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
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	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	95105071448064 / 95367431640625	[-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
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 / ru / 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, 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 / 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
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
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⟩	66.389
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⟩	39.255
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
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 / soso comma	17oo2	289 / 288	[-5 -2 0 0 0 0 2⟩	6.0008

19-limit commas

Name(s)	Color Name	Ratio	Monzo	Cents
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 53-tone 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