Large comma: Difference between revisions
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For commas under 100 cents, see [[Medium comma]] for commas in between 30 and 100 cents or [[Small comma]] for commas under 30 cents. For commas under 3.5 cents, see [[Unnoticeable comma]]. | For commas under 100 cents, see [[Medium comma]] for commas in between 30 and 100 cents or [[Small comma]] for commas under 30 cents. For commas under 3.5 cents, see [[Unnoticeable comma]]. | ||
Except for the 3-limit commas, the [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out. | Except for the 3-limit commas, the [[Color notation|color name]] refers to both the comma and the temperament created when it is [[tempered out]]. | ||
The commas might be numerous, but there is no need to memorise all the names. For pretty much all use cases, it is perfectly acceptable – preferred | The commas might be numerous, but there is no need to memorise all the names. For pretty much all use cases, it is perfectly acceptable – preferred, even – to just refer to a comma by the monzo or ratio, whichever is simpler. | ||
== Disputed status == | |||
To varying degrees, the status of each of the commas on this page as "a comma" is disputed. Due to their large size in [[cents]], many of these commas lead to high-[[damage]] temperaments when tempered out. Which calls into question whether they can actually be used as commas. | |||
Those which have a highly complex monzo and ratio tend to distribute their error more thinly across a wide number of [[JI]] intervals, making them more 'comma-like' than the others on this page. Some still dispute this due to their perhaps limited ability to make [[comma pump]]s. However they are more widely accepted than the ones on this page with simpler monzos and ratios. | |||
== List of commas, by prime limit == | == List of commas, by prime limit == | ||
Line 19: | Line 24: | ||
| [[26-comma]] | | [[26-comma]] | ||
| Wa-26 | | Wa-26 | ||
| | | w-26 | ||
| 2541865828329 / 2199023255552 | | 2541865828329 / 2199023255552 | ||
| {{monzo| -41 26 }} | | {{monzo| -41 26 }} | ||
Line 26: | Line 31: | ||
| 27-comma | | 27-comma | ||
| Wa-27 | | Wa-27 | ||
| | | w-27 | ||
| 8796093022208 / 7625597484987 | | 8796093022208 / 7625597484987 | ||
| {{monzo| 43 -27 }} | | {{monzo| 43 -27 }} | ||
Line 40: | Line 45: | ||
| 43-comma | | 43-comma | ||
| Wa-43 | | Wa-43 | ||
| | | w-43 | ||
| | | | ||
| {{monzo| -68 43 }} | | {{monzo| -68 43 }} | ||
Line 47: | Line 52: | ||
| 63-comma | | 63-comma | ||
| Wa-63 | | Wa-63 | ||
| | | w-63 | ||
| | | | ||
| {{monzo| 100 -63 }} | | {{monzo| 100 -63 }} | ||
Line 54: | Line 59: | ||
| [[31st-octave temperaments|31-comma]] | | [[31st-octave temperaments|31-comma]] | ||
| Wa-31 | | Wa-31 | ||
| | | w-31 | ||
| 617673396283947 / <br>562949953421312 | | 617673396283947 / <br>562949953421312 | ||
| {{monzo| -49 31 }} | | {{monzo| -49 31 }} | ||
Line 61: | Line 66: | ||
| 22-comma | | 22-comma | ||
| Wa-22 | | Wa-22 | ||
| | | w-22 | ||
| 34359738368 / <br>31381059609 | | 34359738368 / <br>31381059609 | ||
| {{monzo| 35 -22 }} | | {{monzo| 35 -22 }} | ||
Line 68: | Line 73: | ||
| 19-comma | | 19-comma | ||
| Wa-19 | | Wa-19 | ||
| | | w-19 | ||
| 1162261467 / 1073741824 | | 1162261467 / 1073741824 | ||
| {{monzo| -30 19 }} | | {{monzo| -30 19 }} | ||
Line 82: | Line 87: | ||
| 46-comma | | 46-comma | ||
| Wa-46 | | Wa-46 | ||
| | | w-46 | ||
| | | | ||
| {{monzo| 73 -46 }} | | {{monzo| 73 -46 }} | ||
Line 106: | Line 111: | ||
| Delorean | | Delorean | ||
| Tribigu | | Tribigu | ||
| | | 6g3 | ||
| 17496 / 15625 | | 17496 / 15625 | ||
| {{monzo| 3 7 -6 }} | | {{monzo| 3 7 -6 }} | ||
| 195.803 | | 195.803 | ||
|- | |- | ||
| 31-3/5-comma | | 31-3/5-comma | ||
| Thiwegu | | Thiwegu | ||
| | | 31g7 | ||
| | | | ||
| {{monzo| 23 31 -31 }} | | {{monzo| 23 31 -31 }} | ||
| 184.88 | | 184.88 | ||
Line 134: | Line 132: | ||
| 5-cycle major second, hexadecathird comma | | 5-cycle major second, hexadecathird comma | ||
| Lala-quadquadyo | | Lala-quadquadyo | ||
| | | LL16y-4 | ||
| 152587890625 / <br>137438953472 | | 152587890625 / <br>137438953472 | ||
| {{monzo| -37 0 16 }} | | {{monzo| -37 0 16 }} | ||
Line 141: | Line 139: | ||
| [[Nadir comma]] | | [[Nadir comma]] | ||
| Lalatrigu | | Lalatrigu | ||
| | | LL3g1 | ||
| 1162261467 / 1048576000 | | 1162261467 / 1048576000 | ||
| {{monzo| -23 19 -3 }} | | {{monzo| -23 19 -3 }} | ||
Line 148: | Line 146: | ||
| | | | ||
| Legu | | Legu | ||
| | | 11g4 | ||
| [[53747712 / 48828125]] | | [[53747712 / 48828125]] | ||
| {{monzo| 13 8 -11 }} | | {{monzo| 13 8 -11 }} | ||
Line 155: | Line 153: | ||
| Enipucrop | | Enipucrop | ||
| Latriyobi | | Latriyobi | ||
| | | L3y1 | ||
| 1125 / 1024 | | 1125 / 1024 | ||
| {{monzo| -10 2 3 }} | | {{monzo| -10 2 3 }} | ||
Line 176: | Line 174: | ||
| [[Rarity comma]] | | [[Rarity comma]] | ||
| Quadla-theyo | | Quadla-theyo | ||
| | | 4L13y-5 | ||
| | | | ||
| {{monzo| -57 17 13 }} | | {{monzo| -57 17 13 }} | ||
Line 183: | Line 181: | ||
| Gorgo, laconic | | Gorgo, laconic | ||
| Latrigubi | | Latrigubi | ||
| | | L3g2 | ||
| 2187 / 2000 | | 2187 / 2000 | ||
| {{monzo| -4 7 -3 }} | | {{monzo| -4 7 -3 }} | ||
Line 190: | Line 188: | ||
| [[2048/1875|Smate]], symbolic comma | | [[2048/1875|Smate]], symbolic comma | ||
| Saquadgu | | Saquadgu | ||
| | | s4g3 | ||
| 2048 / 1875 | | 2048 / 1875 | ||
| {{monzo| 11 -1 -4 }} | | {{monzo| 11 -1 -4 }} | ||
Line 197: | Line 195: | ||
| Acute limma | | Acute limma | ||
| Trila-neyobi | | Trila-neyobi | ||
| | | 3L19y-5 | ||
| 19073486328125 / <br>17592186044416 | | 19073486328125 / <br>17592186044416 | ||
| {{monzo| -44 0 19 }} | | {{monzo| -44 0 19 }} | ||
Line 204: | Line 202: | ||
| 31-15-comma | | 31-15-comma | ||
| Tritrila-thiweyo | | Tritrila-thiweyo | ||
| | | 9L31y-11 | ||
| | | | ||
| {{monzo| -121 31 31 }} | | {{monzo| -121 31 31 }} | ||
Line 225: | Line 223: | ||
| 11-3/5-comma | | 11-3/5-comma | ||
| Leyo | | Leyo | ||
| | | 11y-2 | ||
| 48828125 / 45349632 | | 48828125 / 45349632 | ||
| {{monzo| -8 -11 11 }} | | {{monzo| -8 -11 11 }} | ||
Line 232: | Line 230: | ||
| 27-3/5-comma | | 27-3/5-comma | ||
| Tritritrigu | | Tritritrigu | ||
| | | 27g6 | ||
| | | | ||
| {{monzo| 20 27 -27 }} | | {{monzo| 20 27 -27 }} | ||
Line 239: | Line 237: | ||
| Lemba | | Lemba | ||
| Latribiyo | | Latribiyo | ||
| | | L6y-2 | ||
| 140625 / 131072 | | 140625 / 131072 | ||
| {{monzo| -17 2 6 }} | | {{monzo| -17 2 6 }} | ||
Line 253: | Line 251: | ||
| [[3125/2916|Sixix comma]] | | [[3125/2916|Sixix comma]] | ||
| Quinyo | | Quinyo | ||
| | | 5y1 | ||
| 3125 / 2916 | | 3125 / 2916 | ||
| {{monzo| -2 -6 5 }} | | {{monzo| -2 -6 5 }} | ||
Line 260: | Line 258: | ||
| Diesma | | Diesma | ||
| Lathegu | | Lathegu | ||
| | | L13g3 | ||
| 10460353203 / <br>9765625000 | | 10460353203 / <br>9765625000 | ||
| {{monzo| -3 21 -13 }} | | {{monzo| -3 21 -13 }} | ||
Line 267: | Line 265: | ||
| Comic comma | | Comic comma | ||
| Saquadyobi | | Saquadyobi | ||
| | | s4y2 | ||
| 5120000 / 4782969 | | 5120000 / 4782969 | ||
| {{monzo| 13 -14 4 }} | | {{monzo| 13 -14 4 }} | ||
Line 295: | Line 293: | ||
| Wronecki | | Wronecki | ||
| Latribigu | | Latribigu | ||
| | | L6g2 | ||
| 531441 / 500000 | | 531441 / 500000 | ||
| {{monzo| -5 12 -6 }} | | {{monzo| -5 12 -6 }} | ||
Line 302: | Line 300: | ||
| [[Wesley comma]] | | [[Wesley comma]] | ||
| Lasepyobi | | Lasepyobi | ||
| | | L7y-2 | ||
| 78125 / 73728 | | 78125 / 73728 | ||
| {{monzo| -13 -2 7 }} | | {{monzo| -13 -2 7 }} | ||
Line 319: | Line 317: | ||
| [[Antidilemma]] | | [[Antidilemma]] | ||
| Sasa-theruquad | | Sasa-theruquad | ||
| | | ss13r-2 | ||
| 137438953472 / 96889010407 | | 137438953472 / 96889010407 | ||
| {{monzo| 37 0 0 -13 }} | | {{monzo| 37 0 0 -13 }} | ||
Line 326: | Line 324: | ||
| [[Dilemma]] | | [[Dilemma]] | ||
| Lala-thezoquad | | Lala-thezoquad | ||
| | | LL13z9 | ||
| 96889010407 / 68719476736 | | 96889010407 / 68719476736 | ||
| {{monzo| -36 0 0 13 }} | | {{monzo| -36 0 0 13 }} | ||
Line 341: | Line 339: | ||
| Hexatone comma, 6-7-comma | | Hexatone comma, 6-7-comma | ||
| Satribiru | | Satribiru | ||
| | | s6r-2 | ||
| 131072 / 117649 | | 131072 / 117649 | ||
| {{monzo| 17 0 0 -6 }} | | {{monzo| 17 0 0 -6 }} | ||
Line 348: | Line 346: | ||
| 45-7/5-comma | | 45-7/5-comma | ||
| Quintritriruyo | | Quintritriruyo | ||
| | | 45ry-27 | ||
| | | | ||
| {{monzo| 22 0 45 -45 }} | | {{monzo| 22 0 45 -45 }} | ||
Line 355: | Line 353: | ||
| 63-35-comma | | 63-35-comma | ||
| Tritribila-septritrizoyo | | Tritribila-septritrizoyo | ||
| | | 18L63zy8 | ||
| | | | ||
| {{monzo| -323 0 63 63 }} | | {{monzo| -323 0 63 63 }} | ||
Line 362: | Line 360: | ||
| 8-21-comma | | 8-21-comma | ||
| Lala-quadbizo | | Lala-quadbizo | ||
| | | LL8z4 | ||
| 37822859361 / <br>34359738368 | | 37822859361 / <br>34359738368 | ||
| {{monzo| -35 8 0 8 }} | | {{monzo| -35 8 0 8 }} | ||
Line 369: | Line 367: | ||
| 46-7-comma | | 46-7-comma | ||
| Sepla-twethebizobi | | Sepla-twethebizobi | ||
| | | 7L46z18 | ||
| | | | ||
| {{monzo| -129 0 0 46 }} | | {{monzo| -129 0 0 46 }} | ||
Line 376: | Line 374: | ||
| 25-7/5-comma | | 25-7/5-comma | ||
| Quinquinzogu | | Quinquinzogu | ||
| | | 25zg17 | ||
| | | | ||
| {{monzo| -12 0 -25 25 }} | | {{monzo| -12 0 -25 25 }} | ||
Line 383: | Line 381: | ||
| 43-21-comma | | 43-21-comma | ||
| Quadtrisa-fotherubi | | Quadtrisa-fotherubi | ||
| | | 12s43r-11 | ||
| | | | ||
| {{monzo| 189 -43 0 -43 }} | | {{monzo| 189 -43 0 -43 }} | ||
Line 397: | Line 395: | ||
| 43-7/5-comma | | 43-7/5-comma | ||
| Fotheruyo | | Fotheruyo | ||
| | | 43ry-26 | ||
| | | | ||
| {{monzo| 21 0 43 -43 }} | | {{monzo| 21 0 43 -43 }} | ||
Line 418: | Line 416: | ||
| Hendecatone comma, 11-7-comma | | Hendecatone comma, 11-7-comma | ||
| Sasa-leru | | Sasa-leru | ||
| | | ss11r-4 | ||
| 2147483648 / 1977326743 | | 2147483648 / 1977326743 | ||
| {{monzo| 31 0 0 -11 }} | | {{monzo| 31 0 0 -11 }} | ||
Line 432: | Line 430: | ||
| 55-35-comma | | 55-35-comma | ||
| Quadquadla-lequinzoyobi | | Quadquadla-lequinzoyobi | ||
| | | 16L55zy7 | ||
| | | | ||
| {{monzo| -282 0 55 55 }} | | {{monzo| -282 0 55 55 }} | ||
Line 439: | Line 437: | ||
| 27-7/5-comma | | 27-7/5-comma | ||
| Tritritrizogu | | Tritritrizogu | ||
| | | 27zg18 | ||
| | | | ||
| {{monzo| -13 0 -27 27 }} | | {{monzo| -13 0 -27 27 }} | ||
Line 446: | Line 444: | ||
| 41-7-comma | | 41-7-comma | ||
| Tribila-fowezo | | Tribila-fowezo | ||
| | | 6L41z16 | ||
| | | | ||
| {{monzo| -115 0 0 41 }} | | {{monzo| -115 0 0 41 }} | ||
Line 453: | Line 451: | ||
| 13-21-comma | | 13-21-comma | ||
| Quadla-thezobi | | Quadla-thezobi | ||
| | | 4L13z5 | ||
| | | | ||
| {{monzo| -57 13 0 13 }} | | {{monzo| -57 13 0 13 }} | ||
Line 474: | Line 472: | ||
| 41-7/5-comma | | 41-7/5-comma | ||
| Foweruyo | | Foweruyo | ||
| | | 41ry-25 | ||
| | | | ||
| {{monzo| 20 0 41 -41 }} | | {{monzo| 20 0 41 -41 }} | ||
Line 481: | Line 479: | ||
| 7-35-comma | | 7-35-comma | ||
| Sasa-seprugu | | Sasa-seprugu | ||
| | | ss7rg1 | ||
| 68719476736 / <br>64339296875 | | 68719476736 / <br>64339296875 | ||
| {{monzo| 36 0 -7 -7 }} | | {{monzo| 36 0 -7 -7 }} | ||
Line 488: | Line 486: | ||
| 38-21-comma | | 38-21-comma | ||
| Lesa-nebiru | | Lesa-nebiru | ||
| | | 11s38r-10 | ||
| | | | ||
| {{monzo| 167 -38 0 -38 }} | | {{monzo| 167 -38 0 -38 }} | ||
Line 495: | Line 493: | ||
| [[729/686|Triru comma]] | | [[729/686|Triru comma]] | ||
| Triru | | Triru | ||
| | | 3r-2 | ||
| 729 / 686 | | 729 / 686 | ||
| {{monzo| -1 6 0 -3 }} | | {{monzo| -1 6 0 -3 }} | ||
Line 512: | Line 510: | ||
| 11-cycle major second prote, 33-11-comma | | 11-cycle major second prote, 33-11-comma | ||
| Quinla-letrilobi | | Quinla-letrilobi | ||
| | | 5L33(1o)-7 | ||
| | | | ||
| {{monzo| -114 0 0 0 33 }} | | {{monzo| -114 0 0 0 33 }} | ||
Line 526: | Line 524: | ||
| 11-enipucrop, 9-11-comma | | 11-enipucrop, 9-11-comma | ||
| Latritrilo | | Latritrilo | ||
| | | L9(1o)-2 | ||
| 2357947691 / 2147483648 | | 2357947691 / 2147483648 | ||
| {{monzo| -31 0 0 0 9 }} | | {{monzo| -31 0 0 0 9 }} | ||
Line 557: | Line 555: | ||
| 13-cycle neutral second | | 13-cycle neutral second | ||
| Quadbila-fithethobi | | Quadbila-fithethobi | ||
| | | 8L53(3o)7 | ||
| | | | ||
| {{monzo| -196 0 0 0 0 53 }} | | {{monzo| -196 0 0 0 0 53 }} | ||
Line 578: | Line 576: | ||
| Heptasixth comma, 13-cycle secor | | Heptasixth comma, 13-cycle secor | ||
| Sasepthu | | Sasepthu | ||
| | | s7(3u)1 | ||
| 67108864 / 62748517 | | 67108864 / 62748517 | ||
| {{monzo| 26 0 0 0 0 -7 }} | | {{monzo| 26 0 0 0 0 -7 }} | ||
Line 585: | Line 583: | ||
| Heptadecasixth comma, neutral thirteenth comma | | Heptadecasixth comma, neutral thirteenth comma | ||
| Sasa-sethubi | | Sasa-sethubi | ||
| | | ss17(3u)-2 | ||
| | | | ||
| {{monzo| 63 0 0 0 0 -17 }} | | {{monzo| 63 0 0 0 0 -17 }} | ||
Line 626: | Line 624: | ||
| 19-cycle meantone prima | | 19-cycle meantone prima | ||
| Tribila-foweno | | Tribila-foweno | ||
| | | 6L41(19o)13 | ||
| | | | ||
| {{monzo| -174 0 0 0 0 0 0 41 }} | | {{monzo| -174 0 0 0 0 0 0 41 }} | ||
Line 640: | Line 638: | ||
| 19-cycle meantone secunda | | 19-cycle meantone secunda | ||
| Tribila-quintritrino | | Tribila-quintritrino | ||
| | | 6L45(19o)14 | ||
| | | | ||
| {{monzo| -191 0 0 0 0 0 0 45 }} | | {{monzo| -191 0 0 0 0 0 0 45 }} | ||
Line 647: | Line 645: | ||
| 19-cycle minor tone | | 19-cycle minor tone | ||
| Sepla-sepsepno | | Sepla-sepsepno | ||
| | | 7L49(19o)15 | ||
| | | | ||
| {{monzo| -208 0 0 0 0 0 0 49 }} | | {{monzo| -208 0 0 0 0 0 0 49 }} | ||
Line 661: | Line 659: | ||
| 19-cycle submajor second | | 19-cycle submajor second | ||
| Quadbila-fithenobi | | Quadbila-fithenobi | ||
| | | 8L53(19o)16 | ||
| | | | ||
| {{monzo| -225 0 0 0 0 0 0 53 }} | | {{monzo| -225 0 0 0 0 0 0 53 }} | ||
Line 722: | Line 720: | ||
|- | |- | ||
| [[47/44]] | | [[47/44]] | ||
| | | Fosolu | ||
| | | 47o1u2 | ||
| 47 / 44 | | 47 / 44 | ||
| 2.11.47 {{monzo| -2 -1 1 }} | | 2.11.47 {{monzo| -2 -1 1 }} |