Table of 3-limit commas: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
mNo edit summary |
||
(27 intermediate revisions by 10 users not shown) | |||
Line 1: | Line 1: | ||
A [[3-limit]] comma is the amount which separates m [[3/2| | 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" | ||
|- | |- | ||
!Name(s) | ! colspan="2" | Name(s) | ||
! colspan="2" |[[Color notation|Color Name]] | ! colspan="2" | [[Color notation|Color Name]] | ||
! | ! [[Monzo]] | ||
!Monzo | ! [[Cent]]s | ||
|- | |||
| whole tone | |||
| 2-comma | |||
| wa 2nd | |||
| w2 | |||
| {{Monzo| -3 2 }} | |||
| 203.91 | |||
|- | |- | ||
| | | | ||
|{{ | | 193-comma | ||
| | | wa-193 comma | ||
| w-193 | |||
| {{Monzo| 306 -193 }} | |||
| 202.46 | |||
|- | |- | ||
| | | | ||
|{{ | | 255-comma | ||
| | | wa-255 comma | ||
| w-255 | |||
| {{Monzo| -404 255 }} | |||
| 198.525 | |||
|- | |- | ||
| | | | ||
|{{ | | 104-comma | ||
| | | wa-104 comma | ||
| w-104 | |||
| {{Monzo| 165 -104 }} | |||
| 196.68 | |||
|- | |- | ||
| | | | ||
|{{ | | 157-comma | ||
| | | wa-157 comma | ||
| w-157 | |||
| {{Monzo| 249 -157 }} | |||
| 193.065 | |||
|- | |- | ||
| | | | ||
|{{ | | 149-comma | ||
| | | wa-149 comma | ||
| w-149 | |||
| {{Monzo| -236 149 }} | |||
| 191.295 | |||
|- | |- | ||
| | | | ||
|{{ | | 263-comma | ||
| | | wa-263 comma | ||
| w-263 | |||
| {{Monzo| 417 -263 }} | |||
| 185.835 | |||
|- | |- | ||
| | | | ||
|{{ | | 43-comma | ||
| | | wa-43 comma | ||
| w-43 | |||
| {{Monzo| -68 43 }} | |||
| 184.065 | |||
|- | |- | ||
| | | | ||
|{{ | | 296-comma | ||
| | | wa-296 comma | ||
| w-296 | |||
| {{Monzo| -469 296 }} | |||
| 178.68 | |||
|- | |- | ||
| | | | ||
|{{ | | 63-comma | ||
| | | wa-63 comma | ||
| w-63 | |||
| {{Monzo| 100 -63 }} | |||
| 176.835 | |||
|- | |- | ||
| | | | ||
|{{ | | 243-comma | ||
| | | wa-243 comma | ||
| w-243 | |||
| {{Monzo| -385 243 }} | |||
| 175.605 | |||
|- | |- | ||
| | | | ||
|{{ | | 190-comma | ||
| | | wa-190 comma | ||
| w-190 | |||
| {{Monzo| -301 190 }} | |||
| 171.45 | |||
|- | |- | ||
| | | | ||
|{{ | | 169-comma | ||
| | | wa-169 comma | ||
| w-169 | |||
| {{Monzo| 268 -169}} | |||
| 169.605 | |||
|- | |- | ||
| | | | ||
|{{Monzo| | | 137-comma | ||
| | | wa-137 comma | ||
| w-137 | |||
| {{Monzo| -217 137 }} | |||
| 167.835 | |||
|- | |- | ||
| | | | ||
|{{ | | 275-comma | ||
| | | wa-275 comma | ||
| w-275 | |||
| {{Monzo| 436 -275 }} | |||
| 162.375 | |||
|- | |- | ||
| | | | ||
|{{Monzo|- | | [[31-comma_temperaments|31-comma]] | ||
| | | wa-31 comma | ||
| w-31 | |||
| {{Monzo| -49 31 }} | |||
| 160.605 | |||
|- | |- | ||
| | | | ||
|{{ | | 22-comma | ||
| | | wa-22 comma | ||
| w-22 | |||
| {{Monzo| 35 -22 }} | |||
| 156.99 | |||
|- | |- | ||
| | | | ||
|{{Monzo| | | 75-comma | ||
| | | wa-75 comma | ||
| w-75 | |||
| {{Monzo|119 -75}} | |||
| 153.375 | |||
|- | |- | ||
| | | | ||
|{{Monzo| - | | 128-comma | ||
| | | wa-128 comma | ||
| w-128 | |||
| {{Monzo| 203 -128}} | |||
| 149.76 | |||
|- | |- | ||
| | | | ||
|{{ | | 181-comma | ||
| | | wa-181 comma | ||
| w-181 | |||
| {{Monzo| 287 -181 }} | |||
| 146.145 | |||
|- | |- | ||
| | | | ||
|{{ | | 125-comma | ||
| | | wa-125 comma | ||
| w-125 | |||
| {{Monzo| -198 125}} | |||
| 144.375 | |||
|- | |- | ||
| | | | ||
|{{Monzo| - | | 234-comma | ||
| | | wa-234 comma | ||
| w-234 | |||
| {{Monzo| 371 -234 }} | |||
| 142.53 | |||
|- | |- | ||
| | | | ||
|{{ | | 19-comma | ||
| | | wa-19 comma | ||
| w-19 | |||
| {{Monzo| -30 19 }} | |||
| 137.145 | |||
|- | |- | ||
| | | | ||
|{{Monzo| - | | 272-comma | ||
| | | wa-272 comma | ||
| w-272 | |||
| {{Monzo| -431 272 }} | |||
| 131.75 | |||
|- | |- | ||
| | | | ||
|{{ | | 219-comma | ||
| | | wa-219 comma | ||
| w-219 | |||
| {{Monzo| -347 219 }} | |||
| 128.145 | |||
|- | |- | ||
| | | | ||
|{{ | | 166-comma | ||
| | | wa-166 comma | ||
| w-166 | |||
| {{Monzo| -263 166}} | |||
| 124.53 | |||
|- | |- | ||
| | | | ||
| | | 113-comma | ||
| | | wa-113 comma | ||
| w-113 | |||
|{{ | | {{Monzo| 179 -113 }} | ||
| | | 120.915 | ||
|- | |- | ||
| | | [[2187/2048|Apotome]] | ||
| | | 7-comma | ||
| | | lawa unison | ||
| | | Lw1 | ||
|{{ | | {{Monzo| -11 7 }} | ||
| | | 113.685 | ||
|- | |- | ||
| | | Pythagorean-septendecimal semitone | ||
|wa- | | 207-comma | ||
|w- | | wa-207 comma | ||
| w-207 | |||
|{{ | | {{Monzo| -328 207 }} | ||
| | | 104.685 | ||
|- | |- | ||
| | | | ||
|{{ | | 46-comma | ||
| | | wa-46 comma | ||
| w-46 | |||
| {{Monzo| 73 -46 }} | |||
| 110.07 | |||
|- | |- | ||
| | | | ||
|{{ | | 99-comma | ||
| | | wa-99 comma | ||
| w-99 | |||
| {{Monzo| 157 -99 }} | |||
| 106.455 | |||
|- | |- | ||
| | | | ||
|{{ | | 152-comma | ||
| | | wa-152 comma | ||
| w-152 | |||
| {{Monzo| 241 -152 }} | |||
| 102.84 | |||
|- | |- | ||
| | | | ||
|{{ | | 101-comma | ||
| | | wa-101 comma | ||
| w-101 | |||
| {{Monzo| -160 101 }} | |||
| 97.455 | |||
|- | |- | ||
| | | | ||
|{{ | | 258-comma | ||
| | | wa-258 comma | ||
| w-258 | |||
| {{Monzo| 409 -258 }} | |||
| 95.61 | |||
|- | |- | ||
|Pythagorean | | Limma, Pythagorean minor second | ||
| | | 5-comma | ||
| sawa 2nd | |||
| | | sw2 | ||
|{{ | | {{Monzo| 8 -5 }} | ||
| | | 90.225 | ||
|- | |- | ||
| | | | ||
|{{ | | 301-comma | ||
| | | wa-301 comma | ||
| w-301 | |||
| {{Monzo| -477 301 }} | |||
| 88.455 | |||
|- | |- | ||
| | | | ||
|{{Monzo| | | 248-comma | ||
| | | wa-248 comma | ||
| w-248 | |||
| {{Monzo| -393 248 }} | |||
| 84.840 | |||
|- | |- | ||
| | | | ||
| | | 111-comma | ||
| | | wa-111 comma | ||
| | | w-111 | ||
|{{ | | {{Monzo| 176 -111 }} | ||
| | | 82.995 | ||
|- | |- | ||
| | | | ||
|{{Monzo|- | | 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 | |||
|- | |- | ||
| | | | ||
|{{ | | 89-comma | ||
| | | wa-89 comma | ||
| w-89 | |||
| {{Monzo| -141 89 }} | |||
| 73.995 | |||
|- | |- | ||
| | | | ||
| | | [[17-comma]] | ||
| | | wa-17 comma | ||
| w-17 | |||
|{{Monzo| | | {{Monzo| 27 -17 }} | ||
| | | 66.765 | ||
|- | |- | ||
| | | | ||
|{{ | | 289-comma | ||
| | | wa-289 comma | ||
| w-289 | |||
| {{Monzo| -458 289 }} | |||
| 64.995 | |||
|- | |- | ||
| | | | ||
|{{ | | 70-comma | ||
| | | wa-70 comma | ||
| w-70 | |||
| {{Monzo| 111 -70 }} | |||
| 63.150 | |||
|- | |- | ||
| | | | ||
| | | 183-comma | ||
| | | wa-183 comma | ||
| w-183 | |||
|{{Monzo| - | | {{Monzo| -290 183 }} | ||
| | | 57.765 | ||
|- | |- | ||
| | | | ||
|{{ | | 176-comma | ||
| | | wa-176 comma | ||
| w-176 | |||
| {{Monzo| 279 -176 }} | |||
| 55.920 | |||
|- | |- | ||
| | | | ||
|wa | | 229-comma | ||
| | | wa-229 comma | ||
| w-229 | |||
|{{Monzo| | | {{Monzo| 363 -229 }} | ||
| | | 52.305 | ||
|- | |- | ||
| | | | ||
|{{ | | 77-comma | ||
| | | wa-77 comma | ||
| w-77 | |||
| {{Monzo| -122 77 }} | |||
| 50.535 | |||
|- | |- | ||
| | | | ||
|{{ | | 282-comma | ||
| | | wa-282 comma | ||
| w-282 | |||
| {{Monzo| 447 -282 }} | |||
| 48.69 | |||
|- | |- | ||
| | | | ||
|{{ | | [[29-comma]] | ||
| | | wa-29 comma | ||
| 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 | |||
|- | |- | ||
| | | | ||
|wa- | | 118-comma | ||
|w- | | wa-118 comma | ||
| w-118 | |||
|{{ | | {{Monzo| -187 118 }} | ||
| | | 30.690 | ||
|- | |- | ||
| | | | ||
|{{ | | 241-comma | ||
| | | wa-241 comma | ||
| w-241 | |||
| {{Monzo| 382 -241 }} | |||
| 28.845 | |||
|- | |- | ||
| | | Pythagorean septimal comma | ||
| | | 65-comma | ||
| | | wa-65 comma | ||
| | | w-65 | ||
|{{ | | {{Monzo| -103 65 }} | ||
| | | 27.075 | ||
|- | |- | ||
|[[ | | [[Pythagorean comma]] | ||
| | | 12-comma | ||
| | | lalawa comma | ||
| | | LLw-2 | ||
|{{ | | {{Monzo| -19 12 }} | ||
| | | 23.460 | ||
|- | |- | ||
| | | Pythagorean countercomma, countercomp comma | ||
| | | [[41-comma]] | ||
| wa-41 comma | |||
| w-41 | |||
| {{monzo| 65 -41 }} | |||
| 19.845 | |||
|wa- | |||
|w- | |||
|{{monzo| - | |||
| | |||
|- | |- | ||
|[[ | | [[Stearnsmic clan #Garistearn|Garistearn comma]] | ||
|wa- | | 94-comma | ||
|w- | | wa-94 comma | ||
| w-94 | |||
|{{ | | {{Monzo| 149 -94 }} | ||
| | | 16.230 | ||
|- | |- | ||
| | | | ||
| | | 147-comma | ||
| wa-147 comma | |||
| w-147 | |||
| {{Monzo| 233 -147 }} | |||
| | | 12.615 | ||
| | |||
|{{ | |||
| | |||
|- | |- | ||
| | | Pythagorean integer-cent ET comma | ||
|wa- | | 200-comma | ||
|w- | | wa-200 comma | ||
| w-200 | |||
| {{Monzo| 317 -200 }} | |||
|{{ | | 8.9998 | ||
| | |||
|- | |- | ||
| | | | ||
|{{ | | 253-comma | ||
| | | wa-253 comma | ||
| w-253 | |||
| {{Monzo| 401 -253 }} | |||
| 5.3848 | |||
|- | |- | ||
| | | [[Mercator's comma]] | ||
|wa- | | 53-comma | ||
|w- | | wa-53 comma | ||
| w-53 | |||
|{{ | | {{Monzo| -84 53 }} | ||
| | | 3.6150 | ||
|- | |- | ||
|[[ | |[[Qian's large comma]] | ||
|wa- | | 359-comma | ||
|w- | | wa-359 comma | ||
| w-359 | |||
| {{Monzo| -569 359 }} | |||
|{{ | | 1.8453 | ||
| | |||
|- | |- | ||
| | | [[Qian's small comma]] | ||
|wa- | | 306-comma | ||
|w- | | wa-306 comma | ||
| w-306 | |||
|{{ | | {{Monzo| 485 -306 }} | ||
|1. | | 1.7697 | ||
|- | |- | ||
|[[ | | [[Satanic comma]] | ||
|wa- | | 665-comma | ||
|w- | | wa-665 comma | ||
| w-665 | |||
|{{ | | {{Monzo| -1054 665 }} | ||
| | | 0.075575 | ||
|- | |- | ||
| | | | ||
|{{ | | 15601-comma | ||
|0. | | wa-15601 comma | ||
| w-15601 | |||
| {{Monzo| 24727 -15601 }} | |||
| 0.031499 | |||
|- | |- | ||
| | | | ||
|{{ | | 31867-comma | ||
|0. | | wa-31867 comma | ||
| w-31867 | |||
| {{Monzo| -50508 31867 }} | |||
| 0.012577 | |||
|- | |- | ||
| | | [[Archangelic comma]] | ||
|wa- | | 190537-comma | ||
|w- | | wa-190537 comma | ||
| w-190537 | |||
|{{ | | {{Monzo| 301994 -190537 }} | ||
|0. | | 0.000112 | ||
|} | |} | ||
[[Category:3-limit]] | |||
[[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 |