Table of 3-limit commas: Difference between revisions

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A [[3-limit]] comma is the amount which separates ''m'' [[3/2|fifths]] from ''n'' [[octaves]]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"
Line 12: Line 12:
| wa 2nd
| wa 2nd
| w2
| w2
|{{monzo| -3 2 }}
| {{Monzo| -3 2 }}
| 203.91
| 203.91
|-
|-
|
|
|193-comma
| 255-comma
|wa-193 comma
| wa-255 comma
|w-193
| w-255
|{{monzo| 306 -193 }}
| {{Monzo| -404 255 }}
|202.46
| 198.525
|-
|-
|
|
|255-comma
| 104-comma
|wa-255 comma
| wa-104 comma
|w-255
| w-104
|{{monzo| -404 255 }}
| {{Monzo| 165 -104 }}
|198.525
| 196.68
|-
|-
|
|
|104-comma
| 157-comma
|wa-104 comma
| wa-157 comma
|w-104
| w-157
|{{monzo|165 -104}}
| {{Monzo| 249 -157 }}
|196.68
| 193.065
|-
|-
|
|
|157-comma
| 149-comma
|wa-157 comma
| wa-149 comma
|w-157
| w-149
|{{monzo|249 -157}}
| {{Monzo| -236 149 }}
|193.065
| 191.295
|-
|-
|
|
|149-comma
| 263-comma
|wa-149 comma
| wa-263 comma
|w-149
| w-263
|{{monzo| -236 149 }}
| {{Monzo| 417 -263 }}
|191.295
| 185.835
|-
|
|263-comma
|wa-263 comma
|w-263
|{{monzo| 417 -263 }}
|185.835
|-
|-
|
|
Line 61: Line 54:
| wa-43 comma
| wa-43 comma
| w-43
| w-43
|{{monzo| -68 43 }}
| {{Monzo| -68 43 }}
| 184.065
| 184.065
|-
|-
|
|
|296-comma
| 296-comma
|wa-296 comma
| wa-296 comma
|w-296
| w-296
|{{monzo| -469 296 }}
| {{Monzo| -469 296 }}
|178.68
| 178.68
|-
|-
|
|
Line 75: Line 68:
| wa-63 comma
| wa-63 comma
| w-63
| w-63
|{{monzo| 100 -63 }}
| {{Monzo| 100 -63 }}
| 176.835
| 176.835
|-
|-
|
|
|243-comma
| 243-comma
|wa-243 comma
| wa-243 comma
|w-243
| w-243
|{{monzo| -385 243 }}
| {{Monzo| -385 243 }}
|175.605
| 175.605
|-
|-
|
|
|190-comma
| 190-comma
|wa-190 comma
| wa-190 comma
|w-190
| w-190
|{{monzo| -301 190 }}
| {{Monzo| -301 190 }}
|171.45
| 171.45
|-
|-
|
|
|169-comma
| 169-comma
|wa-169 comma
| wa-169 comma
|w-169
| w-169
|{{monzo| 268 -169}}
| {{Monzo| 268 -169}}
|169.605
| 169.605
|-
|-
|
|
|137-comma
| 137-comma
|wa-137 comma
| wa-137 comma
|w-137
| w-137
|{{monzo| -217 137 }}
| {{Monzo| -217 137 }}
|167.835
| 167.835
|-
|-
|
|
|275-comma
| 275-comma
|wa-275 comma
| wa-275 comma
|w-275
| w-275
|{{monzo| 436 -275 }}
| {{Monzo| 436 -275 }}
|162.375
| 162.375
|-
|-
|
|
|[[31-comma_temperaments|31-comma]]
| [[31-comma_temperaments|31-comma]]
| wa-31 comma
| wa-31 comma
| w-31
| w-31
|{{monzo| -49 31 }}
| {{Monzo| -49 31 }}
| 160.605
| 160.605
|-
|-
Line 124: Line 117:
| wa-22 comma
| wa-22 comma
| w-22
| w-22
|{{monzo| 35 -22 }}
| {{Monzo| 35 -22 }}
| 156.99
| 156.99
|-
|-
Line 131: Line 124:
| wa-75 comma
| wa-75 comma
| w-75
| w-75
|{{monzo|119 -75}}
| {{Monzo|119 -75}}
| 153.375
| 153.375
|-
|-
|
|
|128-comma
| 128-comma
|wa-128 comma
| wa-128 comma
|w-128
| w-128
|{{monzo| 203 -128}}
| {{Monzo| 203 -128}}
|149.76
| 149.76
|-
|-
|
|
|181-comma
| 181-comma
|wa-181 comma
| wa-181 comma
|w-181
| w-181
|{{monzo| 287 -181 }}
| {{Monzo| 287 -181 }}
|146.145
| 146.145
|-
|-
|
|
|125-comma
| 125-comma
|wa-125 comma
| wa-125 comma
|w-125
| w-125
|{{monzo| -198 125}}
| {{Monzo| -198 125}}
|144.375
| 144.375
|-
|-
|
|
|234-comma
| 234-comma
|wa-234 comma
| wa-234 comma
|w-234
| w-234
|{{monzo| 371 -234 }}
| {{Monzo| 371 -234 }}
|142.53
| 142.53
|-
|-
|
|
Line 166: Line 159:
| wa-19 comma
| wa-19 comma
| w-19
| w-19
|{{monzo| -30 19 }}
| {{Monzo| -30 19 }}
| 137.145
| 137.145
|-
|-
|
|
|272-comma
| 272-comma
|wa-272 comma
| wa-272 comma
|w-272
| w-272
|{{monzo| -431 272 }}
| {{Monzo| -431 272 }}
|131.75
| 131.75
|-
|
| 219-comma
| wa-219 comma
| w-219
| {{Monzo| -347 219 }}
| 128.145
|-
|-
|
|
|219-comma
| 166-comma
|wa-219 comma
| wa-166 comma
|w-219
| w-166
|{{monzo| -347 219 }}
| {{Monzo| -263 166}}
|128.145
| 124.53
|-
|-
|
|
|166-comma
| 193-comma
|wa-166 comma
| wa-193 comma
|w-166
| w-193
|{{monzo| -263 166}}
| {{Monzo| 306 -193 }}
|124.53
| 122.68
|-
|-
|
|
|113-comma
| 113-comma
|wa-113 comma
| wa-113 comma
|w-113
| w-113
|{{monzo| 179 -113 }}
| {{Monzo| 179 -113 }}
|120.915
| 120.915
|-
|-
| [[2187/2048|apotome]]
| [[2187/2048|Apotome]]
| 7-comma
| 7-comma
| lawa unison
| lawa unison
| Lw1
| Lw1
|{{monzo| -11 7 }}
| {{Monzo| -11 7 }}
| 113.685
| 113.685
|-
|-
|Pythagorean-Septendecimal semitone  
| Pythagorean-septendecimal semitone  
|207-comma
| 207-comma
|wa-207 comma
| wa-207 comma
|w-207
| w-207
|{{monzo| -328 207 }}
| {{Monzo| -328 207 }}
|104.685
| 104.685
|-
|-
|
|
Line 215: Line 215:
| wa-46 comma
| wa-46 comma
| w-46
| w-46
|{{monzo| 73 -46 }}
| {{Monzo| 73 -46 }}
| 110.07
| 110.07
|-
|-
Line 222: Line 222:
| wa-99 comma
| wa-99 comma
| w-99
| w-99
|{{monzo| 157 -99 }}
| {{Monzo| 157 -99 }}
| 106.455
| 106.455
|-
|-
|
|
|152-comma
| 152-comma
|wa-152 comma
| wa-152 comma
|w-152
| w-152
|{{monzo|241 -152}}
| {{Monzo| 241 -152 }}
|102.84
| 102.84
|-
|-
|
|
Line 236: Line 236:
| wa-101 comma
| wa-101 comma
| w-101
| w-101
|{{monzo| -160 101 }}
| {{Monzo| -160 101 }}
| 97.455
| 97.455
|-
|-
|
|
|258-comma
| 258-comma
|wa-258 comma
| wa-258 comma
|w-258
| w-258
|{{monzo| 409 -258 }}
| {{Monzo| 409 -258 }}
|95.61
| 95.61
|-
|-
| limma, Pythagorean minor second
| Limma, Pythagorean minor second
| 5-comma
| 5-comma
| sawa 2nd
| sawa 2nd
| sw2
| sw2
|{{monzo| 8 -5 }}
| {{Monzo| 8 -5 }}
| 90.225
| 90.225
|-
|-
Line 257: Line 257:
| wa-301 comma
| wa-301 comma
| w-301
| w-301
|{{monzo| -477 301 }}
| {{Monzo| -477 301 }}
| 88.455
| 88.455
|-
|-
Line 264: Line 264:
| wa-248 comma
| wa-248 comma
| w-248
| w-248
|{{monzo| -393 248 }}
| {{Monzo| -393 248 }}
| 84.840
| 84.840
|-
|-
Line 271: Line 271:
| wa-111 comma
| wa-111 comma
| w-111
| w-111
|{{monzo| 176 -111 }}
| {{Monzo| 176 -111 }}
| 82.995
| 82.995
|-
|-
|
|
|195-comma
| 195-comma
|wa-195 comma
| wa-195 comma
|w-195
| w-195
|{{monzo| -309 195 }}
| {{Monzo| -309 195 }}
|81.225
| 81.225
|-
|-
|
|
Line 285: Line 285:
| wa-142 comma
| wa-142 comma
| w-142
| w-142
|{{monzo| -225 142 }}
| {{Monzo| -225 142 }}
| 77.610
| 77.610
|-
|-
Line 292: Line 292:
| wa-217 comma
| wa-217 comma
| w-217
| w-217
|{{monzo| 344 -217 }}
| {{Monzo| 344 -217 }}
| 75.765
| 75.765
|-
|-
Line 299: Line 299:
| wa-89 comma
| wa-89 comma
| w-89
| w-89
|{{monzo| -141 89 }}
| {{Monzo| -141 89 }}
| 73.995
| 73.995
|-
|-
|
|
|[[17-comma]]
| [[17-comma]]
| wa-17 comma
| wa-17 comma
| s<sup>3</sup>w3
| w-17
|{{monzo| 27 -17 }}
| {{Monzo| 27 -17 }}
| 66.765
| 66.765
|-
|-
Line 313: Line 313:
| wa-289 comma
| wa-289 comma
| w-289
| w-289
|{{monzo| -458 289 }}
| {{Monzo| -458 289 }}
| 64.995
| 64.995
|-
|-
Line 320: Line 320:
| wa-70 comma
| wa-70 comma
| w-70
| w-70
|{{monzo| 111 -70 }}
| {{Monzo| 111 -70 }}
| 63.150
| 63.150
|-
|-
Line 327: Line 327:
| wa-183 comma
| wa-183 comma
| w-183
| w-183
|{{monzo| -290 183 }}
| {{Monzo| -290 183 }}
| 57.765
| 57.765
|-
|-
Line 334: Line 334:
| wa-176 comma
| wa-176 comma
| w-176
| w-176
|{{monzo| 279 -176 }}
| {{Monzo| 279 -176 }}
| 55.920
| 55.920
|-
|-
Line 341: Line 341:
| wa-229 comma
| wa-229 comma
| w-229
| w-229
|{{monzo| 363 -229 }}
| {{Monzo| 363 -229 }}
| 52.305
| 52.305
|-
|-
Line 348: Line 348:
| wa-77 comma
| wa-77 comma
| w-77
| w-77
|{{monzo| -122 77 }}
| {{Monzo| -122 77 }}
| 50.535
| 50.535
|-
|-
|
|
|282-comma
| 282-comma
|wa-282 comma
| wa-282 comma
|w-282
| w-282
|{{monzo| 447 -282}}
| {{Monzo| 447 -282 }}
|48.69
| 48.69
|-
|-
|
|
|[[29-comma]]
| [[29-comma]]
| wa-29 comma
| wa-29 comma
| w-29
| w-29
|{{monzo| 46 -29 }}
| {{Monzo| 46 -29 }}
| 43.305
| 43.305
|-
|-
Line 369: Line 369:
| wa-277 comma
| wa-277 comma
| w-277
| w-277
|{{monzo| -439 277 }}
| {{Monzo| -439 277 }}
| 41.535
| 41.535
|-
|-
Line 376: Line 376:
| wa-224 comma
| wa-224 comma
| w-224
| w-224
|{{monzo| -355 224 }}
| {{Monzo| -355 224 }}
| 37.920
| 37.920
|-
|-
Line 383: Line 383:
| wa-135 comma
| wa-135 comma
| w-135
| w-135
|{{monzo| 214 -135 }}
| {{Monzo| 214 -135 }}
| 36.075
| 36.075
|-
|-
Line 390: Line 390:
| wa-171 comma
| wa-171 comma
| w-171
| w-171
|{{monzo| -271 171 }}
| {{Monzo| -271 171 }}
| 34.305
| 34.305
|-
|-
Line 397: Line 397:
| wa-118 comma
| wa-118 comma
| w-118
| w-118
|{{monzo| -187 118 }}
| {{Monzo| -187 118 }}
| 30.690
| 30.690
|-
|-
Line 404: Line 404:
| wa-241 comma
| wa-241 comma
| w-241
| w-241
|{{monzo| 382 -241 }}
| {{Monzo| 382 -241 }}
| 28.845
| 28.845
|-
|-
Line 411: 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 <br>or wa comma
| lalawa comma  
| LLw-2
| LLw-2
|{{monzo| -19 12 }}
| {{Monzo| -19 12 }}
| 23.460
| 23.460
|-
|-
Line 428: Line 428:
| 19.845
| 19.845
|-
|-
|[[Stearnsmic clan #Garistearn|Garistearn comma]]
| [[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 439: Line 439:
| wa-147 comma
| wa-147 comma
| w-147
| w-147
|{{monzo| 233 -147 }}
| {{Monzo| 233 -147 }}
| 12.615
| 12.615
|-
|-
Line 446: Line 446:
| wa-200 comma
| wa-200 comma
| w-200
| w-200
|{{monzo| 317 -200 }}
| {{Monzo| 317 -200 }}
| 8.9998
| 8.9998
|-
|-
Line 453: Line 453:
| wa-253 comma
| wa-253 comma
| w-253
| w-253
|{{monzo| 401 -253 }}
| {{Monzo| 401 -253 }}
| 5.3848
| 5.3848
|-
|-
|[[Mercator's comma]]
| [[Mercator's comma]]
| 53-comma
| 53-comma
| 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
|-
|-
|[[Satanic comma]]
| [[Satanic comma]]
| 665-comma
| 665-comma
| wa-665 comma
| wa-665 comma
| w-665
| w-665
|{{monzo| -1054 665 }}
| {{Monzo| -1054 665 }}
| 0.075575
| 0.075575
|-
|-
Line 488: Line 488:
| wa-15601 comma
| wa-15601 comma
| w-15601
| w-15601
|{{monzo| 24727 -15601 }}
| {{Monzo| 24727 -15601 }}
| 0.031499
| 0.031499
|-
|-
Line 495: Line 495:
| wa-31867 comma
| wa-31867 comma
| w-31867
| w-31867
|{{monzo| -50508 31867 }}
| {{Monzo| -50508 31867 }}
| 0.012577
| 0.012577
|-
|-
Line 502: Line 502:
| wa-190537 comma
| wa-190537 comma
| w-190537
| w-190537
|{{monzo| 301994 -190537 }}
| {{Monzo| 301994 -190537 }}
| 0.000112
| 0.000112
|}
|}
Line 508: Line 508:
[[Category:3-limit]]
[[Category:3-limit]]
[[Category:Lists of commas]]
[[Category:Lists of commas]]
{{Todo| unify precision }}

Latest revision as of 01:16, 16 May 2026

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
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
193-comma wa-193 comma w-193 [306 -193 122.68
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