Table of 3-limit commas

A 3-limit comma is the amount which separates m fifths from n octaves. It is the simplest kind of comma a tuning may temper out. All commas not equal to the perfect fourth listed here generate interlaced pentatonic scales when tempered out.

Name(s)	Color Name		Ratio	Monzo	Cents
24-comma	wa-24 comma	w-24		[-37 24⟩	1246.92
48-comma	wa-48 comma	w-48		[77 -48⟩	1106.16
41b-comma	wa-41b comma	w-41b		[-64 41⟩	1080.155
29b-comma	wa-29b comma	w-29b		[-45 29⟩	1156.695
Pythagorean supermajor seventh, 17b-comma	wa-17b comma	w-17b		[-26 17⟩	1133.235
51-comma	wa-51 comma	w-51		[-80 51⟩	999.705
44-comma	wa-44 comma	w-44		[69 -44⟩	886.02
34-comma	wa-34 comma	w-34		[-53 34⟩	835.485
19b-comma	wa-19b comma	w-19b		[31 -19⟩	1062.855
31b-comma	wa-31b comma	w-31b		[50 -31⟩	1039.395
43b-comma	wa-43b comma	w-43b		[67 -43⟩	1015.395
39b-comma	wa-39b comma	w-39b		[-61 39⟩	976.25
Pythagorean harmonic seventh, 14-comma	wa-14 comma	w-14		[23 -14⟩	972.63
27b-comma	wa-27b comma	w-27b		[-44 27⟩	952.785
Pythagorean supermajor sixth, 15-comma	wa-15 comma	w-15		[-23 15⟩	929.325
38-comma	wa-38 comma	w-38		[-61 38⟩	925.71
21-comma	wa-21 comma	w-21		[34 -21⟩	858.945
20-comma	wa-20 comma	w-20		[-31 20⟩	839.1
33b-comma	wa-33b comma	w-33b		[53 -33⟩	835.485
37b-comma	wa-37b comma	w-37b		[-58 37⟩	772.335
25-comma	wa-25 comma	w-25		[-39 25⟩	748.875
28-comma	wa-28 comma	w-28		[45 -28⟩	745.26
13-comma	wa-13 comma	w-13		[-20 13⟩	725.415
54-comma	wa-54 comma	w-54		[-85 54⟩	705.57
52-comma	wa-52 comma	w-52		[83 -52⟩	698.33
Pythagorean wolf fifth, 11b-comma	small wa 5th	sw5	262144 / 177147	[18 -11⟩	678.495
47b-comma	wa-47b comma	w-47b		[75 -47⟩	610.115
47-comma	wa-47 comma	w-47		[-74 47⟩	591.885
42-comma	wa-42 comma	w-42		[67 -42⟩	517.89
23b-comma	wa-23b comma	w-23b		[37 -23⟩	655.055
30-comma	wa-30 comma	w-30		[-47 30⟩	658.65
18-comma	wa-18 comma	w-18		[29 -18⟩	564.81
23-comma	wa-23 comma	w-23		[-36 23⟩	544.965
Pythagorean wolf fourth, 11-comma	Large wa 4th	Lw4	177147 / 131072	[-17 11⟩	521.505
40-comma	wa-40 comma	w-40		[63 -40⟩	478.2
13b-comma	wa-13b comma	w-13b		[21 -13⟩	474.585
perfect fourth	wa 4th	w4	4 / 3	[2 -1⟩	498.045
Pythagorean supermajor third, 16-comma	wa-16 comma	w-16		[-25 16⟩	431.28
49-comma	wa-49 comma	w-49		[78 -49⟩	404.205
37-comma	wa-37 comma	w-37		[59 -37⟩	427.665
45-comma	wa-45 comma	w-45		[-71 45⟩	387.975
Pythagorean diminished fourth, 8-comma	small wa 4th	sw4	8192 / 6561	[13 -8⟩	384.360
33-comma	wa-33 comma	w-33		[-52 33⟩	364.515
32-comma	wa-32 comma	w-32		[51 -32⟩	337.44
Pythagorean augmented second, 9-comma	large wa 2nd	Lw2	19683/16384	[-14 9⟩	317.595
50-comma	wa-50 comma	w-50		[-79 50⟩	404.205
Pythagorean minor third, 3-comma	wa 3rd	w3	32 / 27	[5 -3⟩	294.135
26-comma	wa-26 comma	w-26		[-41 26⟩	250.83
27-comma	wa-27 comma	w-27		[43 -27⟩	247.215
39-comma	wa-39 comma	w-39		[62 -39⟩	223.75
55-comma	wa-55 comma	w-55		[-87 55⟩	207.525
whole tone	wa 2nd	w2	9 / 8	[-3 2⟩	203.91
43-comma	wa-43 comma	w-43		[-68 43⟩	184.065
63-comma	wa-63 comma	w-63		[100 -63⟩	176.835
31-comma	wa-31 comma	w-31	617673396283947 / 562949953421312	[-49 31⟩	160.605
22-comma	wa-22 comma	w-22	34359738368 / 31381059609	[35 -22⟩	156.99
19-comma	wa-19 comma	w-19	1162261467 / 1073741824	[-30 19⟩	137.145
apotome	large wa unison	Lw1	2187 / 2048	[-11 7⟩	113.685
46-comma	wa-46 comma	w-46		[73 -46⟩	110.07
limma, Pythagorean minor second	small wa 2nd	sw2	256 / 243	[8 -5⟩	90.225
17-comma	wa-17 comma	ssw3	134217728 / 129140163	[27 -17⟩	66.765
70-comma	wa-70 comma	w-70		[111 -70⟩	63.15
77-comma	wa-77 comma	w-77		[-122 77⟩	50.535
29-comma	wa-29 comma	w-29	70368744177664 / 68630377364883	[46 -29⟩	43.305
65-comma	wa-65 comma	w-65		[-103 65⟩	27.075
Pythagorean comma	lalawa comma or wa comma	LLw-2	531441 / 524288	[-19 12⟩	23.460
41-comma	wa-41 comma	w-41	36893488147419103232 / 36472996377170786403	[65 -41⟩	19.845
94-comma	wa-94 comma	w-94		[149 -94⟩	16.230
200-comma, Pythagorean integer cents comma	wa-200 comma	w-200		[317 -200⟩	8.9998
Mercator's comma, 53-comma	wa-53 comma	w-53	19383245667680019896796723 / 19342813113834066795298816	[-84 53⟩	3.6150
359-comma	wa-359 comma	w-359		[-569 359⟩	1.8453
Sasktel comma	wa-306 comma	w-306		[485 -306⟩	1.7697
Satanic comma	wa-665 comma	w-665		[-1054 665⟩	0.075575
15601-comma	wa-15601 comma	w-15601		[24727 -15601⟩	0.031499
31867-comma	wa-31867 comma	w-31867		[-50508 31867⟩	0.012577