Table of 3-limit commas: Difference between revisions
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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" | ||
|- | |- | ||
! colspan="2" |Name(s) | ! colspan="2" | Name(s) | ||
! colspan="2" |[[Color notation|Color Name]] | ! colspan="2" | [[Color notation|Color Name]] | ||
! | ! [[Monzo]] | ||
! [[Cent]]s | |||
! | |||
|- | |- | ||
| | | whole tone | ||
| | | 2-comma | ||
| wa | | wa 2nd | ||
| w2 | |||
| | | {{Monzo| -3 2 }} | ||
| {{ | | 203.91 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 193-comma | ||
| wa- | | wa-193 comma | ||
| w- | | w-193 | ||
| {{Monzo| 306 -193 }} | |||
| {{ | | 202.46 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 255-comma | ||
| wa- | | wa-255 comma | ||
| w- | | w-255 | ||
| {{Monzo| -404 255 }} | |||
| {{ | | 198.525 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 104-comma | ||
| wa- | | wa-104 comma | ||
| w- | | w-104 | ||
| {{Monzo| 165 -104 }} | |||
| {{ | | 196.68 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 157-comma | ||
| wa- | | wa-157 comma | ||
| w- | | w-157 | ||
| {{Monzo| 249 -157 }} | |||
| {{ | | 193.065 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 149-comma | ||
| wa- | | wa-149 comma | ||
| w- | | w-149 | ||
| {{Monzo| -236 149 }} | |||
| {{ | | 191.295 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 263-comma | ||
| wa- | | wa-263 comma | ||
| w- | | w-263 | ||
| {{Monzo| 417 -263 }} | |||
| {{ | | 185.835 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 43-comma | ||
| wa- | | wa-43 comma | ||
| w- | | w-43 | ||
| {{Monzo| -68 43 }} | |||
| {{ | | 184.065 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 296-comma | ||
| wa- | | wa-296 comma | ||
| w- | | w-296 | ||
| {{Monzo| -469 296 }} | |||
| {{ | | 178.68 | ||
| | |||
|- | |- | ||
| | | | ||
| {{ | | 63-comma | ||
| | | wa-63 comma | ||
| w-63 | |||
| {{Monzo| 100 -63 }} | |||
| 176.835 | |||
|- | |- | ||
| | | | ||
| | | 243-comma | ||
| wa- | | wa-243 comma | ||
| w- | | w-243 | ||
| {{Monzo| -385 243 }} | |||
| {{ | | 175.605 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 190-comma | ||
| wa- | | wa-190 comma | ||
| w- | | w-190 | ||
| {{Monzo| -301 190 }} | |||
| {{ | | 171.45 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 169-comma | ||
| wa- | | wa-169 comma | ||
| w- | | w-169 | ||
| {{Monzo| 268 -169}} | |||
| {{ | | 169.605 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 137-comma | ||
| wa- | | wa-137 comma | ||
| w- | | w-137 | ||
| {{Monzo| -217 137 }} | |||
| {{ | | 167.835 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 275-comma | ||
| wa- | | wa-275 comma | ||
| w- | | w-275 | ||
| {{Monzo| 436 -275 }} | |||
| {{ | | 162.375 | ||
| | |||
|- | |- | ||
| | | | ||
| | | [[31-comma_temperaments|31-comma]] | ||
| wa- | | wa-31 comma | ||
| w- | | w-31 | ||
| {{Monzo| -49 31 }} | |||
| {{ | | 160.605 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 22-comma | ||
| wa- | | wa-22 comma | ||
| w- | | w-22 | ||
| {{Monzo| 35 -22 }} | |||
| 156.99 | |||
| {{Monzo| | |||
| | |||
|- | |- | ||
| | | | ||
Line 789: | Line 131: | ||
| wa-75 comma | | wa-75 comma | ||
| w-75 | | w-75 | ||
| {{Monzo|119 -75}} | |||
| {{ | | 153.375 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 128-comma | ||
| wa- | | wa-128 comma | ||
| w- | | w-128 | ||
| {{Monzo| 203 -128}} | |||
| {{ | | 149.76 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 181-comma | ||
| wa- | | wa-181 comma | ||
| w- | | w-181 | ||
| {{Monzo| 287 -181 }} | |||
| {{ | | 146.145 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 125-comma | ||
| wa- | | wa-125 comma | ||
| w- | | w-125 | ||
| {{Monzo| -198 125}} | |||
| {{ | | 144.375 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 234-comma | ||
| wa- | | wa-234 comma | ||
| w- | | w-234 | ||
| {{Monzo| 371 -234 }} | |||
| {{ | | 142.53 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 19-comma | ||
| wa- | | wa-19 comma | ||
| w- | | w-19 | ||
| {{Monzo| -30 19 }} | |||
| 137.145 | |||
| {{ | |||
| | |||
|- | |- | ||
| | | | ||
| | | 272-comma | ||
| wa- | | wa-272 comma | ||
| w- | | w-272 | ||
| {{Monzo| -431 272 }} | |||
| {{ | | 131.75 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 219-comma | ||
| wa- | | wa-219 comma | ||
| w- | | w-219 | ||
| {{Monzo| -347 219 }} | |||
| {{ | | 128.145 | ||
| | |||
|- | |- | ||
| | | | ||
| | | 166-comma | ||
| wa- | | wa-166 comma | ||
| w- | | w-166 | ||
| {{Monzo| -263 166}} | |||
| 124.53 | |||
| {{ | |||
| | |||
|- | |- | ||
| | | | ||
| | | 113-comma | ||
| wa- | | wa-113 comma | ||
| w- | | w-113 | ||
| {{Monzo| 179 -113 }} | |||
| {{ | | 120.915 | ||
| | |||
|- | |- | ||
| | | [[2187/2048|Apotome]] | ||
| 7-comma | | 7-comma | ||
| | | lawa unison | ||
| Lw1 | | Lw1 | ||
| {{Monzo| -11 7 }} | |||
| {{ | |||
| 113.685 | | 113.685 | ||
|- | |||
| Pythagorean-septendecimal semitone | |||
| 207-comma | |||
| wa-207 comma | |||
| w-207 | |||
| {{Monzo| -328 207 }} | |||
| 104.685 | |||
|- | |- | ||
| | | | ||
Line 901: | Line 215: | ||
| wa-46 comma | | wa-46 comma | ||
| w-46 | | w-46 | ||
| {{Monzo| 73 -46 }} | |||
| {{ | |||
| 110.07 | | 110.07 | ||
|- | |- | ||
Line 909: | Line 222: | ||
| wa-99 comma | | wa-99 comma | ||
| w-99 | | w-99 | ||
| {{Monzo| 157 -99 }} | |||
| 106.455 | |||
|- | |||
| | | | ||
| {{ | | 152-comma | ||
| | | wa-152 comma | ||
| w-152 | |||
| {{Monzo| 241 -152 }} | |||
| 102.84 | |||
|- | |- | ||
| | | | ||
Line 917: | Line 236: | ||
| wa-101 comma | | wa-101 comma | ||
| w-101 | | w-101 | ||
| {{Monzo| -160 101 }} | |||
| 97.455 | |||
|- | |||
| | | | ||
| {{ | | 258-comma | ||
| | | wa-258 comma | ||
| w-258 | |||
| {{Monzo| 409 -258 }} | |||
| 95.61 | |||
|- | |- | ||
| | | Limma, Pythagorean minor second | ||
| 5-comma | | 5-comma | ||
| | | sawa 2nd | ||
| sw2 | | sw2 | ||
| {{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 933: | Line 299: | ||
| wa-89 comma | | wa-89 comma | ||
| w-89 | | w-89 | ||
| {{Monzo| -141 89 }} | |||
| {{ | |||
| 73.995 | | 73.995 | ||
|- | |- | ||
Line 940: | Line 305: | ||
| [[17-comma]] | | [[17-comma]] | ||
| wa-17 comma | | wa-17 comma | ||
| | | w-17 | ||
| {{Monzo| 27 -17 }} | |||
| {{ | |||
| 66.765 | | 66.765 | ||
|- | |||
| | |||
| 289-comma | |||
| wa-289 comma | |||
| w-289 | |||
| {{Monzo| -458 289 }} | |||
| 64.995 | |||
|- | |- | ||
| | | | ||
Line 949: | Line 320: | ||
| wa-70 comma | | wa-70 comma | ||
| w-70 | | w-70 | ||
| {{Monzo| 111 -70 }} | |||
| 63.150 | |||
|- | |||
| | |||
| 183-comma | |||
| 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 957: | Line 348: | ||
| wa-77 comma | | wa-77 comma | ||
| w-77 | | w-77 | ||
| {{Monzo| -122 77 }} | |||
| 50.535 | |||
|- | |||
| | | | ||
| {{ | | 282-comma | ||
| | | wa-282 comma | ||
| w-282 | |||
| {{Monzo| 447 -282 }} | |||
| 48.69 | |||
|- | |- | ||
| | | | ||
Line 965: | 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 | |||
|- | |||
| | | | ||
| {{ | | 241-comma | ||
| | | wa-241 comma | ||
| w-241 | |||
| {{Monzo| 382 -241 }} | |||
| 28.845 | |||
|- | |- | ||
| Pythagorean septimal comma | | Pythagorean septimal comma | ||
Line 973: | Line 411: | ||
| wa-65 comma | | wa-65 comma | ||
| w-65 | | w-65 | ||
| {{Monzo| -103 65 }} | |||
| {{ | |||
| 27.075 | | 27.075 | ||
|- | |- | ||
| [[Pythagorean comma]] | | [[Pythagorean comma]] | ||
| 12-comma | | 12-comma | ||
| lalawa | | lalawa comma | ||
| LLw-2 | | LLw-2 | ||
| {{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 }} | |||
| {{ | |||
| 16.230 | | 16.230 | ||
|- | |- | ||
Line 1,006: | Line 439: | ||
| wa-147 comma | | wa-147 comma | ||
| w-147 | | w-147 | ||
| {{Monzo| 233 -147 }} | |||
| {{ | |||
| 12.615 | | 12.615 | ||
|- | |- | ||
| Pythagorean integer cent | | Pythagorean integer-cent ET comma | ||
| 200-comma | | 200-comma | ||
| wa-200 comma | | wa-200 comma | ||
| w-200 | | w-200 | ||
| {{Monzo| 317 -200 }} | |||
| 8.9998 | |||
|- | |||
| | | | ||
| {{ | | 253-comma | ||
| | | wa-253 comma | ||
| w-253 | |||
| {{Monzo| 401 -253 }} | |||
| 5.3848 | |||
|- | |- | ||
| [[Mercator's comma]] | | [[Mercator's comma]] | ||
Line 1,022: | Line 460: | ||
| wa-53 comma | | wa-53 comma | ||
| w-53 | | w-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 }} | |||
| {{ | |||
| 1.8453 | | 1.8453 | ||
|- | |- | ||
| [[ | | [[Qian's small comma]] | ||
| 306-comma | | 306-comma | ||
| wa-306 comma | | wa-306 comma | ||
| w-306 | | w-306 | ||
| {{Monzo| 485 -306 }} | |||
| {{ | |||
| 1.7697 | | 1.7697 | ||
|- | |- | ||
Line 1,046: | Line 481: | ||
| wa-665 comma | | wa-665 comma | ||
| w-665 | | w-665 | ||
| {{Monzo| -1054 665 }} | |||
| {{ | |||
| 0.075575 | | 0.075575 | ||
|- | |- | ||
Line 1,054: | Line 488: | ||
| wa-15601 comma | | wa-15601 comma | ||
| w-15601 | | w-15601 | ||
| {{Monzo| 24727 -15601 }} | |||
| {{ | |||
| 0.031499 | | 0.031499 | ||
|- | |- | ||
Line 1,062: | Line 495: | ||
| wa-31867 comma | | wa-31867 comma | ||
| w-31867 | | w-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: | [[Category:Lists of commas]] | ||
{{Todo| unify precision }} |