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. The color name refers to both the comma and the temperament created when it is tempered out, except for 3-limit commas, which create edos.

For commas over 100 cents in size, see Large commas; for commas in between 30 and 100 cents in size, see Medium 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
Pythagorean comma	wa comma	LLw-2	531441 / 524288	[-19 12⟩	23.46
41-comma	wa-41 comma	s6w5	36893488147419103232 / 36472996377170786403	[65 -41⟩	19.845
200-comma, Pythagorean integer cents comma	wa-200 comma	w-200		[317 -200⟩	8.9998
Mercator's comma, 53-comma	wa-53 comma	L8w-6	19383245667680019896796723 / 19342813113834066795298816	[-84 53⟩	3.615
51-Pythagorean comma				| -970 612 >	3.5395

5-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents
small diesis, magic comma	Laquinyo	Ly5-2	3125 / 3072	[-10 -1 5⟩	29.614
11-15-comma, hendecatonic comma	Trisa-legu	s3g115	8796093022208 / 8649755859375	[43 -11 -11⟩	29.044
minimal diesis, tetracot comma	Saquadyo	sy41	20000 / 19683	[5 -9 4⟩	27.660
semaja	Lalaneyo	LLy19-5	19073486328125 / 18786186952704	[-33 -7 19⟩	26.276
quanic comma	Sepsa-quinyo	s7y55		[74 -54 5⟩	25.999
roda	Sasa-triyo	ssy32	131072000 / 129140163	[20 -17 3⟩	25.706
trisedodge comma	Saquintrigu	sg154	30958682112 / 30517578125	[19 10 -15⟩	24.844
maja	Saseyo	sy17-3	762939453125 / 753145430616	[-3 -23 17⟩	22.368
satin comma	Quinbisa-triyo	s10y37		[104 -70 3⟩	22.091
misneb	Quadla-quintriyo	L4y15-6		[-57 14 15⟩	22.076
syntonic / Didymos / meantone comma	Gu	g1	81 / 80	[-4 4 -1⟩	21.506
maquila comma	Trisa-segu	s3g176	562949953421312 / 556182861328125	[49 -6 -17⟩	20.937
diaschisma	Sagugu	sgg2	2048 / 2025	[11 -4 -2⟩	19.553
countermeantone comma	Quinquadgu	g204	96402615118848 / 95367431640625	[10 23 -20⟩	18.691
ditonma	Lala-theyo	LLy13-4	1220703125 / 1207959552	[-27 -2 13⟩	18.168
misty comma	Sasa-trigu	ssg33	67108864 / 66430125	[26 -12 -3⟩	17.599
pental comma	Trila-quingu	L3g5-2	847288609443 / 838860800000	[-28 25 -5⟩	17.306
undim comma	Trisa-quadgu	s3g44	2199023255552 / 2179240250625	[41 -20 -4⟩	15.645
graviton, gravity comma	Lala-tribigu	LLg61	129140163 / 128000000	[-13 17 -6⟩	15.353
majvam	Sasa-lebigu	ssg226		[40 7 -22⟩	14.783
quartonic	Saleyo	sy11-2	390625000 / 387420489	[3 -18 11⟩	14.261
untritonic comma	Quadla-tritriyo	L4y9-5		[-51 19 9⟩	13.968
medium semicomma, sensipent comma	Sepgu	g72	78732 / 78125	[2 9 -7⟩	13.399
tertiosec comma	Laquadtribiyo	L6y24-9		[-89 21 24⟩	12.584
Würschmidt comma	Saquadbigu	sg83	393216 / 390625	[17 1 -8⟩	11.445
counterhanson comma	Quinquinyo	y25-5		[-20 -24 25⟩	10.923
semicomma, Fokker comma	Lasepyo	Ly7-3	2109375 / 2097152	[-21 3 7⟩	10.061
escapade comma	Sasa-tritrigu	ssg94	4294967296 / 4271484375	[32 -7 -9⟩	9.4916
kleisma, semicomma majeur	Tribiyo	y6-2	15625 / 15552	[-6 -5 6⟩	8.1073
qintosec comma	Quadsa-quinbigu	s4g105	140737488355328 / 140126044921875	[47 -15 -10⟩	7.5378
59-5-comma				[137 0 -59⟩	7.4909
unidecma	Laquadtrigu	Lg122	31381059609 / 31250000000	[-7 22 -12⟩	7.2455
mutt comma	Trila-septriyo	L3y21-6	476837158203125 / 474989023199232	[-44 -3 21⟩	6.7230
amity comma	Saquinyo	sy51	1600000 / 1594323	[9 -13 5⟩	6.1536
parakleisma	Thegu	g133	1224440064 / 1220703125	[8 14 -13⟩	5.2917
gammic comma	Laquinquadyo	Ly20-5	95367431640625 / 95105071448064	[-29 -11 20⟩	4.7693
squarschmidt comma	Quadsa-twenty-negu	s4g298		[61 4 -29⟩	4.7223
Huntian 15-cycle comma	Quadtrisa-forty-thegu	s12g4316		[168 -43 -43⟩	4.4453
56-syntonic comma	Quadtribila-sepquadbigu	L24g56-8		[-225 224 -56⟩	4.3522
vulture comma	Sasa-quadyo	ssy42	10485760000 / 10460353203	[24 -21 4⟩	4.1998
lafa comma	Tribisa-quadtrigu	s6g127		[77 -31 -12⟩	3.6304

7-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents
senga	Trizo-agugu	z3gg3	686 / 675	[1 -3 -2 3⟩	27.985
23-21-comma	Sepla-twentythezo	L7z237		[-101 23 0 23⟩	27.961
septimal / Archytas' comma, Leipziger Komma	Ru	r1	64 / 63	[6 -2 0 -1⟩	27.264
mandos	Birugugu	rrg41	31104 / 30625	[7 5 -4 -2⟩	26.868
33-7/5-comma				[-16 0 -33 33⟩	22.902
Huntian 35-cycle comma				[277 0 -54 -54⟩	22.461
blackjackisma	Lasepru-aquadbiyo	Lr7y8-6	854296875 / 843308032	[-10 7 8 -7⟩	22.413
squalentine	Laquadzo-atrigu	Lz4g33	64827 / 64000	[-9 3 -3 4⟩	22.227
keema	Zotriyo	zy31	875 / 864	[-5 -3 3 1⟩	21.902
gariboh	Triru-aquinyo	r3y5-3	3125 / 3087	[0 -2 5 -3⟩	21.181
nuwell	Quadru-ayo	r4y-3	2430 / 2401	[1 5 1 -4⟩	20.785
small quadruple bluish	Saquadzogu	sz4g44	153664 / 151875	[6 -5 -4 4⟩	20.274
tolerma	Sazoyoyo	szyy2	179200 / 177147	[10 -11 2 1⟩	19.948
25-36/35-comma, icosipentatonic comma	quinquinrugu	r25g25-8		[49 50 -25 -25⟩	19.26
Huntian 21-cycle comma				[123 -28 0 -28⟩	18.135
mirwomo	Labizoyo	Lzzyy1	33075 / 32768	[-15 3 2 2⟩	16.144
trimyna	Quinzogu	z5g54	50421 / 50000	[-4 1 -5 5⟩	14.516
sensamagic	Zozoyo	zzy2	245 / 243	[0 -5 1 2⟩	14.191
septimal semicomma, starling comma	Zotrigu	zg32	126 / 125	[1 2 -3 1⟩	13.795
slendro 34-comma				[-137 -34 0 68⟩	13.692
octagar	Rurutriyo	rry3-2	4000 / 3969	[5 -4 3 -2⟩	13.469
orwellisma, orwell comma	Triru-agu	r3g-2	1728 / 1715	[6 3 -1 -3⟩	13.074
35-7/5-comma				[17 0 35 -35⟩	12.073
218edo (stacked 7/4 and 10/9) comma	Trisa-triru-aquadquadyo	s3r3y16-3	640000000000000000 / 635585924776181463	[22 -32 16 -3⟩	11.982
34-jubilismic comma	sequadzogu	z68g6842		[-33 0 -68 68⟩	10.829
Hunt 7-cycle comma				[73 0 0 -26⟩	10.526
31-35-comma				[-159 0 31 31⟩	9.3282
quince	Lasepzo-agugu	Lz7gg4	823543 / 819200	[-15 0 -2 7⟩	9.1539
gamelisma	Latrizo	Lz32	1029 / 1024	[-10 1 0 3⟩	8.4327
varunisma	Labizogugu	Lzzg42	321489 / 320000	[-9 8 -4 2⟩	8.037
septimal kleisma, marvel comma	Ruyoyo	ryy-2	225 / 224	[-5 2 2 -1⟩	7.7115
dimcomp	Quadruyoyo	r4y8-4	390625 / 388962	[-1 -4 8 -4⟩	7.3861
cataharry	Labirugu	Lrrgg-2	19683 / 19600	[-4 9 -2 -2⟩	7.3158
mirkwai	Quinru-aquadyo	r5y4-4	16875 / 16807	[0 3 4 -5⟩	6.9903
stearnsma	Latribiru	Lr6-4	118098 / 117649	[1 10 0 -6⟩	6.5946
hemimage	Satrizo-agu	sz3g3	10976 / 10935	[5 -7 -1 3⟩	6.479
hemimean	Zozoquingu	zzg53	3136 / 3125	[6 0 -5 2⟩	6.0832
hemifamity	Saruyo	sry1	5120 / 5103	[10 -6 1 -1⟩	5.7578
linus comma	Saquinbizogu	sz10g108	578509309952 / 576650390625	[11 -10 -10 10⟩	5.5719
porwell	Sarurutrigu	srrg31	6144 / 6125	[11 1 -3 -2⟩	5.362
garischisma	Sasaru	ssr2	33554432 / 33480783	[25 -14 0 -1⟩	3.8041
wadisma	Latritrizo-ayo	Lz9y4	201768035 / 201326592	[-26 -1 1 9⟩	3.7919
quasiorwellisma	Sazoquinbigu	szg104	29360128 / 29296875	[22 -1 -10 1⟩	3.7338

11-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents
thuja comma	Saquinlu-ayo	s1u5y2	163840 / 161051	[15 0 1 0 -5⟩	29.724
sensmus	Salozogu	s1ozg2	1232 / 1215	[4 -5 -1 1 1⟩	24.055
sevnothrush	Loquingu	1og52	3168 / 3125	[5 2 -5 0 1⟩	23.659
cassacot	Biluzo-ayo	1uuzzy2	245 / 242	[-1 0 1 2 -2⟩	21.330
mothwellsma	Loruru	1orr-2	99 / 98	[-1 2 0 -2 1⟩	17.576
ptolemisma	Luyoyo	1uyy1	100 / 99	[2 -2 2 0 -1⟩	17.399
hemimin	Trilu-azo	1u3z2	1344 / 1331	[6 1 0 1 -3⟩	16.827
biyatisma	Lologu	1oog1	121 / 120	[-3 -1 -1 0 2⟩	14.367
aphrowe	Trilo-aruru	1o3rr-2	1331 / 1323	[0 -3 0 -2 3⟩	10.437
valinorsma	Lorugugu	1orgg1	176 / 175	[4 0 -2 -1 1⟩	9.8646
pentacircle	Saluzo	s1uz2	896 / 891	[7 -4 0 1 -1⟩	9.688
orgonisma	Satrilu-aruru	s1u3rr1	65536 / 65219	[16 0 0 -2 -3⟩	8.3944
pentadecatonic comma	Sasaquintriloru	ss1o15r15-8		[14 -15 0 -15 15⟩	8.0555
rastma	Lulu	1uu1	243 / 242	[-1 5 0 0 -2⟩	7.1391
myhemiwell	Lolozotrigu	1oozg32	3388 / 3375	[2 -3 -3 1 2⟩	6.6556
octatonic comma	Quadbilu	1u82	214990848 / 214358881	[15 8 0 0 -8⟩	5.0965
keenanisma	Lozoyo	1ozy1	385 / 384	[-7 -1 1 1 1⟩	4.5026
werckisma	Luzozogu	1uzzg2	441 / 440	[-3 2 -1 2 -1⟩	3.9302
moctdel	Lotriruyo	1or3y3-3	1375 / 1372	[-2 0 3 -3 1⟩	3.7814

13-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents
wilsorma	Thoyo	3oy1	65 / 64	[-6 0 1 0 0 1⟩	26.841
winmeanma	Thulogu	3u1og1	66 / 65	[1 1 -1 0 1 -1⟩	26.432
negustma	Tholuru	3o1ur1	78 / 77	[1 1 0 -1 -1 1⟩	22.339
superleap	Thozogu	3ozg2	91 / 90	[-1 -2 -1 1 0 1⟩	19.130
animist	Thuzoyo	3uzy1	105 / 104	[-3 1 1 1 0 -1⟩	16.567
secorian	Sathuzo	s3uz2	28672 / 28431	[12 -7 0 1 0 -1⟩	14.613
mosaic	Lathoruru	L3orr-2	3159 / 3136	[-6 5 0 -2 0 1⟩	12.651
gassorma	Thuloruyoyo	3u1oryy-2	275 / 273	[0 -1 2 -1 1 -1⟩	12.637
grossma	Thulu	3u1u1	144 / 143	[4 2 0 0 -1 -1⟩	12.064
buzurgisma, dhanvantarisma	Thothoru	3oor1	169 / 168	[-3 -1 0 -1 0 2⟩	10.274
catadictma	Thologu	3o1og1	1287 / 1280	[-8 2 -1 0 1 1⟩	9.4419
mynucuma	Thuzozogu	3uzzg2	196 / 195	[2 -1 -1 2 0 -1⟩	8.8554
huntma, nelindic comma	Thururuyo	3urry-2	640 / 637	[7 0 1 -2 0 -1⟩	8.1342
threedie	Satritho	s3o32	2197 / 2187	[0 -7 0 0 0 3⟩	7.8980
kestrel comma	Thuthuloru	3uu1or-2	1188 / 1183	[2 3 0 -1 1 -2⟩	7.3017
marveltwin	Thoyoyo	3oyy1	325 / 324	[-2 -4 2 0 0 1⟩	5.3351
Hunt 13-cycle comma	Laquinbitho	L3o102	137858491849 / 137438953472	[-37 0 0 0 0 10⟩	5.2766
ratwolfsma	Thorugugu	3orgg1	351 / 350	[-1 3 -2 -1 0 1⟩	4.9393
minthma	Thulo	3u1o1	352 / 351	[5 -3 0 0 1 -1⟩	4.9253
gentle comma	Tholuluzo	3o1uuz2	364 / 363	[2 -1 0 1 -2 1⟩	4.7627
cuthbert	Bithulo-azogu	3uu1oozg1	847 / 845	[0 0 -1 1 2 -2⟩	4.0928

17-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents
soruyo unison	Soruyo	17ory1	85 / 84	[-2 -1 1 -1 0 0 1⟩	20.488
Hunt flat 2 comma	Laso	L17o1	4131 / 4096	[-12 5 0 0 0 0 1⟩	14.73
suruyo comma	Suruyo	17ury-2	120 / 119	[3 1 1 -1 0 0 -1⟩	14.487
23 semitone comma				[-94 0 0 0 0 0 23⟩	13.974
Blume comma	Sololo	17o1oo1	2057 / 2048	[-11 0 0 0 2 0 1⟩	7.5913
septendecimal kleisma	Sugu	17ug1	256 / 255	[8 -1 -1 0 0 0 -1⟩	6.7759
tannisma	Suthozo	17u3oz1	273 / 272	[-4 1 0 1 0 1 -1⟩	6.3532
septendecimal integer cents comma	Soso	17oo2	289 / 288	[-5 -2 0 0 0 0 2⟩	6.0008
17-ripple integer cents comma				[327 0 0 0 0 0 -80⟩	3.5672

19-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents
nuruyo comma	Nuruyo	19ury-2	135 / 133	[0 3 1 -1 0 0 0 -1⟩	25.84
nogugu 2nd	Nogugu	19ogg2	76 / 75	[2 -1 -2 0 0 0 0 1⟩	22.931
nulozo unison (approximation to the adjacent step of 53edo)	Nulozo	19u1oz1	77 / 76	[-2 0 0 1 1 0 0 -1⟩	22.631
19th-partial chroma	Nugu	19ug1	96 / 95	[5 1 -1 0 0 0 0 -1⟩	18.128
noluzo 2nd	Noluzo	19o1uz2	133 / 132	[-2 -1 0 1 -1 0 0 1⟩	13.066
Ganassi's comma	Nuso	19u17o1	153 / 152	[-3 2 0 0 0 0 1 -1⟩	11.352
nosugu unison	Nosugu	19o17ug1	171 / 170	[-1 2 -1 0 0 0 -1 1⟩	10.154
Hunt 19-cycle comma	Saquadnu	s19u4-2	131072 / 130321	[17 0 0 0 0 0 0 -4⟩	9.9479
binulo comma	Binulo	19uu1oo-2	363 / 361	[0 1 0 0 2 0 0 -2⟩	9.5649
nothulo comma	Nothulo	19o3u1o1	209 / 208	[-4 0 0 0 1 -1 0 1⟩	8.3033
spleen comma	Nuluzoyo	19u1uzy1	210 / 209	[1 1 1 1 -1 0 0 -1⟩	8.2637
nuthologu comma	Nuthologu	19u3o1og1	286 / 285	[1 -1 -1 0 1 1 0 -1⟩	6.0639
nusu comma	Nusu	19u17u-2	324 / 323	[2 4 0 0 0 0 -1 -1⟩	5.3516
go comma	Nonogu	19oog2	361 / 360	[-3 -2 -1 0 0 0 0 2⟩	4.8023