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

This page needs reworking. It is so broken, that Unnoticeable commas are not listed here, and many of the ratios are missing.

List of commas, by prime limit

3-limit commas

Name(s)	Ratio	Monzo	Cents
limma, Pythagorean minor second	256 / 243	[8 -5⟩	90.225
Pythagorean comma	531441/524288	[-19 12⟩	23.460
17-comma	134217728 / 129140163	[27 -17⟩	66.765
29-comma		[46 -29⟩	43.305
41-comma		[65 -41⟩	19.845
Pythagorean integer cents comma		[317 -200⟩	8.9998
Mercator's comma, 53-comma	19383245667680019896796723/19342813113834066795298816	[-84 53⟩	3.6150
70-comma		[111 -70⟩	63.150

5-limit commas

Name(s)	Ratio	Monzo	Cents
Twenty-two thirds limma		[-51 0 22⟩	98.902
sibbolet		[-58 0 25⟩	57.843
Hunt 5-cycle comma		[-65 0 28⟩	16.784
acute thirds comma		[72 0 -31⟩	24.275
34-5-comma		[79 0 -34⟩	65.334
Schismic thirds chromatic semitone		[-123 0 53⟩	74.627
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	135 / 128	[-7 3 1⟩	92.179
ripple	6561 / 6250	[-1 8 -5⟩	84.071
doublewide	390625 / 373248	[-9 -6 8⟩	78.780
sevond	5000000 / 4782969	[6 -14 7⟩	76.826
nusecond	51018336 / 48828125	[5 13 -11⟩	75.964
sentinel	8968066875 / 8589934592	[-33 15 4⟩	74.580
chromatic semitone	25 / 24	[-3 -1 2⟩	70.672
superpyth, grave minor second	20480 / 19683	[12 -9 1⟩	68.719
major diesis, diminished comma	648 / 625	[3 4 -4⟩	62.565
passion	262144 / 253125	[18 -4 -5⟩	60.611
shibboleth	1953125 / 1889568	[-5 -10 9⟩	57.273
mynic	10077696 / 9765625	[9 9 -10⟩	54.458
tritonic	553584375 / 536870912	[-29 11 5⟩	53.074
negri comma, double augmentation diesis	16875 / 16384	[-14 3 4⟩	51.120
maximal diesis, porcupine comma	250 / 243	[1 -5 3⟩	49.166
immunity	1638400 / 1594323	[16 -13 2⟩	47.212
diesis, augmented comma	128 / 125	[7 0 -3⟩	41.059
wizard	2197265625 / 2147483648	[-31 2 12⟩	39.675
sycamore	48828125 / 47775744	[-16 -6 11⟩	37.721
fifive	9765625 / 9565938	[-1 -14 10⟩	35.767
unicorn	1594323 / 1562500	[-2 13 -8⟩	34.905
valensixthtone	1990656 / 1953125	[13 5 -9⟩	32.952
ampersand, Ampersand's comma	34171875 / 33554432	[-25 7 6⟩	31.567
small diesis, magic comma	3125 / 3072	[-10 -1 5⟩	29.614
minimal diesis, tetracot comma	20000 / 19683	[5 -9 4⟩	27.660
roda	131072000 / 129140163	[20 -17 3⟩	25.706
maja		[-3 -23 17⟩	22.368
syntonic comma, Didymos comma, meantone comma	81 / 80	[-4 4 -1⟩	21.506
maquila comma		[49 -6 -17⟩	20.937
diaschisma	2048 / 2025	[11 -4 -2⟩	19.553
ditonma	1220703125 / 1207959552	[-27 -2 13⟩	18.168
misty comma	67108864 / 66430125	[26 -12 -3⟩	17.599
pental comma		[-28 25 -5⟩	17.306
graviton, gravity comma	129140163 / 128000000	[-13 17 -6⟩	15.353
quartonic	390625000 / 387420489	[3 -18 11⟩	14.261
medium semicomma, sensipent comma	78732 / 78125	[2 9 -7⟩	13.399
Würschmidt comma	393216 / 390625	[17 1 -8⟩	11.445
semicomma, Fokker comma	2109375 / 2097152	[-21 3 7⟩	10.061
escapade comma	4294967296 / 4271484375	[32 -7 -9⟩	9.4916
kleisma, semicomma majeur	15625 / 15552	[-6 -5 6⟩	8.1073
unidecma	31381059609 / 31250000000	[-7 22 -12⟩	7.2455
mutt comma		[-44 -3 21⟩	6.7230
amity comma	1600000 / 1594323	[9 -13 5⟩	6.1536
parakleisma	1224440064 / 1220703125	[8 14 -13⟩	5.2917
gammic comma		[-29 -11 20⟩	4.7693
vulture comma	10485760000 / 10460353203	[24 -21 4⟩	4.1998
23-3/5-comma		[17 23 -23⟩	59.750
34-3/5-comma		[-25 -34 34⟩	68.196
53-3/5-comma		[-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
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