean integer cents comma wa-200 comma w-200 | 317 -200 > 8.9998

5-limit commas

Name(s) Color Name Ratio Monzo Cents
Twenty-two thirds limma L3y22-6 2384185791015625 / 2251799813685248 | -51 0 22 > 98.902
sibbolet L4y25-7 298023223876953125 / 288230376151711744 | -58 0 25 > 57.843
Hunt 5-cycle comma L4y28-8 37252902984619140625 / 36893488147419103232 | -65 0 28 > 16.784
acute thirds comma s4g319 | 72 0 -31 > 24.275
34-5-comma s5g3410 | 79 0 -34 > 65.334
Schismic thirds chromatic semitone L8y53-14 | -123 0 53 > 74.627
59-5-comma s9g5916 | 137 0 -59 > 7.4909
10-15-comma L3y10-4 576650390625 / 549755813888 | -39 10 10 > 82.687
11-15-comma s3g115 8796093022208 / 8649755859375 | 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 Ly1 135 / 128 | -7 3 1 > 92.179
ripple quintgu 2nd g52 6561 / 6250 | -1 8 -5 > 84.071
doublewide y8-2 390625 / 373248 | -9 -6 8 > 78.780
sevond sy71 5000000 / 4782969 | 6 -14 7 > 76.826
nusecond g113 51018336 / 48828125 | 5 13 -11 > 75.964
sentinel L3y4-3 8968066875 / 8589934592 | -33 15 4 > 74.580
chromatic semitone yoyo semitone yy1 25 / 24 | -3 -1 2 > 70.672
superpyth, grave minor second sy2 20480 / 19683 | 12 -9 1 > 68.719
major diesis, diminished comma quadgu 2nd g42 648 / 625 | 3 4 -4 > 62.565
passion small quintgu 3rd sg53 262144 / 253125 | 18 -4 -5 > 60.611
shibboleth y9-2 1953125 / 1889568 | -5 -10 9 > 57.273
mynic g103 10077696 / 9765625 | 9 9 -10 > 54.458
tritonic LLy5-3 553584375 / 536870912 | -29 11 5 > 53.074
negri comma, double augmentation diesis Ly4-2 16875 / 16384 | -14 3 4 > 51.120
maximal diesis, porcupine triple-yo comma y31 250 / 243 | 1 -5 3 > 49.166
immunity yoyo comma ssyy2 1638400 / 1594323 | 16 -13 2 > 47.212
diesis, augmented comma triple-gu comma g32 128 / 125 | 7 0 -3 > 41.059
wizard LLy12-4 2197265625 / 2147483648 | -31 2 12 > 39.675
sycamore Ly11-3 48828125 / 47775744 | -16 -6 11 > 37.721
fifive sy10-2 9765625 / 9565938 | -1 -14 10 > 35.767
unicorn Lg82 1594323 / 1562500 | -2 13 -8 > 34.905
valensixthtone sg93 1990656 / 1953125 | 13 5 -9 > 32.952
ampersand, Ampersand's comma LLy6-3 34171875 / 33554432 | -25 7 6 > 31.567
small diesis, magic comma quintyo comma Ly5-2 3125 / 3072 | -10 -1 5 > 29.614
minimal diesis, tetracot comma quadyo comma sy41 20000 / 19683 | 5 -9 4 > 27.660
roda ssy32 131072000 / 129140163 | 20 -17 3 > 25.706
maja sy17-3 762939453125 / 753145430616 | -3 -23 17 > 22.368
syntonic / Didymos / meantone gu comma g1 81 / 80 | -4 4 -1 > 21.506
maquila comma s3g176 562949953421312 / 556182861328125 | 49 -6 -17 > 20.937
diaschisma gugu comma sgg2 2048 / 2025 | 11 -4 -2 > 19.553
ditonma LLy13-4 1220703125 / 1207959552 | -27 -2 13 > 18.168
misty comma ssg33 67108864 / 66430125 | 26 -12 -3 > 17.599
pental comma L3g5-2 847288609443 / 838860800000 | -28 25 -5 > 17.306
graviton, gravity comma LLg61 129140163 / 128000000 | -13 17 -6 > 15.353
quartonic sy11-2 390625000 / 387420489 | 3 -18 11 > 14.261
medium semicomma, sensipent comma g72 78732 / 78125 | 2 9 -7 > 13.399
Würschmidt comma sg83 393216 / 390625 | 17 1 -8 > 11.445
semicomma, Fokker comma Ly7-3 2109375 / 2097152 | -21 3 7 > 10.061
escapade comma ssg94 4294967296 / 4271484375 | 32 -7 -9 > 9.4916
kleisma, semicomma majeur sixfold yo comma y6-2 15625 / 15552 | -6 -5 6 > 8.1073
qintosec comma s4g105 140737488355328 / 140126044921875 | 47 -15 -10 > 7.5378
unidecma Lg122 31381059609 / 31250000000 | -7 22 -12 > 7.2455
mutt comma L3y21-6 476837158203125 / 474989023199232 | -44 -3 21 > 6.7230
amity comma sy51 1600000 / 1594323 | 9 -13 5 > 6.1536
parakleisma g133 1224440064 / 1220703125 | 8 14 -13 > 5.2917
gammic comma Ly20-5 95367431640625 / 95105071448064 | -29 -11 20 > 4.7693
vulture comma ssy42 10485760000 / 10460353203 | 24 -21 4 > 4.1998
23-3/5-comma g235 12339534735212544 / 11920928955078125 | 17 23 -23 > 59.750
34-3/5-comma y343 | -25 -34 34 > 68.196
53-3/5-comma y537 | -39 -53 53 > 71.012

7-limit commas

Name(s) Color Name Ratio Monzo Cents
Archytas' 1/3-tone zo 2nd z2 28 / 27 | 2 -3 0 1 > 62.961
minor semitone zogu 2nd zg2 21 / 20 | -2 1 -1 1 > 84.467
hexadecatone comma, 16-7-comma 35184372088832 / 33232930569601 | 45 0 0 -16 > 98.785
21-7-comma 576460752303423488 / 558545864083284007 | 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 ruru negative 2nd Lrr-2 6561 / 6272 | -7 8 0 -2 > 77.988
36-7-comma | -101 0 0 36 > 77.733
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 quintru comma sr5-2 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 LLz8y82 2251875390625 / 2199023255552 | -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 rry-2 405 / 392 | -3 4 1 -2 > 56.482
Harrison's comma Lr-2 59049 / 57344 | -13 10 0 -1 > 50.724
keega triple-zogu comma z3g33 1029 / 1000 | -3 1 -3 3 > 49.492
septimal quarter tone rugu comma rg1 36 / 35 | 2 2 -1 -1 > 48.770
quarter tone comma | 49 50 -25 -25 > 19.260
cloudy quintzo comma Lz53 16807 / 16384 | -14 0 0 5 > 44.130
Avicenna, Avicenna's enharmonic diesis zoyoyo comma Lzyy1 525 / 512 | -9 1 2 1 > 43.408
slendro diesis zozo comma zz2 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 double-ruyo comma rryy-2 50 / 49 | 1 0 2 -2 > 34.976
eric r7-4 839808 / 823543 | 7 8 0 -7 > 33.859
senga triple-zo gugu comma z3gg3 686 / 675 | 1 -3 -2 3 > 27.985
septimal / Archytas' comma, Leipziger Komma ru comma r1 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 zo-triple-yo comma zy31 875 / 864 | -5 -3 3 1 > 21.902
gariboh r3y5-3 3125 / 3087 | 0 -2 5 -3 > 21.181
nuwell r4y-3 2430 / 2401 | 1 5 1 -4 > 20.785
tolerma szyy2 179200 / 177147 | 10 -11 2 1 > 19.948
mirwomo double-zoyo comma Lzzyy1 33075 / 32768 | -15 3 2 2 > 16.144
trimyna quintzogu comma z5g54 50421 / 50000 | -4 1 -5 5 > 14.516
sensamagic zozoyo comma zzy2 245 / 243 | 0 -5 1 2 > 14.191
septimal semicomma, starling comma zogugugu comma zg32 126 / 125 | 1 2 -3 1 > 13.795
octagar ruru-triple-yo comma rry3-2 4000 / 3969 | 5 -4 3 -2 > 13.469
orwellisma, orwell comma triple-ru gu comma r3g-2 1728 / 1715 | 6 3 -1 -3 > 13.074
quince 823543 / 819200 | -15 0 -2 7 > 9.1539
gamelisma Lz32 1029 / 1024 | -10 1 0 3 > 8.4327
varunisma zozoquadgu comma Lzzg42 321489 / 320000 | -9 8 -4 2 > 8.0370
septimal kleisma, marvel comma ruyoyo comma ryy-2 225 / 224 | -5 2 2 -1 > 7.7115
dimcomp 390625 / 388962 | -1 -4 8 -4 > 7.3861
cataharry Lrrgg-2 19683 / 19600 | -4 9 -2 -2 > 7.3158
mirkwai 16875 / 16807 | 0 3 4 -5 > 6.9903
stearnsma Lr6-4 118098 / 117649 | 1 10 0 -6 > 6.5946
hemimage sz3g3 10976 / 10935 | 5 -7 -1 3 > 6.4790
hemimean zzg53 3136 / 3125 | 6 0 -5 2 > 6.0832
hemifamity small ruyo comma sry1 5120 / 5103 | 10 -6 1 -1 > 5.7578
linus 578509309952 / 576650390625 | 11 -10 -10 10 > 5.5719
porwell srrg31 6144 / 6125 | 11 1 -3 -2 > 5.3620
garischisma ssr2 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 640000000000000000 / 635585924776181463 | 22 -32 16 -3 > 11.982
bapbo rurugu comma rrg1 256 / 245 | 8 0 -1 -2 > 76.034

11-limit commas

Name(s) Color Name Ratio Monzo Cents
undecimal comma, al-Farabi's 1/4-tone ilo 1o1 33 / 32 | -5 1 0 0 1 > 53.273
undecimal minor semitone loru semitone 1or1 22 / 21 | 1 -1 0 -1 1 > 80.537
11-cycle major seventh prote, 35-11-comma | -121 0 0 0 35 > 96.128
11-cycle chroma, 11-11-comma 285311670611 / 274877906944 | -38 0 0 0 11 > 64.497
Large lu unison L1u1 729 / 704 | -6 6 0 0 -1 > 60.412
Hunt 11-cycle comma | -83 0 0 0 24 > 31.631
Hunt flat 5 comma lu comma s1u2 8192 / 8019 | 13 -6 0 0 -1 > 36.952
sterno lorururu comma 1or3-2 352 / 343 | 5 0 0 -3 1 > 44.840
1/5-tone luyo comma 1uy1 45 / 44 | -2 2 1 0 -1 > 38.906
the Igs boson, 13-11-comma 35184372088832 / 34522712143931 | 45 0 0 0 -13 > 32.867
undecimal diesis luzogu comma 1uzg2 56 / 55 | 3 0 -1 1 -1 > 31.194
telepathma loyo comma 1oy1 55 / 54 | -1 -3 1 0 1 > 31.767
thuja comma s1u5y2 163840 / 161051 | 15 0 1 0 -5 > 29.724
sensmus s1ozg2 1232 / 1215 | 4 -5 -1 1 1 > 24.055
sevnothrush 1og52 3168 / 3125 | 5 2 -5 0 1 > 23.659
cassacot 1uuzzy2 245 / 242 | -1 0 1 2 -2 > 21.330
mothwellsma loruru comma 1orr-2 99 / 98 | -1 2 0 -2 1 > 17.576
ptolemisma luyoyo comma 1uyy1 100 / 99 | 2 -2 2 0 -1 > 17.399
hemimin lululuzo comma 1u3z2 1344 / 1331 | 6 1 0 1 -3 > 16.827
biyatisma lologu comma 1oog1 121 / 120 | -3 -1 -1 0 2 > 14.367
aphrowe 1o3rr-2 1331 / 1323 | 0 -3 0 -2 3 > 10.437
valinorsma lorugugu comma 1orgg1 176 / 175 | 4 0 -2 -1 1 > 9.8646
pentacircle luzo comma s1uz2 896 / 891 | 7 -4 0 1 -1 > 9.6880
orgonisma s1u3rr1 65536 / 65219 | 16 0 0 -2 -3 > 8.3944
rastma lulu comma 1uu1 243 / 242 | -1 5 0 0 -2 > 7.1391
myhemiwell 1oozg32 3388 / 3375 | 2 -3 -3 1 2 > 6.6556
keenanisma lozoyo comma 1ozy1 385 / 384 | -7 -1 1 1 1 > 4.5026
werckisma luzozogu comma 1uzzg2 441 / 440 | -3 2 -1 2 -1 > 3.9302
moctdel 1or3y3-3 1375 / 1372 | -2 0 3 -3 1 > 3.7814

13-limit commas

Name(s) Color Name Ratio Monzo Cents
tridecimal comma thu unison 3u1 27 / 26 | -1 3 0 0 0 -1 > 65.337
tridecimal 1/3-tone thogu 2nd 3og2 26 / 25 | 1 0 -2 0 0 1 > 67.900
Hunt 13-cycle comma L3o102 137858491849 / 137438953472 | -37 0 0 0 0 10 > 5.2766
silver half cents comma | -8881 0 0 0 0 2400 > 66.388
Hunt minor submediant comma L3o1 1053 / 1024 | -10 4 0 0 0 1 > 48.348
tridecimal minor diesis thuyo comma 3uy1 40 / 39 | 3 -1 1 0 0 -1 > 43.831
astburyp L3o62 4826809 / 4718592 | -19 -2 0 0 0 6 > 39.256
wilsorma thoyo comma 3oy1 65 / 64 | -6 0 1 0 0 1 > 26.841
winmeanma thulogu comma 3u1og1 66 / 65 | 1 1 -1 0 1 -1 > 26.432
negustma tholuru comma 3o1ur1 78 / 77 | 1 1 0 -1 -1 1 > 22.339
superleap thozogu comma 3ozg2 91 / 90 | -1 -2 -1 1 0 1 > 19.130
animist thuzoyo comma 3uzy1 105 / 104 | -3 1 1 1 0 -1 > 16.567
secorian s3uz2 28672 / 28431 | 12 -7 0 1 0 -1 > 14.613
mosaic L3orr-2 3159 / 3136 | -6 5 0 -2 0 1> 12.651
gassorma 3u1oryy-2 275 / 273 | 0 -1 2 -1 1 -1 > 12.637
grossma thulu comma 3u1u1 144 / 143 | 4 2 0 0 -1 -1 > 12.064
buzurgisma, dhanvantarisma 3oor1 169 / 168 | -3 -1 0 -1 0 2 > 10.274
catadictma thologu comma 3o1og1 1287 / 1280 | -8 2 -1 0 1 1 > 9.4419
mynucuma thuzozogu comma 3uzzg2 196 / 195 | 2 -1 -1 2 0 -1 > 8.8554
huntma thururuyo comma 3urry-2 640 / 637 | 7 0 1 -2 0 -1 > 8.1342
threedie triple-tho comma s3o32 2197 / 2187 | 0 -7 0 0 0 3 > 7.8980
kestrel comma 3uu1or-2 1188 / 1183 | 2 3 0 -1 1 -2 > 7.3017
marveltwin thoyoyo comma 3oyy1 325 / 324 | -2 -4 2 0 0 1 > 5.3351
ratwolfsma thorugugu comma 3orgg1 351 / 350 | -1 3 -2 -1 0 1 > 4.9393
minthma thulo comma 3u1o1 352 / 351 | 5 -3 0 0 1 -1 > 4.9253
gentle comma 3o1uuz2 364 / 363 | 2 -1 0 1 -2 1 > 4.7627
cuthbert 3uu1oozg1 847 / 845 | 0 0 -1 1 2 -2 > 4.0928

17-limit commas

Name(s) Color Name Ratio Monzo Cents
septendecimal 1/4-tone suzoyo unison 17uzy1 35 / 34 | -1 0 1 1 0 0 -1 > 50.184
solu 2nd 17o1u2 34 / 33 | 1 -1 0 0 -1 0 1 > 51.682
Arabic lute index finger su unison 17u1 18 / 17 | 1 2 0 0 0 0 -1 > 98.955
11 semitone comma 35184372088832 / 34271896307633 | 45 0 0 0 0 0 -11 > 45.490
12 semitone comma 582622237229761 / 562949953421312 | -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
17th-partial chroma sogugu comma 17ogg2 51 / 50 | -1 1 -2 0 0 0 1 > 34.283
sutho comma 17u3o1 52 / 51 | 2 -1 0 0 0 1 -1 > 33.617
soruyo comma 17ory1 85 / 84 | -2 -1 1 -1 0 0 1 > 20.488
Hunt flat 2 comma so comma L17o1 4131 / 4096 | -12 5 0 0 0 0 1 > 14.730
suruyo comma 17ury-2 120 / 119 | 3 1 1 -1 0 0 -1 > 14.487
Blume comma sololo comma 17o1oo1 2057 / 2048 | -11 0 0 0 2 0 1 > 7.5913
septendecimal kleisma sugu comma 17ug1 256 / 255 | 8 -1 -1 0 0 0 -1 > 6.7759
tannisma suthozo comma 17u3oz1 273 / 272 | -4 1 0 1 0 1 -1> 6.3532
septendecimal integer cents comma soso comma 17oo2 289 / 288 | -5 -2 0 0 0 0 2 > 6.0008

19-limit commas

Name(s) Color Name Ratio Monzo Cents
undevicesimal semitone ino 2nd 19o2 19 / 18 | -1 -2 0 0 0 0 0 1 > 93.603
small undevicesimal semitone nuyo unison 19uy1 20 / 19 | 2 0 1 0 0 0 0 -1 > 88.801
nutho comma 19u3o1 39 / 38 | -1 1 0 0 0 1 0 -1 > 44.970
noru comma 19or1 57 / 56 | -3 1 0 -1 0 0 0 1 > 30.642
nuruyo comma 19ury-2 135 / 133 | 0 3 1 -1 0 0 0 -1 > 25.840
nogugu comma 19ogg2 76 / 75 | 2 -1 -2 0 0 0 0 1 > 22.931
approximation to Pyth 53-comma nulozo comma 19u1o1 77 / 76 | -2 0 0 1 1 0 0 -1 > 22.631
19th-partial chroma nugu comma 19ug1 96 / 95 | 5 1 -1 0 0 0 0 -1 > 18.128
noluzo comma 19o1uz2 133 / 132 | -2 -1 0 1 -1 0 0 1 > 13.066
Ganassi's comma nuso comma 19u17o1 153 / 152 | -3 2 0 0 0 0 1 -1 > 11.352
nosugu comma 19o17ug1 171 / 170 | -1 2 -1 0 0 0 -1 1 > 10.154
Hunt 19-cycle comma quadnu comma s19u4-2 131072 / 130321 | 17 0 0 0 0 0 0 -4 > 9.9479
spleen comma nuluzoyo comma 19u1uzy1 210 / 209 | 1 1 1 1 -1 0 0 -1 > 8.2637
nusu comma 19u17u-2 324 / 323 | 2 4 0 0 0 0 -1 -1 > 5.3516
go comma nonogu comma 19oog2 361 / 360 | -3 -2 -1 0 0 0 0 2 > 4.8023