Table of 3-limit commas: Difference between revisions

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A [[3-limit]] comma is the amount which separates m [[3/2|fifth]]<nowiki/>s from n [[octave]]<nowiki/>s. It is the simplest kind of comma a tuning may [[Tempering out|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.
A [[3-limit]] comma is the amount which separates ''m'' [[3/2|fifths]] from ''n'' [[octave]]s. It is the simplest kind of comma a tuning may [[Tempering out|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.


{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="2" |Name(s)
! colspan="2" | Name(s)
! colspan="2" |[[Color notation|Color Name]]
! colspan="2" | [[Color notation|Color Name]]
! Ratio
! [[Monzo]]
! Monzo
! [[Cent]]s
! Cents
|-
|-
|
| whole tone
| 53b-comma
| 2-comma
| wa-53b comma
| wa 2nd
| w-53b
| w2
|
| {{Monzo| -3 2 }}
| {{monzo| 85 -53 }}
| 203.91
| 1196.385
|-
|-
|
|
| 41b-comma
| 193-comma
| wa-41b comma
| wa-193 comma
| w-41b
| w-193
|
| {{Monzo| 306 -193 }}
| {{monzo| -64 41 }}
| 202.46
| 1180.155
|-
|-
|
|
| 65b-comma
| 255-comma
| wa-65b comma
| wa-255 comma
| w-65b
| w-255
|
| {{Monzo| -404 255 }}
| {{monzo| 102 -65}}
| 198.525
| 1172.925
|-
|-
|
|
| 82-comma
| 104-comma
| wa-82 comma
| wa-104 comma
| w-82
| w-104
|
| {{Monzo| 165 -104 }}
| {{monzo| 129 -82 }}
| 196.68
| 1160.31
|-
|-
|
|
| 29b-comma
| 157-comma
| wa-29b comma
| wa-157 comma
| w-29b
| w-157
|
| {{Monzo| 249 -157 }}
| {{monzo| -45 29 }}
| 193.065
| 1156.695
|-
|-
| Pythagorean supermajor seventh
| 17b-comma
| Large wa 7th
| Lw7
|
|
| {{monzo| -26 17 }}
| 149-comma
| 1133.235
| wa-149 comma
| w-149
| {{Monzo| -236 149 }}
| 191.295
|-
|-
|
|
| 89b-comma
| 263-comma
| wa-89b comma
| wa-263 comma
| w-89b
| w-263
|
| {{Monzo| 417 -263 }}
| {{monzo| 142 -89 }}
| 185.835
| 1126.005
|-
|-
|
|
| 58-comma
| 43-comma
| wa-58 comma
| wa-43 comma
| w-58
| w-43
|
| {{Monzo| -68 43 }}
| {{monzo| -91 58 }}
| 184.065
| 1113.39
|-
|-
|
|
| 48-comma
| 296-comma
| wa-48 comma
| wa-296 comma
| w-48
| w-296
|
| {{Monzo| -469 296 }}
| {{monzo| 77 -48 }}
| 178.68
| 1106.16
|-
|-
|
|
| 101b-comma
| 63-comma
| wa-101b comma
| wa-63 comma
| w-101b
| w-63
|
| {{Monzo| 100 -63 }}
| {{monzo| 159 -101 }}
| 176.835
| 1102.545
|-
|-
|
|
| 87-comma
| 243-comma
| wa-87 comma
| wa-243 comma
| w-87
| w-243
|
| {{Monzo| -385 243 }}
| {{monzo| -137 87 }}
| 175.605
| 1070.085
|-
|-
|
|
| 34-comma
| 190-comma
| wa-34 comma
| wa-190 comma
| w-34
| w-190
|
| {{Monzo| -301 190 }}
| {{monzo| -53 34 }}
| 171.45
| 1066.47
|-
|-
|
|
| 19b-comma
| 169-comma
| wa-19b comma
| wa-169 comma
| w-19b
| w-169
|
| {{Monzo| 268 -169}}
| {{monzo|31 -19}}
| 169.605
| 1062.855
|-
|-
|
|
| 72-comma
| 137-comma
| wa-72 comma
| wa-137 comma
| w-72
| w-137
|
| {{Monzo| -217 137 }}
| {{monzo|115 -72}}
| 167.835
| 1059.24
|-
|-
|
|
| 77b-comma
| 275-comma
| wa-77b comma
| wa-275 comma
| w-77b
| w-275
|
| {{Monzo| 436 -275 }}
| {{monzo| 123 -77 }}
| 162.375
| 1049.465
|-
|-
|
|
| 75b-comma
| [[31-comma_temperaments|31-comma]]
| wa-75b comma
| wa-31 comma
| w-75b
| w-31
|
| {{Monzo| -49 31 }}
| {{monzo|-118 75}}
| 160.605
| 1046.625
|-
|-
|
|
| 31b-comma
| 22-comma
| wa-31b comma
| wa-22 comma
| w-31b
| w-22
|
| {{Monzo| 35 -22 }}
| {{monzo| 50 -31 }}
| 156.99
| 1039.395
|-
|
| 43b-comma
| wa-43b comma
| w-43b
|
| {{monzo| 67 -43 }}
| 1015.395
|-
|
| 51-comma
| wa-51 comma
| w-51
|
| {{monzo| -80 51 }}
| 999.705
|-
|
| 92-comma
| wa-92 comma
| w-92
|
| {{monzo| -145 92 }}
| 979.86
|-
|
| 39b-comma
| wa-39b comma
| w-39b
|
| {{monzo| -61 39 }}
| 976.25
|-
|
| 14-comma
| small wa 7th
| sw7
|
| {{Monzo|23 -14}}
| 972.63
|-
| Pythagorean harmonic seventh
| 67b-comma
| wa-67b comma
| w-67b
|
| {{monzo| 107 -67 }}
| 969.015
|-
|
| 27b-comma
| wa-27b comma
| w-27b
|
| {{monzo| -44 27}}
| 952.785
|-
|
| 79b-comma
| wa-79b comma
| w-79b
|
| {{monzo| 126 -79 }}
| 945.555
|-
|
| 68-comma
| wa-68 comma
| w-68
|
| {{monzo| -107 68 }}
| 932.94
|-
| Pythagorean supermajor sixth
| 15-comma
| Large wa 6th
| Lw6
|
| {{Monzo|-23 15}}
| 929.325
|-
|
| 38-comma
| wa-38 comma
| w-38
|
| {{monzo| -61 38 }}
| 925.71
|-
|
| 103-comma
| wa-103 comma
| w-103
|
| {{monzo| -164 103 }}
| 898.63
|-
|
| 97b-comma
| wa-97b comma
| w-97b
|
| {{monzo|153 -97 }}
| 889.365
|-
|
| 44-comma
| wa-44 comma
| w-44
|
| {{monzo| 69 -44 }}
| 886.02
|-
|
| 62-comma
| wa-62 comma
| w-62
|
| {{monzo| 99 -62 }}
| 878.79
|-
|
| 85-comma
| wa-85 comma
| w-85
|
| {{monzo| -134 85 }}
| 866.175
|-
|
| 21-comma
| wa-21 comma
| w-21
|
| {{Monzo| 34 -21}}
| 858.945
|-
|
| 73b-comma
| wa-73b comma
| w-73b
|
| {{monzo|-115 73}}
| 842.715
|-
|
| 20-comma
| wa-20 comma
| w-20
|
| {{Monzo| -31 20}}
| 839.1
|-
|
| 33b-comma
| wa-33b comma
| w-33b
|
| {{monzo| 53 -33 }}
| 835.485
|-
|
| 86-comma
| wa-86 comma
| w-86
|
| {{monzo| 137 -86 }}
| 831.87
|-
|
| 61b-comma
| wa-61b comma
| w-61b
|
| {{monzo| -96 61 }}
| 819.255
|-
|
| 102-comma
| wa-102 comma
| w-102
|
| {{monzo| -161 102 }}
| 799.41
|-
|
| 57-comma
| wa-57 comma
| w-57
|
| {{monzo| 91 -57 }}
| 788.565
|-
|
| 37b-comma
| wa-37b comma
| w-37b
|
| {{monzo| -58 37 }}
| 772.335
|-
|
| 69b-comma
| wa-69b comma
| w-69b
|
| {{monzo| 110 -69 }}
| 765.105
|-
|
| 25-comma
| wa-25 comma
| w-25
|
| {{Monzo| -39 25}}
| 748.875
|-
|
| 28-comma
| wa-28 comma
| w-28
|
| {{monzo| 45 -28}}
| 745.26
|-
|
| 13b-comma
| wa-13b comma
| w-13b
|
| {{Monzo| -20 13}}
| 725.415
|-
|
| 93-comma
| wa-93 comma
| w-93
|
| {{monzo| 148 -93 }}
| 718.185
|-
|
| 54-comma
| wa-54 comma
| w-54
|
| {{monzo| -85 54 }}
| 705.57
|-
|
| 52-comma
| wa-52 comma
| w-52
|
| {{monzo| 83 -52 }}
| 698.33
|-
| Pythagorean wolf fifth
| 11b-comma
| small wa 5th
| sw5
| 262144 / 177147
| {{monzo| 18 -11}}
| 678.495
|-
|
| 83-comma
| wa-83 comma
| w-83
|
| {{monzo| -132 83 }}
| 662.265
|-
|
| 30-comma
| wa-30 comma
| w-30
|
| {{monzo| -47 30 }}
| 658.65
|-
|
| 23b-comma
| wa-23b comma
| w-23b
|
| {{monzo| 37 -23}}
| 655.055
|-
|
| 76-comma
| wa-76 comma
| w-76
|
| {{monzo| -121 76 }}
| 651.42
|-
|
| 71b-comma
| wa-71b comma
| w-71b
|
| {{monzo|-112 71}}
| 638.805
|-
|
| 59b-comma
| wa-59b comma
| w-59b
|
| {{monzo| -93 59 }}
| 615.345
|-
|
| 47b-comma
| wa-47b comma
| w-47b
|
| {{monzo| 75 -47 }}
| 610.115
|-
|
| 100-comma
| wa-100 comma
| w-100
|
| {{monzo| 159 -100 }}
| 604.49
|-
|
| 47-comma
| wa-47 comma
| w-47
|
| {{monzo| -74 47 }}
| 591.885
|-
|
| 59-comma
| wa-59 comma
| w-59
|
| {{monzo| 94 -59 }}
| 584.655
|-
|
| 88-comma
| wa-88 comma
| w-88
|
| {{monzo| 139 -88 }}
| 572.04
|-
|
| 18-comma
| wa-18 comma
| w-18
|
| {{monzo|29 -18}}
| 564.81
|-
|
| 23-comma
| wa-23 comma
| w-23
|
| {{monzo| -36 23}}
| 544.965
|-
|
| 83-comma
| wa-83 comma
| w-83
|
| {{monzo| 133 -83 }}
| 537.735
|-
|
| 71-comma
| wa-71 comma
| w-71
|
| {{monzo|113 -71}}
| 561.195
|-
| Pythagorean-[[Armodue]] fourth
| 64-comma
| wa-64 comma
| w-64
|
| {{monzo| -101 64 }}
| 525.12
|-
| Pythagorean wolf fourth
| 11-comma
| Large wa 4th
| Lw4
| 177147 / 131072
| {{monzo| -17 11}}
| 521.505
|-
|
| 42-comma
| wa-42 comma
| w-42
|
| {{monzo| 67 -42 }}
| 517.89
|-
|
| 95-comma
| wa-95 comma
| w-95
|
| {{monzo| 151 -95 }}
| 514.275
|-
|perfect fourth
| 1-comma
| wa 4th
| w4
| [[4/3|4 / 3]]
| {{monzo| 2 -1}}
| 498.045
|-
|
| 40-comma
| wa-40 comma
| w-40
|
| {{monzo| 63 -40 }}
| 478.2
|-
|
| 13-comma
| wa-13 comma
| w-13
|
| {{Monzo| 21 -13}}
| 474.585
|-
|
| 81-comma
| wa-81 comma
| w-81
|
| {{monzo| -128 81 }}
| 458.355
|-
|
| 69-comma
| wa-69 comma
| w-69
|
| {{monzo| -109 69 }}
| 434.895
|-
| Pythagorean supermajor third
| 16-comma
| Large wa 3rd
| Lw3
|
| {{Monzo|-25 16}}
| 431.28
|-
|
| 37-comma
| wa-37 comma
| w-37
|
| {{monzo| 59 -37 }}
| 427.665
|-
|
| 90-comma
| wa-90 comma
| w-90
|
| {{monzo| -143 90 }}
| 424.05
|-
|
| 49-comma
| wa-49 comma
| w-49
|
| {{monzo| 78 -49 }}
| 404.205
|-
|
| 98-comma
| wa-98 comma
| w-98
|
| {{monzo| -155 98 }}
| 391.59
|-
|
| 45-comma
| wa-45 comma
| w-45
|
| {{monzo| -71 45 }}
| 387.975
|-
| Pythagorean diminished fourth
| 8-comma
| small wa 4th
| sw4
| [[8192/6561|8192 / 6561]]
| {{Monzo| 13 -8 }}
| 384.360
|-
| Pythagorean 1/5 tritave
| 61-comma
| wa-61 comma
| w-61
|
| {{monzo| 97 -61 }}
| 380.745
|-
|
| 33-comma
| wa-33 comma
| w-33
|
| {{monzo| -52 33 }}
| 364.515
|-
|
| 73-comma
| wa-73 comma
| w-73
|
| {{monzo|116 -73}}
| 357.285
|-
|
| 74-comma
| wa-74 comma
| w-74
|
| {{monzo|117 -74}}
| 344.67
|-
|
| 32-comma
| wa-32 comma
| w-32
|
| {{monzo| 51 -32 }}
| 337.44
|-
| Pythagorean augmented second
| 9-comma
| large wa 2nd
| Lw2
| [[19683/16384]]
| {{Monzo| -14 9 }}
| 317.595
|-
|
| 97-comma
| wa-97 comma
| w-97
|
| {{monzo| 153 -97 }}
| 310.365
|-
|
| 50-comma
| wa-50 comma
| w-50
|
| {{monzo| -79 50 }}
| 297.75
|-
| Pythagorean minor third
| 3-comma
| wa 3rd
| w3
| [[32/27|32 / 27]]
| {{Monzo| 5 -3 }}
| 294.135
|-
|
| 56-comma
| wa-56 comma
| w-56
|
| {{monzo| 89 -56 }}
| 290.52
|-
|
| 91-comma
| wa-91 comma
| w-91
|
| {{monzo| -144 91 }}
| 277.905
|-
|
| 79-comma
| wa-79 comma
| w-79
|
| {{monzo| -125 79 }}
| 254.445
|-
|-
|
|
Line 757: Line 131:
| wa-75 comma
| wa-75 comma
| w-75
| w-75
|
| {{Monzo|119 -75}}
| {{monzo|119 -75}}
| 153.375
| 253.375
|-
|-
|
|
| 26-comma
| 128-comma
| wa-26 comma
| wa-128 comma
| w-26
| w-128
|
| {{Monzo| 203 -128}}
| {{monzo| -41 26 }}
| 149.76
| 250.83
|-
|-
|
|
| 27-comma
| 181-comma
| wa-27 comma
| wa-181 comma
| w-27
| w-181
|
| {{Monzo| 287 -181 }}
| {{monzo| 43 -27 }}
| 146.145
| 247.215
|-
|-
|
|
| 80-comma
| 125-comma
| wa-80 comma
| wa-125 comma
| w-80
| w-125
|
| {{Monzo| -198 125}}
| {{monzo| 127 -80 }}
| 144.375
| 243.6
|-
|-
|
|
| 67-comma
| 234-comma
| wa-67 comma
| wa-234 comma
| w-67
| w-234
|
| {{Monzo| 371 -234 }}
| {{monzo| -106 67 }}
| 142.53
| 230.985
|-
|-
|
|
| 39-comma
| 19-comma
| wa-39 comma
| wa-19 comma
| w-39
| w-19
|
| {{Monzo| -30 19 }}
| {{monzo| 62 -39 }}
| 137.145
| 223.75
|-
|
| 55-comma
| wa-55 comma
| w-55
|
| {{monzo| -87 55 }}
| 207.525
|-
| whole tone
| 2-comma
| wa 2nd
| w2
| [[9/8|9 / 8]]
| {{monzo| -3 2 }}
| 203.91
|-
|-
|
|
| 43-comma
| 272-comma
| wa-43 comma
| wa-272 comma
| w-43
| w-272
|
| {{Monzo| -431 272 }}
| {{monzo| -68 43 }}
| 131.75
| 184.065
|-
|-
|
|
| 63-comma
| 219-comma
| wa-63 comma
| wa-219 comma
| w-63
| w-219
|
| {{Monzo| -347 219 }}
| {{monzo| 100 -63 }}
| 128.145
| 176.835
|-
|-
|
|
| [[31-comma_temperaments|31-comma]]
| 166-comma
| wa-31 comma
| wa-166 comma
| w-31
| w-166
|
| {{Monzo| -263 166}}
| {{monzo| -49 31 }}
| 124.53
| 160.605
|-
|-
|
|
| 22-comma
| 113-comma
| wa-22 comma
| wa-113 comma
| w-22
| w-113
|
| {{Monzo| 179 -113 }}
| {{monzo| 35 -22 }}
| 120.915
| 156.99
|-
|-
|
| [[2187/2048|Apotome]]
| 19-comma
| wa-19 comma
| w-19
| 1162261467 / 1073741824
| {{monzo| -30 19 }}
| 137.145
|-
| apotome
| 7-comma
| 7-comma
| large wa unison
| lawa unison
| Lw1
| Lw1
| [[2187/2048|2187 / 2048]]
| {{Monzo| -11 7 }}
| {{monzo| -11 7 }}
| 113.685
| 113.685
|-
| Pythagorean-septendecimal semitone
| 207-comma
| wa-207 comma
| w-207
| {{Monzo| -328 207 }}
| 104.685
|-
|-
|
|
Line 869: Line 215:
| wa-46 comma
| wa-46 comma
| w-46
| w-46
|
| {{Monzo| 73 -46 }}
| {{monzo| 73 -46 }}
| 110.07
| 110.07
|-
|-
Line 877: Line 222:
| wa-99 comma
| wa-99 comma
| w-99
| w-99
| {{Monzo| 157 -99 }}
| 106.455
|-
|
|
| {{monzo| 157 -99 }}
| 152-comma
| 106.455
| wa-152 comma
| w-152
| {{Monzo| 241 -152 }}
| 102.84
|-
|-
|
|
Line 885: Line 236:
| wa-101 comma
| wa-101 comma
| w-101
| w-101
| {{Monzo| -160 101 }}
| 97.455
|-
|
|
| {{monzo| -160 101 }}
| 258-comma
| 97.455
| wa-258 comma
| w-258
| {{Monzo| 409 -258 }}
| 95.61
|-
|-
| limma, Pythagorean minor second
| Limma, Pythagorean minor second
| 5-comma
| 5-comma
| small wa 2nd
| sawa 2nd
| sw2
| sw2
| [[256/243|256 / 243]]
| {{Monzo| 8 -5 }}
| {{monzo| 8 -5 }}
| 90.225
| 90.225
|-
|
| 301-comma
| wa-301 comma
| w-301
| {{Monzo| -477 301 }}
| 88.455
|-
|
| 248-comma
| wa-248 comma
| w-248
| {{Monzo| -393 248 }}
| 84.840
|-
|
| 111-comma
| wa-111 comma
| w-111
| {{Monzo| 176 -111 }}
| 82.995
|-
|
| 195-comma
| wa-195 comma
| w-195
| {{Monzo| -309 195 }}
| 81.225
|-
|
| 142-comma
| wa-142 comma
| w-142
| {{Monzo| -225 142 }}
| 77.610
|-
|
| 217-comma
| wa-217 comma
| w-217
| {{Monzo| 344 -217 }}
| 75.765
|-
|-
|
|
Line 901: Line 299:
| wa-89 comma
| wa-89 comma
| w-89
| w-89
|
| {{Monzo| -141 89 }}
| {{monzo| -141 89 }}
| 73.995
| 73.995
|-
|-
Line 908: Line 305:
| [[17-comma]]
| [[17-comma]]
| wa-17 comma
| wa-17 comma
| ssw3
| w-17
| 134217728 / 129140163
| {{Monzo| 27 -17 }}
| {{monzo| 27 -17 }}
| 66.765
| 66.765
|-
|
| 289-comma
| wa-289 comma
| w-289
| {{Monzo| -458 289 }}
| 64.995
|-
|-
|
|
Line 917: Line 320:
| wa-70 comma
| wa-70 comma
| w-70
| w-70
| {{Monzo| 111 -70 }}
| 63.150
|-
|
|
| {{monzo| 111 -70 }}
| 183-comma
| 63.15
| wa-183 comma
| w-183
| {{Monzo| -290 183 }}
| 57.765
|-
|
| 176-comma
| wa-176 comma
| w-176
| {{Monzo| 279 -176 }}
| 55.920
|-
|
| 229-comma
| wa-229 comma
| w-229
| {{Monzo| 363 -229 }}
| 52.305
|-
|-
|
|
Line 925: Line 348:
| wa-77 comma
| wa-77 comma
| w-77
| w-77
| {{Monzo| -122 77 }}
| 50.535
|-
|
|
| {{monzo| -122 77 }}
| 282-comma
| 50.535
| wa-282 comma
| w-282
| {{Monzo| 447 -282 }}
| 48.69
|-
|-
|
|
Line 933: Line 362:
| wa-29 comma
| wa-29 comma
| w-29
| w-29
| {{Monzo| 46 -29 }}
| 43.305
|-
|
| 277-comma
| wa-277 comma
| w-277
| {{Monzo| -439 277 }}
| 41.535
|-
|
| 224-comma
| wa-224 comma
| w-224
| {{Monzo| -355 224 }}
| 37.920
|-
|
| 135-comma
| wa-135 comma
| w-135
| {{Monzo| 214 -135 }}
| 36.075
|-
|
| 171-comma
| wa-171 comma
| w-171
| {{Monzo| -271 171 }}
| 34.305
|-
|
| 118-comma
| wa-118 comma
| w-118
| {{Monzo| -187 118 }}
| 30.690
|-
|
|
| {{monzo| 46 -29 }}
| 241-comma
| 43.305
| wa-241 comma
| w-241
| {{Monzo| 382 -241 }}
| 28.845
|-
|-
| Pythagorean septimal comma
| Pythagorean septimal comma
Line 941: Line 411:
| wa-65 comma
| wa-65 comma
| w-65
| w-65
|
| {{Monzo| -103 65 }}
| {{monzo| -103 65}}
| 27.075
| 27.075
|-
|-
| [[Pythagorean comma]]
| [[Pythagorean comma]]
| 12-comma
| 12-comma
| lalawa comma
| lalawa comma  
or wa comma
| LLw-2
| LLw-2
| 531441 / 524288
| {{Monzo| -19 12 }}
| {{monzo| -19 12 }}
| 23.460
| 23.460
|-
|-
|
| Pythagorean countercomma, countercomp comma
| [[41-comma]]
| [[41-comma]]
| wa-41 comma
| wa-41 comma
| w-41
| w-41
|
| {{monzo| 65 -41 }}
| {{monzo| 65 -41 }}
| 19.845
| 19.845
|-
|-
|
| [[Stearnsmic clan #Garistearn|Garistearn comma]]
| 94-comma
| 94-comma
| wa-94 comma
| wa-94 comma
| w-94
| w-94
|
| {{Monzo| 149 -94 }}
| {{monzo| 149 -94 }}
| 16.230
| 16.230
|-
|-
Line 974: Line 439:
| wa-147 comma
| wa-147 comma
| w-147
| w-147
|
| {{Monzo| 233 -147 }}
| {{monzo| 233 -147 }}
| 12.615
| 12.615
|-
|-
| Pythagorean integer cent et comma
| Pythagorean integer-cent ET comma
| 200-comma
| 200-comma
| wa-200 comma
| wa-200 comma
| w-200
| w-200
| {{Monzo| 317 -200 }}
| 8.9998
|-
|
|
| {{monzo| 317 -200 }}
| 253-comma
| 8.9998
| wa-253 comma
| w-253
| {{Monzo| 401 -253 }}
| 5.3848
|-
|-
| [[Mercator's comma]]
| [[Mercator's comma]]
Line 990: Line 460:
| wa-53 comma
| wa-53 comma
| w-53
| w-53
|
| {{Monzo| -84 53 }}
| {{monzo| -84 53 }}
| 3.6150
| 3.6150
|-
|-
|
|[[Qian's large comma]]
| 359-comma
| 359-comma
| wa-359 comma
| wa-359 comma
| w-359
| w-359
|
| {{Monzo| -569 359 }}
| {{monzo| -569 359 }}
| 1.8453
| 1.8453
|-
|-
| [[Sasktel comma]]
| [[Qian's small comma]]
| 306-comma
| 306-comma
| wa-306 comma
| wa-306 comma
| w-306
| w-306
|
| {{Monzo| 485 -306 }}
| {{monzo| 485 -306 }}
| 1.7697
| 1.7697
|-
|-
Line 1,014: Line 481:
| wa-665 comma
| wa-665 comma
| w-665
| w-665
|
| {{Monzo| -1054 665 }}
| {{monzo| -1054 665 }}
| 0.075575
| 0.075575
|-
|-
Line 1,022: Line 488:
| wa-15601 comma
| wa-15601 comma
| w-15601
| w-15601
|
| {{Monzo| 24727 -15601 }}
| {{monzo| 24727 -15601 }}
| 0.031499
| 0.031499
|-
|-
Line 1,030: Line 495:
| wa-31867 comma
| wa-31867 comma
| w-31867
| w-31867
|
| {{Monzo| -50508 31867 }}
| {{monzo| -50508 31867 }}
| 0.012577
| 0.012577
|-
| [[Archangelic comma]]
| 190537-comma
| wa-190537 comma
| w-190537
| {{Monzo| 301994 -190537 }}
| 0.000112
|}
|}


[[Category:3-limit]]
[[Category:3-limit]]
[[Category:Comma]]
[[Category:Lists of commas]]
 
{{Todo| unify precision }}

Latest revision as of 23:07, 3 May 2025

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
whole tone 2-comma wa 2nd w2 [-3 2⟩ 203.91
193-comma wa-193 comma w-193 [306 -193⟩ 202.46
255-comma wa-255 comma w-255 [-404 255⟩ 198.525
104-comma wa-104 comma w-104 [165 -104⟩ 196.68
157-comma wa-157 comma w-157 [249 -157⟩ 193.065
149-comma wa-149 comma w-149 [-236 149⟩ 191.295
263-comma wa-263 comma w-263 [417 -263⟩ 185.835
43-comma wa-43 comma w-43 [-68 43⟩ 184.065
296-comma wa-296 comma w-296 [-469 296⟩ 178.68
63-comma wa-63 comma w-63 [100 -63⟩ 176.835
243-comma wa-243 comma w-243 [-385 243⟩ 175.605
190-comma wa-190 comma w-190 [-301 190⟩ 171.45
169-comma wa-169 comma w-169 [268 -169⟩ 169.605
137-comma wa-137 comma w-137 [-217 137⟩ 167.835
275-comma wa-275 comma w-275 [436 -275⟩ 162.375
31-comma wa-31 comma w-31 [-49 31⟩ 160.605
22-comma wa-22 comma w-22 [35 -22⟩ 156.99
75-comma wa-75 comma w-75 [119 -75⟩ 153.375
128-comma wa-128 comma w-128 [203 -128⟩ 149.76
181-comma wa-181 comma w-181 [287 -181⟩ 146.145
125-comma wa-125 comma w-125 [-198 125⟩ 144.375
234-comma wa-234 comma w-234 [371 -234⟩ 142.53
19-comma wa-19 comma w-19 [-30 19⟩ 137.145
272-comma wa-272 comma w-272 [-431 272⟩ 131.75
219-comma wa-219 comma w-219 [-347 219⟩ 128.145
166-comma wa-166 comma w-166 [-263 166⟩ 124.53
113-comma wa-113 comma w-113 [179 -113⟩ 120.915
Apotome 7-comma lawa unison Lw1 [-11 7⟩ 113.685
Pythagorean-septendecimal semitone 207-comma wa-207 comma w-207 [-328 207⟩ 104.685
46-comma wa-46 comma w-46 [73 -46⟩ 110.07
99-comma wa-99 comma w-99 [157 -99⟩ 106.455
152-comma wa-152 comma w-152 [241 -152⟩ 102.84
101-comma wa-101 comma w-101 [-160 101⟩ 97.455
258-comma wa-258 comma w-258 [409 -258⟩ 95.61
Limma, Pythagorean minor second 5-comma sawa 2nd sw2 [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
195-comma wa-195 comma w-195 [-309 195⟩ 81.225
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 w-17 [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
282-comma wa-282 comma w-282 [447 -282⟩ 48.69
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 LLw-2 [-19 12⟩ 23.460
Pythagorean countercomma, countercomp comma 41-comma wa-41 comma w-41 [65 -41⟩ 19.845
Garistearn comma 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
Qian's large comma 359-comma wa-359 comma w-359 [-569 359⟩ 1.8453
Qian's small 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
Archangelic comma 190537-comma wa-190537 comma w-190537 [301994 -190537⟩ 0.000112
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