Xenharmonic Wiki

Table of 3-limit commas

Revision as of 01:49, 13 July 2021 by TallKite (talk | contribs)

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 Monzo Cents Name Color Name Monzo Cents
106-comma wa-106 comma w-106 [169 -106⟩ 1192.77
82-comma wa-82 comma w-82 [129 -82⟩ 1160.31
130-comma wa-130 comma w-130 [207 -130⟩ 1145.85
123-comma wa-123 comma w-123 [-194 123⟩ 1140.465
58-comma wa-58 comma w-58 [-91 58⟩ 1113.39
48-comma wa-48 comma w-48 [77 -48⟩ 1106.16
140-comma wa-140 comma w-140 [-221 140⟩ 1073.7
87-comma wa-87 comma w-87 [-137 87⟩ 1070.085
34-comma wa-34 comma w-34 [-53 34⟩ 1066.47
72-comma wa-72 comma w-72 [115 -72⟩ 1059.24
116-comma wa-116 comma w-116 [-183 116⟩ 1026.78
51-comma wa-51 comma w-51 [-80 51⟩ 999.705
145-comma wa-145 comma w-145 [-229 145⟩ 983.475
92-comma wa-92 comma w-92 [-145 92⟩ 979.86
14-comma sawa 7th sw7 [23 -14⟩ 972.63
120-comma wa-120 comma w-120 [191 -120⟩ 965.4
68-comma wa-68 comma w-68 [-107 68⟩ 932.94
Pythagorean supermajor sixth 15-comma lawa 6th Lw6 [-23 15⟩ 929.325
38-comma wa-38 comma w-38 [-61 38⟩ 925.71
144-comma wa-144 comma w-144 [229 -144⟩ 918.48
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
126-comma wa-126 comma w-126 [-199 126⟩ 846.33
20-comma wa-20 comma w-20 [-31 20⟩ 839.1
86-comma wa-86 comma w-86 [137 -86⟩ 831.87
102-comma wa-102 comma w-102 [-161 102⟩ 799.41
57-comma wa-57 comma w-57 [91 -57⟩ 788.565
25-comma wa-25 comma w-25 [-39 25⟩ 748.875
28-comma wa-28 comma w-28 [45 -28⟩ 745.26
134-comma wa-134 comma w-134 [213 -134⟩ 738.03
119-comma wa-119 comma w-119 [-188 119⟩ 732.645
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
136-comma wa-136 comma w-136 [-215 136⟩ 665.88
83-comma wa-83 comma w-83 [-132 83⟩ 662.265
30-comma wa-30 comma w-30 [-47 30⟩ 658.65
76-comma wa-76 comma w-76 [-121 76⟩ 651.42
129-comma wa-129 comma w-129 [205 -129⟩ 647.805
112-comma wa-112 comma w-112 [177 -112⟩ 618.96
100-comma wa-100 comma w-100 [159 -100⟩ 604.49
47-comma wa-47 comma w-47 [-74 47⟩ 591.885 wa-47b comma w-47b [75 -47⟩ 610.115
59-comma wa-59 comma w-59 [94 -59⟩ 584.655 wa-59b comma w-59b [-93 59⟩ 615.345
141-comma wa-141 comma w-141 [-223 141⟩ 575.655 wa-141b comma w-141b [224 -141⟩ 624.345
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 wa-23b comma w-23b [37 -23⟩ 655.055
83-comma wa-83 comma w-83 [133 -83⟩ 537.735
71-comma wa-71 comma w-71 [113 -71⟩ 561.195 wa-71b comma w-71b [-112 71⟩ 638.805
124-comma wa-124 comma w-124 [197 -124⟩ 557.58
117-comma wa-117 comma w-117 [-185 117⟩ 528.735
Pythagorean-Armodue fourth 64-comma wa-64 comma w-64 [-101 64⟩ 525.12
Pythagorean wolf fourth 11-comma lawa 4th Lw4 [-17 11⟩ 521.505 Pythagorean wolf fifth sawa 5th sw5 [18 -11⟩ 678.495
42-comma wa-42 comma w-42 [67 -42⟩ 517.89
95-comma wa-95 comma w-95 [151 -95⟩ 514.275
148-comma wa-148 comma w-148 [235 -148⟩ 510.66
105-comma wa-105 comma w-105 [-166 105⟩ 505.275 wa-105b comma w-105b [167 -105⟩ 694.725
perfect fourth 1-comma wa 4th w4 [2 -1⟩ 498.045 perfect fifth wa 5th w5 [-1 1⟩ 701.955
107-comma wa-107 comma w-107 [170 -107⟩ 490.815 wa-107b comma w-107b [-169 107⟩ 709.185
146-comma wa-146 comma w-146 [-229 146⟩ 485.43
40-comma wa-40 comma w-40 [63 -40⟩ 478.2
13-comma sawa 4th sw4 [21 -13⟩ 474.585 lawa 5th Lw5 [-20 13⟩ 725.415
81-comma wa-81 comma w-81 [-128 81⟩ 458.355
131-comma wa-131 comma w-131 [208 -131⟩ 443.895 wa-131b comma w-131b [-207 131⟩ 756.195
122-comma wa-122 comma w-122 [-193 122⟩ 438.51
69-comma wa-69 comma w-69 [-109 69⟩ 434.895 wa-69b comma w-69b [110 -69⟩ 765.105
Pythagorean supermajor third 16-comma lawa 3rd Lw3 [-25 16⟩ 431.28
37-comma wa-37 comma w-37 [59 -37⟩ 427.665 wa-37b comma w-37b [-58 37⟩ 772.335
90-comma wa-90 comma w-90 [-143 90⟩ 424.05
143-comma wa-143 comma w-143 [-227 143⟩ 420.435 wa-143b comma w-143b [228 -143⟩ 779.565
49-comma wa-49 comma w-49 [78 -49⟩ 404.205
151-comma wa-151 comma w-151 [-239 151⟩ 395.205 wa-151b comma w-151b [240 -151⟩ 804.795
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 sawa 4th sw4 [13 -8⟩ 384.360
Pythagorean 1/5 tritave 61-comma wa-61 comma w-61 [97 -61⟩ 380.745 wa-61b comma w-61b [-96 61⟩ 819.255
114-comma wa-114 comma w-114 [181 -114⟩ 377.13
139-comma wa-139 comma w-139 [-220 139⟩ 371.745 wa-139b comma w-139b [221 -139⟩ 828.255
33-comma wa-33 comma w-33 [-52 33⟩ 364.515 wa-33b comma w-33b [53 -33⟩ 835.485
73-comma wa-73 comma w-73 [116 -73⟩ 357.285 wa-73b comma w-73b [-115 73⟩ 842.715
127-comma wa-127 comma w-127 [-201 127⟩ 348.285 wa-127 comma w-127 [202 -127⟩ 851.715
74-comma wa-74 comma w-74 [117 -74⟩ 344.67
32-comma wa-32 comma w-32 [51 -32⟩ 337.44
115-comma wa-115 comma w-115 [-182 115⟩ 324.825 wa-115b comma w-115b [183 -115⟩ 875.175
Pythagorean augmented second 9-comma lawa 2nd Lw2 [-14 9⟩ 317.595
97-comma wa-97 comma w-97 [153 -97⟩ 310.365 wa-97b comma w-97b [153 -97⟩ 889.365
103-comma wa-103 comma w-103 [-163 103⟩ 301.37 wa-103b comma w-103b [164 -103⟩ 898.63
50-comma wa-50 comma w-50 [-79 50⟩ 297.75
Pythagorean minor third 3-comma wa 3rd w3 [5 -3⟩ 294.135 Pythagorean major sixth wa 6th w6 [-4 3⟩ 905.865
56-comma wa-56 comma w-56 [89 -56⟩ 290.52
109-comma wa-109 comma w-109 [173 -109⟩ 286.905 wa-109b comma w-109b [-172 109⟩ 913.095
91-comma wa-91 comma w-91 [-144 91⟩ 277.905 wa-91b comma w-91b [145 -91⟩ 922.095
121-comma wa-121 comma w-121 [192 -121⟩ 263.445 wa-121b comma w-121b [-191 121⟩ 936.555
131-comma wa-131 comma w-131 [208 -131⟩ 258.06
79-comma wa-79 comma w-79 [-125 79⟩ 254.445 wa-79b comma w-79b [126 -79⟩ 945.555
26-comma wa-26 comma w-26 [-41 26⟩ 250.83
27-comma wa-27 comma w-27 [43 -27⟩ 247.215 wa-27b comma w-27b [-44 27⟩ 952.785
80-comma wa-80 comma w-80 [127 -80⟩ 243.6
67-comma wa-67 comma w-67 [-106 67⟩ 230.985 Pythagorean harmonic seventh wa-67b comma w-67b [107 -67⟩ 969.015
39-comma wa-39 comma w-39 [62 -39⟩ 223.75 wa-39b comma w-39b [-61 39⟩ 976.25
55-comma wa-55 comma w-55 [-87 55⟩ 207.525
whole tone 2-comma wa 2nd w2 [-3 2⟩ 203.91
104-comma wa-104 comma w-104 [165 -104⟩ 196.68
149-comma wa-149 comma w-149 [-236 149⟩ 191.295 wa-149b comma w-149b [237 -149⟩ 1008.705
43-comma wa-43 comma w-43 [-68 43⟩ 184.065 wa-43b comma w-43b [67 -43⟩ 1015.395
63-comma wa-63 comma w-63 [100 -63⟩ 176.835
137-comma wa-137 comma w-137 [-217 137⟩ 167.835 wa-137b comma w-137b [218 -137⟩ 1032.165
31-comma wa-31 comma w-31 [-49 31⟩ 160.605 wa-31b comma w-31b [50 -31⟩ 1039.395
22-comma wa-22 comma w-22 [35 -22⟩ 156.99
75-comma wa-75 comma w-75 [119 -75⟩ 153.375 wa-75b comma w-75b [-118 75⟩ 1046.625
128-comma wa-128 comma w-128 [203 -128⟩ 149.76
125-comma wa-125 comma w-125 [-198 125⟩ 144.375 wa-125b comma w-125b [199 -125⟩ 1055.625
19-comma wa-19 comma w-19 [-30 19⟩ 137.145 wa-19b comma w-19b [31 -19⟩ 1062.855
113-comma wa-113 comma w-113 [179 -113⟩ 120.915 wa-113b comma w-113b [180 -113⟩ 1079.085
apotome 7-comma lawa unison Lw1 [-11 7⟩ 113.685 sawa octave Sw8 [12 -7⟩ 1086.315
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 wa-101b comma w-101b [159 -101⟩ 1102.545
limma, Pythagorean minor second 5-comma sawa 2nd sw2 [8 -5⟩ 90.225 Pythagorean major seventh lawa 7th Lw7 [-7 5⟩ 1109.775
301-comma wa-301 comma w-301 [-477 301⟩ 88.455 wa-301b comma w-301b [478 -301⟩ 1111.545
248-comma wa-248 comma w-248 [-393 248⟩ 84.840
111-comma wa-111 comma w-111 [176 -111⟩ 82.995 wa-111b comma w-111b [-175 111⟩ 1117.005
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 wa-89b comma w-89b [142 -89⟩ 1126.005
17-comma wa-17 comma ssw3 [27 -17⟩ 66.765 Pythagorean supermajor seventh lawa 7th Lw7 [-26 17⟩ 1133.235
289-comma wa-289 comma w-289 [-458 289⟩ 64.995 wa-289b comma w-289b [459 -289⟩ 1135.005
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 wa-229b comma w-229b [-362 229⟩ 1147.695
77-comma wa-77 comma w-77 [-122 77⟩ 50.535 wa-77b comma w-77b [123 -77⟩ 1149.465
29-comma wa-29 comma w-29 [46 -29⟩ 43.305 wa-29b comma w-29b [-45 29⟩ 1156.695
277-comma wa-277 comma w-277 [-439 277⟩ 41.535 wa-277b comma w-277b [440 -277⟩ 1158.465
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 wa-241b comma w-241b [-381 241⟩ 1171.155
Pythagorean septimal comma 65-comma wa-65 comma w-65 [-103 65⟩ 27.075 wa-65b comma w-65b [102 -65⟩ 1172.925
Pythagorean comma 12-comma lalawa comma
or wa comma 		LLw-2 [-19 12⟩ 23.460
Counterpyth comma 41-comma wa-41 comma w-41 [65 -41⟩ 19.845 wa-41b comma w-41b [-64 41⟩ 1180.155
Garistearn comma 94-comma wa-94 comma w-94 [149 -94⟩ 16.230
147-comma wa-147 comma w-147 [233 -147⟩ 12.615 wa-147b comma w-147b [-232 147⟩ 1187.385
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 wa-253b comma w-253b [-400 253⟩ 1194.6152
Mercator's comma 53-comma wa-53 comma w-53 [-84 53⟩ 3.6150 wa-53b comma w-53b [85 -53⟩ 1196.385
359-comma wa-359 comma w-359 [-569 359⟩ 1.8453 wa-359b comma w-359b [570 -359⟩ 1198.8547
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 wa-15601b comma w-15601b [-24726 15601⟩ 1199.968501
31867-comma wa-31867 comma w-31867 [-50508 31867⟩ 0.012577 wa-31867b comma w-31867b [50509 -31867⟩ 1199.987423
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