Small comma

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	sw2, small wa 2nd	256 / 243	[8 -5⟩	90.225
Pythagorean comma	LLw-2, wa comma	531441/524288	[-19 12⟩	23.460
17-comma	ssw3, wa-17 comma	134217728/129140163	[27 -17⟩	66.765
29-comma	s4w4, wa-29 comma	70368744177664/68630377364883	[46 -29⟩	43.305
41-comma	s6w5, wa-41 comma	36893488147419103232/ 36472996377170786403	[65 -41⟩	19.845
Pythagorean integer cents comma	w-200, wa-200 comma		[317 -200⟩	8.9998
Mercator's comma, 53-comma	L8w-6, wa-53 comma	19383245667680019896796723/ 19342813113834066795298816	[-84 53⟩	3.6150
70-comma	s10w8, wa-70 comma		[111 -70⟩	63.150

5-limit commas

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

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

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
gentle comma	364 / 363	[2 -1 0 1 -2 1⟩	4.7627
cuthbert	847 / 845	[0 0 -1 1 2 -2⟩	4.0928

17-limit commas

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

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