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
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
Pythagorean integer cents comma	w-200	wa-200 comma		[317 -200⟩	8.9998

5-limit commas

Name(s)	Color name	Ratio	Monzo	Cents
Twenty-two thirds limma	L3y22-6		[-51 0 22⟩	98.902
sibbolet	L4y25-7		[-58 0 25⟩	57.843
Hunt 5-cycle comma	L4y28-8		[-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	135 / 128	[-7 3 1⟩	92.179
ripple	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	yy1	25 / 24	[-3 -1 2⟩	70.672
superpyth, grave minor second	sy2	20480 / 19683	[12 -9 1⟩	68.719
major diesis, diminished comma	g42	648 / 625	[3 4 -4⟩	62.565
passion	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 comma	y31	250 / 243	[1 -5 3⟩	49.166
immunity	ssyy2	1638400 / 1594323	[16 -13 2⟩	47.212
diesis, augmented 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	Ly5-2	3125 / 3072	[-10 -1 5⟩	29.614
minimal diesis, tetracot 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 comma	g1	81 / 80	[-4 4 -1⟩	21.506
maquila comma	s3g176	562949953421312 / 556182861328125	[49 -6 -17⟩	20.937
diaschisma	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	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	95105071448064 / 95367431640625	[-29 -11 20⟩	4.7693
vulture comma	ssy42	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)	Color Name	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 ruru negative 2nd	Lrr-2	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	rg1	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	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	rryy-2	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	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		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	zggg2	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	Lz32	1029 / 1024	[-10 1 0 3⟩	8.4327
varunisma		321489 / 320000	[-9 8 -4 2⟩	8.0370
septimal kleisma, marvel comma	ryy-2	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	rrg1	256 / 245	[8 0 -1 -2⟩	76.034

11-limit commas

Name(s)	Color Name	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	1oy1	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	1orr-2	99 / 98	[-1 2 0 -2 1⟩	17.576
ptolemisma	1uyy1	100 / 99	[2 -2 2 0 -1⟩	17.399
hemimin		1344 / 1331	[6 1 0 1 -3⟩	16.827
biyatisma	1oog1	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	1uzzg2	441 / 440	[-3 2 -1 2 -1⟩	3.9302
moctdel		1375 / 1372	[-2 0 3 -3 1⟩	3.7814

13-limit commas

Name(s)	Color Name	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	L3o1	1053 / 1024	[-10 4 0 0 0 1⟩	48.348
astburyp		4826809 / 4718592	[-19 -2 0 0 0 6⟩	39.255
wilsorma	3oy1	65 / 64	[-6 0 1 0 0 1⟩	26.841
winmeanma	3u1og1	66 / 65	[1 1 -1 0 1 -1⟩	26.432
negustma	3o1ur1	78 / 77	[1 1 0 -1 -1 1⟩	22.339
superleap	3ozg2	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)	Color Name	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	17oo2	289 / 288	[-5 -2 0 0 0 0 2⟩	6.0008
Tannisma	17u3oz1	273 / 272	[-4 1 0 1 0 1 -1⟩	6.3532

19-limit commas

Name(s)	Color Name	Ratio	Monzo	Cents
Hunt 19-cycle comma		131072 / 130321	[17 0 0 0 0 0 0 -4⟩	9.9479
spleen comma	19u1uzy1	210 / 209	[1 1 1 1 -1 0 0 -1⟩	8.2637
go comma	19oog2	361 / 360	[-3 -2 -1 0 0 0 0 2⟩	4.8023