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 and fifths tempered by up to one step of n edo when tempered out.

Name(s)		Color Name		Ratio	Monzo	Cents
	31867b-comma	wa-31867b comma	w-31867b		[50509 -31867⟩	1199.987423
	15601b-comma	wa-15601b comma	w-15601b		[-24726 15601⟩	1199.968501
	359b-comma	wa-359b comma	w-359b		[570 -359⟩	1198.8547
	53b-comma	wa-53b comma	w-53b		[85 -53⟩	1196.385
	147b-comma	wa-147b comma	w-147b		[-232 147⟩	1187.385
	41b-comma	wa-41b comma	w-41b		[-64 41⟩	1180.155
	65b-comma	wa-65b comma	w-65b		[102 -65⟩	1172.925
	82-comma	wa-82 comma	w-82		[129 -82⟩	1160.31
	29b-comma	wa-29b comma	w-29b		[-45 29⟩	1156.695
Pythagorean supermajor seventh	17b-comma	Large wa 7th	Lw7		[-26 17⟩	1133.235
	89b-comma	wa-89b comma	w-89b		[142 -89⟩	1126.005
	58-comma	wa-58 comma	w-58		[-91 58⟩	1113.39
	48-comma	wa-48 comma	w-48		[77 -48⟩	1106.16
	101b-comma	wa-101b comma	w-101b		[159 -101⟩	1102.545
	87-comma	wa-87 comma	w-87		[-137 87⟩	1070.085
	34-comma	wa-34 comma	w-34		[-53 34⟩	1066.47
	19b-comma	wa-19b comma	w-19b		[31 -19⟩	1062.855
	72-comma	wa-72 comma	w-72		[115 -72⟩	1059.24
	77b-comma	wa-77b comma	w-77b		[123 -77⟩	1049.465
	75b-comma	wa-75b comma	w-75b		[-118 75⟩	1046.625
	31b-comma	wa-31b comma	w-31b		[50 -31⟩	1039.395
	43b-comma	wa-43b comma	w-43b		[67 -43⟩	1015.395
	51-comma	wa-51 comma	w-51		[-80 51⟩	999.705
	92-comma	wa-92 comma	w-92		[-145 92⟩	979.86
	39b-comma	wa-39b comma	w-39b		[-61 39⟩	976.25
	14-comma	small wa 7th	sw7		[23 -14⟩	972.63
Pythagorean harmonic seventh	67b-comma	wa-67b comma	w-67b		[107 -67⟩	969.015
	27b-comma	wa-27b comma	w-27b		[-44 27⟩	952.785
	79b-comma	wa-79b comma	w-79b		[126 -79⟩	945.555
	68-comma	wa-68 comma	w-68		[-107 68⟩	932.94
Pythagorean supermajor sixth	15-comma	Large wa 6th	Lw6		[-23 15⟩	929.325
	38-comma	wa-38 comma	w-38		[-61 38⟩	925.71
	103-comma	wa-103 comma	w-103		[-164 103⟩	898.63
	97b-comma	wa-97b comma	w-97b		[153 -97⟩	889.365
	44-comma	wa-44 comma	w-44		[69 -44⟩	886.02
	62-comma	wa-62 comma	w-62		[99 -62⟩	878.79
	85-comma	wa-85 comma	w-85		[-134 85⟩	866.175
	21-comma	wa-21 comma	w-21		[34 -21⟩	858.945
	73b-comma	wa-73b comma	w-73b		[-115 73⟩	842.715
	20-comma	wa-20 comma	w-20		[-31 20⟩	839.1
	33b-comma	wa-33b comma	w-33b		[53 -33⟩	835.485
	86-comma	wa-86 comma	w-86		[137 -86⟩	831.87
	61b-comma	wa-61b comma	w-61b		[-96 61⟩	819.255
	102-comma	wa-102 comma	w-102		[-161 102⟩	799.41
	57-comma	wa-57 comma	w-57		[91 -57⟩	788.565
	37b-comma	wa-37b comma	w-37b		[-58 37⟩	772.335
	69b-comma	wa-69b comma	w-69b		[110 -69⟩	765.105
	25-comma	wa-25 comma	w-25		[-39 25⟩	748.875
	28-comma	wa-28 comma	w-28		[45 -28⟩	745.26
	13b-comma	wa-13b comma	w-13b		[-20 13⟩	725.415
	93-comma	wa-93 comma	w-93		[148 -93⟩	718.185
	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
	83-comma	wa-83 comma	w-83		[-132 83⟩	662.265
	30-comma	wa-30 comma	w-30		[-47 30⟩	658.65
	23b-comma	wa-23b comma	w-23b		[37 -23⟩	655.055
	76-comma	wa-76 comma	w-76		[-121 76⟩	651.42
	71b-comma	wa-71b comma	w-71b		[-112 71⟩	638.805
	59b-comma	wa-59b comma	w-59b		[-93 59⟩	615.345
	47b-comma	wa-47b comma	w-47b		[75 -47⟩	610.115
	100-comma	wa-100 comma	w-100		[159 -100⟩	604.49
	47-comma	wa-47 comma	w-47		[-74 47⟩	591.885
	59-comma	wa-59 comma	w-59		[94 -59⟩	584.655
	88-comma	wa-88 comma	w-88		[139 -88⟩	572.04
	18-comma	wa-18 comma	w-18		[29 -18⟩	564.81
	23-comma	wa-23 comma	w-23		[-36 23⟩	544.965
	83-comma	wa-83 comma	w-83		[133 -83⟩	537.735
	71-comma	wa-71 comma	w-71		[113 -71⟩	561.195
Pythagorean-Armodue fourth	64-comma	wa-64 comma	w-64		[-101 64⟩	525.12
Pythagorean wolf fourth	11-comma	Large wa 4th	Lw4	177147 / 131072	[-17 11⟩	521.505
	42-comma	wa-42 comma	w-42		[67 -42⟩	517.89
	95-comma	wa-95 comma	w-95		[151 -95⟩	514.275
perfect fourth	1-comma	wa 4th	w4	4 / 3	[2 -1⟩	498.045
	40-comma	wa-40 comma	w-40		[63 -40⟩	478.2
	13-comma	wa-13 comma	w-13		[21 -13⟩	474.585
	81-comma	wa-81 comma	w-81		[-128 81⟩	458.355
	69-comma	wa-69 comma	w-69		[-109 69⟩	434.895
Pythagorean supermajor third	16-comma	Large wa 3rd	Lw3		[-25 16⟩	431.28
	37-comma	wa-37 comma	w-37		[59 -37⟩	427.665
	90-comma	wa-90 comma	w-90		[-143 90⟩	424.05
	49-comma	wa-49 comma	w-49		[78 -49⟩	404.205
	98-comma	wa-98 comma	w-98		[-155 98⟩	391.59
	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
Pythagorean 1/5 tritave	61-comma	wa-61 comma	w-61		[97 -61⟩	380.745
	33-comma	wa-33 comma	w-33		[-52 33⟩	364.515
	73-comma	wa-73 comma	w-73		[116 -73⟩	357.285
	74-comma	wa-74 comma	w-74		[117 -74⟩	344.67
	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
	97-comma	wa-97 comma	w-97		[153 -97⟩	310.365
	50-comma	wa-50 comma	w-50		[-79 50⟩	297.75
Pythagorean minor third	3-comma	wa 3rd	w3	32 / 27	[5 -3⟩	294.135
	56-comma	wa-56 comma	w-56		[89 -56⟩	290.52
	91-comma	wa-91 comma	w-91		[-144 91⟩	277.905
	79-comma	wa-79 comma	w-79		[-125 79⟩	254.445
	75-comma	wa-75 comma	w-75		[119 -75⟩	253.375
	26-comma	wa-26 comma	w-26		[-41 26⟩	250.83
	27-comma	wa-27 comma	w-27		[43 -27⟩	247.215
	80-comma	wa-80 comma	w-80		[127 -80⟩	243.6
	67-comma	wa-67 comma	w-67		[-106 67⟩	230.985
	39-comma	wa-39 comma	w-39		[62 -39⟩	223.75
	55-comma	wa-55 comma	w-55		[-87 55⟩	207.525
whole tone	2-comma	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		[-49 31⟩	160.605
	22-comma	wa-22 comma	w-22		[35 -22⟩	156.99
	19-comma	wa-19 comma	w-19		[-30 19⟩	137.145
apotome	7-comma	large wa unison	Lw1	2187 / 2048	[-11 7⟩	113.685
	46-comma	wa-46 comma	w-46		[73 -46⟩	110.07
	99-comma	wa-99 comma	w-99		[157 -99⟩	106.455
	101-comma	wa-101 comma	w-101		[-160 101⟩	97.455
limma, Pythagorean minor second	5-comma	small wa 2nd	sw2	256 / 243	[8 -5⟩	90.225
	301-comma	wa-301 comma	w-301		[-477 301⟩	88.455
	248-comma	wa-248 comma	w-248		[-393 248⟩	84.840
	111-comma	wa-111 comma	w-111		[176 -111⟩	82.995
	142-comma	wa-142 comma	w-142		[-225 142⟩	77.610
	217-comma	wa-217 comma	w-217		[344 -217⟩	75.765
	89-comma	wa-89 comma	w-89		[-141 89⟩	73.995
	17-comma	wa-17 comma	ssw3	134217728 / 129140163	[27 -17⟩	66.765
	289-comma	wa-289 comma	w-289		[-458 289⟩	64.995
	70-comma	wa-70 comma	w-70		[111 -70⟩	63.150
	183-comma	wa-183 comma	w-183		[-290 183⟩	57.765
	176-comma	wa-176 comma	w-176		[279 -176⟩	55.920
	229-comma	wa-229 comma	w-229		[363 -229⟩	52.305
	77-comma	wa-77 comma	w-77		[-122 77⟩	50.535
	29-comma	wa-29 comma	w-29		[46 -29⟩	43.305
	277-comma	wa-277 comma	w-277		[-439 277⟩	41.535
	224-comma	wa-224 comma	w-224		[-355 224⟩	37.920
	135-comma	wa-135 comma	w-135		[214 -135⟩	36.075
	171-comma	wa-171 comma	w-171		[-271 171⟩	34.305
	118-comma	wa-118 comma	w-118		[-187 118⟩	30.690
	241-comma	wa-241 comma	w-241		[382 -241⟩	28.845
Pythagorean septimal comma	65-comma	wa-65 comma	w-65		[-103 65⟩	27.075
Pythagorean comma	12-comma	lalawa comma or wa comma	LLw-2	531441 / 524288	[-19 12⟩	23.460
Counterpyth comma	41-comma	wa-41 comma	w-41		[65 -41⟩	19.845
Garistearn	94-comma	wa-94 comma	w-94		[149 -94⟩	16.230
	147-comma	wa-147 comma	w-147		[233 -147⟩	12.615
Pythagorean integer-cent ET comma	200-comma	wa-200 comma	w-200		[317 -200⟩	8.9998
	253-comma	wa-253 comma	w-253		[401 -253⟩	5.3848
Mercator's comma	53-comma	wa-53 comma	w-53		[-84 53⟩	3.6150
	359-comma	wa-359 comma	w-359		[-569 359⟩	1.8453
Sasktel comma	306-comma	wa-306 comma	w-306		[485 -306⟩	1.7697
Satanic comma	665-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