Table of 3-limit commas
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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 | s3w3 | [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 |
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 | |
Archangelic comma | 190537-comma | wa-190537 comma | w-190537 | [301994 -190537⟩ | 0.000112 |