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	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