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== Definition == | == Definition == | ||
A '''comma''' is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 (0 [[cent]]s) and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is ''[[tempering_out|tempered out]]'', which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between [[10/9]] and [[9/8]], as well as [[81/64]] and [[5/4]], is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s. | A '''comma''' is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 (0 [[cent]]s) and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is ''[[tempering_out|tempered out]]'', which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between [[10/9]] and [[9/8]], as well as [[81/64]] and [[5/4]], is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s. The [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out, except for 3-limit commas, which create edos. | ||
For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]] | For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]] | ||
| Line 90: | Line 90: | ||
! [[Cents]] | ! [[Cents]] | ||
|- | |- | ||
| | | double large yoyo negative 2nd | ||
| lala-yoyo | | lala-yoyo | ||
| LLyy-2 | | LLyy-2 | ||
| Line 287: | Line 287: | ||
|- | |- | ||
| small diesis, [[magic comma]] | | small diesis, [[magic comma]] | ||
| | | laquinyo | ||
| Ly<sup>5</sup>-2 | | Ly<sup>5</sup>-2 | ||
| 3125 / 3072 | | 3125 / 3072 | ||
| Line 406: | Line 406: | ||
|- | |- | ||
| [[Würschmidt comma]] | | [[Würschmidt comma]] | ||
| | | saquadbigu | ||
| sg<sup>8</sup>3 | | sg<sup>8</sup>3 | ||
| 393216 / 390625 | | 393216 / 390625 | ||
| Line 504: | Line 504: | ||
|- | |- | ||
| 21-15-comma | | 21-15-comma | ||
| | |tribila-septriyo | ||
| | |L<sup>6</sup>y<sup>21</sup>-8 | ||
| | | | ||
| {{Monzo| -82 21 21 }} | | {{Monzo| -82 21 21 }} | ||
| Line 539: | Line 539: | ||
|- | |- | ||
| acute thirds comma | | acute thirds comma | ||
| | |quadsa-thirty-wegu | ||
| s<sup>4</sup>g<sup>31</sup>9 | | s<sup>4</sup>g<sup>31</sup>9 | ||
| | | | ||
| Line 546: | Line 546: | ||
|- | |- | ||
| 32-15-comma | | 32-15-comma | ||
| | |tritrila-quadquadbiyo | ||
| | |L<sup>9</sup>y<sup>32</sup>-12 | ||
| | | | ||
| {{Monzo| -125 32 32 }} | | {{Monzo| -125 32 32 }} | ||
| Line 553: | Line 553: | ||
|- | |- | ||
| 34-5-comma | | 34-5-comma | ||
| | |quinsa-sebigu | ||
| s<sup>5</sup>g<sup>34</sup>10 | | s<sup>5</sup>g<sup>34</sup>10 | ||
| | | | ||
| Line 575: | Line 575: | ||
| Schismic thirds chromatic semitone | | Schismic thirds chromatic semitone | ||
| | | | ||
| | | | ||
| | | | ||
| {{Monzo| -123 0 53 }} | | {{Monzo| -123 0 53 }} | ||
| Line 610: | Line 610: | ||
| 59-5-comma | | 59-5-comma | ||
| | | | ||
| | | | ||
| | | | ||
| {{Monzo| 137 0 -59 }} | | {{Monzo| 137 0 -59 }} | ||
| Line 639: | Line 639: | ||
| 84.467 | | 84.467 | ||
|- | |- | ||
| | | laruru negative 2nd | ||
| laruru | | laruru | ||
| Lrr-2 | | Lrr-2 | ||
| Line 745: | Line 745: | ||
|- | |- | ||
| blackjackisma | | blackjackisma | ||
| | | lasepru'aquadbiyo | ||
| Lr<sup>7</sup>y<sup>8</sup>-6 | | Lr<sup>7</sup>y<sup>8</sup>-6 | ||
| 854296875 / 843308032 | | 854296875 / 843308032 | ||
| Line 752: | Line 752: | ||
|- | |- | ||
| squalentine | | squalentine | ||
| | | laquadzo'atrigu | ||
| Lz<sup>4</sup>g<sup>3</sup>3 | | Lz<sup>4</sup>g<sup>3</sup>3 | ||
| 64827 / 64000 | | 64827 / 64000 | ||
| Line 766: | Line 766: | ||
|- | |- | ||
| gariboh | | gariboh | ||
| | | triru'aquinyo | ||
| r<sup>3</sup>y<sup>5</sup>-3 | | r<sup>3</sup>y<sup>5</sup>-3 | ||
| 3125 / 3087 | | 3125 / 3087 | ||
| Line 773: | Line 773: | ||
|- | |- | ||
| nuwell | | nuwell | ||
| | | quadru'ayo | ||
| r<sup>4</sup>y-3 | | r<sup>4</sup>y-3 | ||
| 2430 / 2401 | | 2430 / 2401 | ||
| Line 829: | Line 829: | ||
|- | |- | ||
| quince | | quince | ||
| | | lasepzo'agugu | ||
| Lz<sup>7</sup>gg4 | | Lz<sup>7</sup>gg4 | ||
| 823543 / 819200 | | 823543 / 819200 | ||
| Line 871: | Line 871: | ||
|- | |- | ||
| mirkwai | | mirkwai | ||
| | | quinru'aquadyo | ||
| r<sup>5</sup>y<sup>4</sup>-4 | | r<sup>5</sup>y<sup>4</sup>-4 | ||
| 16875 / 16807 | | 16875 / 16807 | ||
| Line 885: | Line 885: | ||
|- | |- | ||
| hemimage | | hemimage | ||
| | | satrizo'agu | ||
| sz<sup>3</sup>g3 | | sz<sup>3</sup>g3 | ||
| 10976 / 10935 | | 10976 / 10935 | ||
| Line 948: | Line 948: | ||
|- | |- | ||
| 8-35-comma | | 8-35-comma | ||
| lala- | | lala-quadbizoyo | ||
| LLz<sup>8</sup>y<sup>8</sup>2 | | LLz<sup>8</sup>y<sup>8</sup>2 | ||
| 2251875390625 / 2199023255552 | | 2251875390625 / 2199023255552 | ||
| Line 962: | Line 962: | ||
|- | |- | ||
| hexadecatone comma, 16-7-comma | | hexadecatone comma, 16-7-comma | ||
| sasa- | | sasa-quadquadru | ||
| ssr<sup>16</sup>-6 | | ssr<sup>16</sup>-6 | ||
| 35184372088832 / 33232930569601 | | 35184372088832 / 33232930569601 | ||
| Line 997: | Line 997: | ||
|- | |- | ||
| quarter tone comma | | quarter tone comma | ||
| | | | ||
| | | | ||
| | | | ||
| Line 1,153: | Line 1,153: | ||
| 80.537 | | 80.537 | ||
|- | |- | ||
| | | lalu unison | ||
| lalu | | lalu | ||
| L1u1 | | L1u1 | ||
| Line 1,203: | Line 1,203: | ||
|- | |- | ||
| thuja comma | | thuja comma | ||
| | | saquinlu'ayo | ||
| s1u<sup>5</sup>y2 | | s1u<sup>5</sup>y2 | ||
| 163840 / 161051 | | 163840 / 161051 | ||
| Line 1,280: | Line 1,280: | ||
|- | |- | ||
| orgonisma | | orgonisma | ||
| | | satrilu'aruru | ||
| s1u<sup>3</sup>rr1 | | s1u<sup>3</sup>rr1 | ||
| 65536 / 65219 | | 65536 / 65219 | ||
| Line 1,572: | Line 1,572: | ||
| 50.184 | | 50.184 | ||
|- | |- | ||
| | |solu 2nd | ||
| solu | | solu | ||
| 17o1u2 | | 17o1u2 | ||
| Line 1,586: | Line 1,586: | ||
| 34.283 | | 34.283 | ||
|- | |- | ||
| | |sutho unison | ||
| sutho | | sutho | ||
| 17u3o1 | | 17u3o1 | ||
| Line 1,593: | Line 1,593: | ||
| 33.617 | | 33.617 | ||
|- | |- | ||
| | |soruyo unison | ||
| soruyo | | soruyo | ||
| 17ory1 | | 17ory1 | ||
| Line 1,607: | Line 1,607: | ||
| 14.730 | | 14.730 | ||
|- | |- | ||
| | |suruyo comma | ||
| suruyo | | suruyo | ||
| 17ury-2 | | 17ury-2 | ||
| Line 1,701: | Line 1,701: | ||
| 88.801 | | 88.801 | ||
|- | |- | ||
| | |nutho unison | ||
| nutho | | nutho | ||
| 19u3o1 | | 19u3o1 | ||
| Line 1,708: | Line 1,708: | ||
| 44.970 | | 44.970 | ||
|- | |- | ||
| | |noru unison | ||
| noru | | noru | ||
| 19or1 | | 19or1 | ||
| Line 1,715: | Line 1,715: | ||
| 30.642 | | 30.642 | ||
|- | |- | ||
| | |nuruyo comma | ||
| nuruyo | | nuruyo | ||
| 19ury-2 | | 19ury-2 | ||
| Line 1,722: | Line 1,722: | ||
| 25.840 | | 25.840 | ||
|- | |- | ||
| | |nogugu 2nd | ||
| nogugu | | nogugu | ||
| 19ogg2 | | 19ogg2 | ||
| Line 1,743: | Line 1,743: | ||
| 18.128 | | 18.128 | ||
|- | |- | ||
| | |noluzo 2nd | ||
| noluzo | | noluzo | ||
| 19o1uz2 | | 19o1uz2 | ||
| Line 1,757: | Line 1,757: | ||
| 11.352 | | 11.352 | ||
|- | |- | ||
| | |nosugu unison | ||
| nosugu | | nosugu | ||
| 19o17ug1 | | 19o17ug1 | ||
| Line 1,778: | Line 1,778: | ||
| 8.2637 | | 8.2637 | ||
|- | |- | ||
| | |nusu comma | ||
| nusu | | nusu | ||
| 19u17u-2 | | 19u17u-2 | ||
Revision as of 01:04, 15 January 2019
Definition
A comma is a small interval that occurs in just intonation, between two intervals which are close in pitch. Commas are always greater than 1 (0 cents) and not a power such as a square or cube of any other interval, and generally in a low prime limit. The word is often used in reference to regular tempering when the comma is tempered out, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by meantone temperament. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in cents. The color name refers to both the comma and the temperament created when it is tempered out, except for 3-limit commas, which create edos.
For commas over 100 cents in size, see Large commas; and for commas under 3.5 cents in size, see Unnoticeable commas
Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the convention elsewhere on the wiki.
List of commas, by prime limit
3-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| limma, Pythagorean minor second | small wa 2nd | sw2 | 256 / 243 | [8 -5⟩ | 90.225 |
| Pythagorean comma | wa comma | LLw-2 | 531441 / 524288 | [-19 12⟩ | 23.460 |
| 17-comma | wa-17 comma | ssw3 | 134217728 / 129140163 | [27 -17⟩ | 66.765 |
| 29-comma | wa-29 comma | s4w4 | 70368744177664 / 68630377364883 | [46 -29⟩ | 43.305 |
| 41-comma | wa-41 comma | s6w5 | 36893488147419103232 / 36472996377170786403 |
[65 -41⟩ | 19.845 |
| Mercator's comma, 53-comma | wa-53 comma | L8w-6 | 19383245667680019896796723 / 19342813113834066795298816 |
[-84 53⟩ | 3.6150 |
| 70-comma | wa-70 comma | s10w8 | [111 -70⟩ | 63.150 | |
| 77-comma | wa-77 comma | L11w-8 | [-122 77⟩ | 50.535 | |
| 200-comma, Pythagorean integer cents comma | wa-200 comma | w-200 | [317 -200⟩ | 8.9998 | |
5-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| double large yoyo negative 2nd | lala-yoyo | LLyy-2 | 4428675 / 4194304 | [-22 11 2⟩ | 94.132 |
| major chroma, major limma, pelogic comma | layo-unison | Ly1 | 135 / 128 | [-7 3 1⟩ | 92.179 |
| double small gu 3rd | sasagu | ssg3 | 8388608 / 7971615 | [23 -13 -1⟩ | 88.271 |
| ripple | quingu | g52 | 6561 / 6250 | [-1 8 -5⟩ | 84.071 |
| doublewide | quadbiyo | y8-2 | 390625 / 373248 | [-9 -6 8⟩ | 78.780 |
| sevond | sasepyo | sy71 | 5000000 / 4782969 | [6 -14 7⟩ | 76.826 |
| nusecond | legu | g113 | 51018336 / 48828125 | [5 13 -11⟩ | 75.964 |
| sentinel | trila-quadyo | L3y4-3 | 8968066875 / 8589934592 | [-33 15 4⟩ | 74.580 |
| large triyo negative 2nd | latriyo | Ly3-2 | 273375 / 262144 | [-18 7 3⟩ | 72.626 |
| chromatic semitone | yoyo | yy1 | 25 / 24 | [-3 -1 2⟩ | 70.672 |
| superpyth, grave minor second | sayo | sy2 | 20480 / 19683 | [12 -9 1⟩ | 68.719 |
| major diesis, diminished comma | quadgu | g42 | 648 / 625 | [3 4 -4⟩ | 62.565 |
| passion | saquingu | sg53 | 262144 / 253125 | [18 -4 -5⟩ | 60.611 |
| shibboleth | tritriyo | y9-2 | 1953125 / 1889568 | [-5 -10 9⟩ | 57.273 |
| mynic | quinbigu | g103 | 10077696 / 9765625 | [9 9 -10⟩ | 54.458 |
| tritonic | lalaquinyo | LLy5-3 | 553584375 / 536870912 | [-29 11 5⟩ | 53.074 |
| negri comma, double augmentation diesis | laquadyo | Ly4-2 | 16875 / 16384 | [-14 3 4⟩ | 51.120 |
| maximal diesis, porcupine | triyo | y31 | 250 / 243 | [1 -5 3⟩ | 49.166 |
| immunity | sasayoyo | ssyy2 | 1638400 / 1594323 | [16 -13 2⟩ | 47.212 |
| double large green comma | lalagu | LLg-2 | 43046721 / 41943040 | [-23 16 -1⟩ | 44.966 |
| diesis, augmented comma | trigu | g32 | 128 / 125 | [7 0 -3⟩ | 41.059 |
| wizard | lala-quadtriyo | LLy12-4 | 2197265625 / 2147483648 | [-31 2 12⟩ | 39.675 |
| sycamore | laleyo | Ly11-3 | 48828125 / 47775744 | [-16 -6 11⟩ | 37.721 |
| fifive | saquinbiyo | sy10-2 | 9765625 / 9565938 | [-1 -14 10⟩ | 35.767 |
| unicorn | laquadbigu | Lg82 | 1594323 / 1562500 | [-2 13 -8⟩ | 34.905 |
| valentine comma | satritrigu | sg93 | 1990656 / 1953125 | [13 5 -9⟩ | 32.952 |
| ampersand, Ampersand's comma | lala-tribiyo | LLy6-3 | 34171875 / 33554432 | [-25 7 6⟩ | 31.567 |
| mabila comma | sasa-quinbigu | ssg104 | 268435456 / 263671875 | [28 -3 -10⟩ | 30.998 |
| small diesis, magic comma | laquinyo | Ly5-2 | 3125 / 3072 | [-10 -1 5⟩ | 29.614 |
| minimal diesis, tetracot comma | saquadyo | sy41 | 20000 / 19683 | [5 -9 4⟩ | 27.660 |
| quanic comma | sepsa-quinyo | s7y55 | [74 -54 5⟩ | 25.999 | |
| roda | sasa-triyo | ssy32 | 131072000 / 129140163 | [20 -17 3⟩ | 25.706 |
| trisedodge comma | saquintrigu | sg154 | 30958682112 / 30517578125 | [19 10 -15⟩ | 24.844 |
| maja | saseyo | sy17-3 | 762939453125 / 753145430616 | [-3 -23 17⟩ | 22.368 |
| syntonic / Didymos / meantone comma | gu | g1 | 81 / 80 | [-4 4 -1⟩ | 21.506 |
| maquila comma | trisa-segu | s3g176 | 562949953421312 / 556182861328125 | [49 -6 -17⟩ | 20.937 |
| diaschisma | sagugu | sgg2 | 2048 / 2025 | [11 -4 -2⟩ | 19.553 |
| ditonma | lala-theyo | LLy13-4 | 1220703125 / 1207959552 | [-27 -2 13⟩ | 18.168 |
| misty comma | sasa-trigu | ssg33 | 67108864 / 66430125 | [26 -12 -3⟩ | 17.599 |
| pental comma | trila-quingu | L3g5-2 | 847288609443 / 838860800000 | [-28 25 -5⟩ | 17.306 |
| undim comma | trisa-quadgu | s3g44 | 2199023255552 / 2179240250625 | [41 -20 -4⟩ | 15.645 |
| graviton, gravity comma | lala-tribigu | LLg61 | 129140163 / 128000000 | [-13 17 -6⟩ | 15.353 |
| majvam | sasa-lebigu | ssg226 | [40 7 -22⟩ | 14.783 | |
| quartonic | saleyo | sy11-2 | 390625000 / 387420489 | [3 -18 11⟩ | 14.261 |
| medium semicomma, sensipent comma | sepgu | g72 | 78732 / 78125 | [2 9 -7⟩ | 13.399 |
| Würschmidt comma | saquadbigu | sg83 | 393216 / 390625 | [17 1 -8⟩ | 11.445 |
| semicomma, Fokker comma | lasepyo | Ly7-3 | 2109375 / 2097152 | [-21 3 7⟩ | 10.061 |
| escapade comma | sasa-tritrigu | ssg94 | 4294967296 / 4271484375 | [32 -7 -9⟩ | 9.4916 |
| kleisma, semicomma majeur | tribiyo | y6-2 | 15625 / 15552 | [-6 -5 6⟩ | 8.1073 |
| qintosec comma | quadsa-quinbigu | s4g105 | 140737488355328 / 140126044921875 | [47 -15 -10⟩ | 7.5378 |
| unidecma | laquadtrigu | Lg122 | 31381059609 / 31250000000 | [-7 22 -12⟩ | 7.2455 |
| mutt comma | trila-septriyo | L3y21-6 | 476837158203125 / 474989023199232 | [-44 -3 21⟩ | 6.7230 |
| amity comma | saquinyo | sy51 | 1600000 / 1594323 | [9 -13 5⟩ | 6.1536 |
| parakleisma | thegu | g133 | 1224440064 / 1220703125 | [8 14 -13⟩ | 5.2917 |
| gammic comma | laquinquadyo | Ly20-5 | 95367431640625 / 95105071448064 | [-29 -11 20⟩ | 4.7693 |
| vulture comma | sasa-quadyo | ssy42 | 10485760000 / 10460353203 | [24 -21 4⟩ | 4.1998 |
| lafa comma | tribisa-quatrigu | s6g127 | [77 -31 -12⟩ | 3.6304 | |
| 10-15-comma | trila-quinbiyo | L3y10-4 | 576650390625 / 549755813888 | [-39 10 10⟩ | 82.687 |
| 11-15-comma | trisa-legu | s3g115 | 8796093022208 / 8649755859375 | [43 -11 -11⟩ | 29.044 |
| 21-15-comma | tribila-septriyo | L6y21-8 | [-82 21 21⟩ | 53.643 | |
| Twenty-two thirds limma | trila-lebiyo | L3y22-6 | 2384185791015625 / 2251799813685248 | [-51 0 22⟩ | 98.902 |
| 23-3/5-comma | twenty-thegu | g235 | 12339534735212544 / 11920928955078125 | [17 23 -23⟩ | 59.750 |
| sibbolet | quadla-quinquinyo | L4y25-7 | 298023223876953125 / 288230376151711744 | [-58 0 25⟩ | 57.843 |
| Hunt 5-cycle comma | quadla-sepquadyo | L4y28-8 | 37252902984619140625 / 36893488147419103232 | [-65 0 28⟩ | 16.784 |
| acute thirds comma | quadsa-thirty-wegu | s4g319 | [72 0 -31⟩ | 24.275 | |
| 32-15-comma | tritrila-quadquadbiyo | L9y32-12 | [-125 32 32⟩ | 24.599 | |
| 34-5-comma | quinsa-sebigu | s5g3410 | [79 0 -34⟩ | 65.334 | |
| 34-3/5-comma | sebiyo | y343 | [-25 -34 34⟩ | 68.196 | |
| Huntian 15-cycle comma | [168 -43 -43⟩ | 4.4453 | |||
| Schismic thirds chromatic semitone | [-123 0 53⟩ | 74.627 | |||
| 53-15-comma | [-207 53 53⟩ | 78.242 | |||
| 53-3/5-comma | fifty-theyo | y537 | [-39 -53 53⟩ | 71.012 | |
| 54-15-comma | [211 -54 -54⟩ | 33.489 | |||
| 56-syntonic comma | [-225 224 -56⟩ | 4.3522 | |||
| 59-5-comma | [137 0 -59⟩ | 7.4909 | |||
| 76-15-comma | [297 -76 -76⟩ | 91.578 | |||
7-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| minor semitone | zogu | zg2 | 21 / 20 | [-2 1 -1 1⟩ | 84.467 |
| laruru negative 2nd | laruru | Lrr-2 | 6561 / 6272 | [-7 8 0 -2⟩ | 77.988 |
| bapbo | rurugu | rrg1 | 256 / 245 | [8 0 -1 -2⟩ | 76.034 |
| Archytas' 1/3-tone | zo | z2 | 28 / 27 | [2 -3 0 1⟩ | 62.961 |
| greenwoodma | ruruyo | rry-2 | 405 / 392 | [-3 4 1 -2⟩ | 56.482 |
| Harrison's comma | laru | Lr-2 | 59049 / 57344 | [-13 10 0 -1⟩ | 50.724 |
| keega | trizogu | z3g33 | 1029 / 1000 | [-3 1 -3 3⟩ | 49.492 |
| septimal quarter tone | rugu | rg1 | 36 / 35 | [2 2 -1 -1⟩ | 48.770 |
| 5-21-comma | saquinru | sr5-2 | 4194304 / 4084101 | [22 -5 0 -5⟩ | 46.095 |
| cloudy | laquinzo | Lz53 | 16807 / 16384 | [-14 0 0 5⟩ | 44.130 |
| Avicenna, Avicenna's enharmonic diesis | lazoyoyo | Lzyy1 | 525 / 512 | [-9 1 2 1⟩ | 43.408 |
| slendro diesis | zozo | zz2 | 49 / 48 | [-4 -1 0 2⟩ | 35.697 |
| tritonic diesis, jubilisma | biruyo | rryy-2 | 50 / 49 | [1 0 2 -2⟩ | 34.976 |
| eric | sepru | r7-4 | 839808 / 823543 | [7 8 0 -7⟩ | 33.859 |
| senga | trizoagugu | z3gg3 | 686 / 675 | [1 -3 -2 3⟩ | 27.985 |
| septimal / Archytas' comma, Leipziger Komma | ru | r1 | 64 / 63 | [6 -2 0 -1⟩ | 27.264 |
| blackjackisma | lasepru'aquadbiyo | Lr7y8-6 | 854296875 / 843308032 | [-10 7 8 -7⟩ | 22.413 |
| squalentine | laquadzo'atrigu | Lz4g33 | 64827 / 64000 | [-9 3 -3 4⟩ | 22.227 |
| keema | zotriyo | zy31 | 875 / 864 | [-5 -3 3 1⟩ | 21.902 |
| gariboh | triru'aquinyo | r3y5-3 | 3125 / 3087 | [0 -2 5 -3⟩ | 21.181 |
| nuwell | quadru'ayo | r4y-3 | 2430 / 2401 | [1 5 1 -4⟩ | 20.785 |
| tolerma | sazoyoyo | szyy2 | 179200 / 177147 | [10 -11 2 1⟩ | 19.948 |
| mirwomo | labizoyo | Lzzyy1 | 33075 / 32768 | [-15 3 2 2⟩ | 16.144 |
| trimyna | quinzogu | z5g54 | 50421 / 50000 | [-4 1 -5 5⟩ | 14.516 |
| sensamagic | zozoyo | zzy2 | 245 / 243 | [0 -5 1 2⟩ | 14.191 |
| septimal semicomma, starling comma | zotrigu | zg32 | 126 / 125 | [1 2 -3 1⟩ | 13.795 |
| octagar | rurutriyo | rry3-2 | 4000 / 3969 | [5 -4 3 -2⟩ | 13.469 |
| orwellisma, orwell comma | triruagu | r3g-2 | 1728 / 1715 | [6 3 -1 -3⟩ | 13.074 |
| quince | lasepzo'agugu | Lz7gg4 | 823543 / 819200 | [-15 0 -2 7⟩ | 9.1539 |
| gamelisma | latrizo | Lz32 | 1029 / 1024 | [-10 1 0 3⟩ | 8.4327 |
| varunisma | labizogugu | Lzzg42 | 321489 / 320000 | [-9 8 -4 2⟩ | 8.0370 |
| septimal kleisma, marvel comma | ruyoyo | ryy-2 | 225 / 224 | [-5 2 2 -1⟩ | 7.7115 |
| dimcomp | quadruyoyo | r4y8-4 | 390625 / 388962 | [-1 -4 8 -4⟩ | 7.3861 |
| cataharry | labirugu | Lrrgg-2 | 19683 / 19600 | [-4 9 -2 -2⟩ | 7.3158 |
| mirkwai | quinru'aquadyo | r5y4-4 | 16875 / 16807 | [0 3 4 -5⟩ | 6.9903 |
| stearnsma | latribiru | Lr6-4 | 118098 / 117649 | [1 10 0 -6⟩ | 6.5946 |
| hemimage | satrizo'agu | sz3g3 | 10976 / 10935 | [5 -7 -1 3⟩ | 6.4790 |
| hemimean | zozoquingu | zzg53 | 3136 / 3125 | [6 0 -5 2⟩ | 6.0832 |
| hemifamity | saruyo | sry1 | 5120 / 5103 | [10 -6 1 -1⟩ | 5.7578 |
| linus | saquinbizogu | sz10g108 | 578509309952 / 576650390625 | [11 -10 -10 10⟩ | 5.5719 |
| porwell | sarurutrigu | srrg31 | 6144 / 6125 | [11 1 -3 -2⟩ | 5.3620 |
| garischisma | sasaru | ssr2 | 33554432 / 33480783 | [25 -14 0 -1⟩ | 3.8041 |
| wadisma | latritrizoayo | Lz9y4 | 201768035 / 201326592 | [-26 -1 1 9⟩ | 3.7919 |
| quasiorwellisma | sazoquinbigu | szg104 | 29360128 / 29296875 | [22 -1 -10 1⟩ | 3.7338 |
| 218edo (stacked 7/4 and 10/9) comma | trisa-triru-quadquadyo | s3r3y16-3 | 640000000000000000 / 635585924776181463 | [22 -32 16 -3⟩ | 11.982 |
| 8-35-comma | lala-quadbizoyo | LLz8y82 | 2251875390625 / 2199023255552 | [-41 0 8 8⟩ | 41.117 |
| 15-35-comma | [77 0 -15 -15⟩ | 72.906 | |||
| hexadecatone comma, 16-7-comma | sasa-quadquadru | ssr16-6 | 35184372088832 / 33232930569601 | [45 0 0 -16⟩ | 98.785 |
| 18-21-comma | [-79 18 0 18⟩ | 74.056 | |||
| 21-7-comma | 576460752303423488 / 558545864083284007 | [59 0 0 -21⟩ | 54.656 | ||
| 23-21-comma | [-101 23 0 23⟩ | 27.961 | |||
| 23-35-comma | [118 0 -23 -23⟩ | 31.789 | |||
| quarter tone comma | [49 50 -25 -25⟩ | 19.260 | |||
| Hunt 7-cycle comma | [73 0 0 -26⟩ | 10.526 | |||
| Huntian 21-cycle comma | [123 -28 0 -28⟩ | 18.135 | |||
| 29-7/5-comma | [-14 0 -29 29⟩ | 92.854 | |||
| German sixth comma | [-87 0 0 31⟩ | 33.603 | |||
| 31-7/5-comma | [-15 0 -31 31⟩ | 57.878 | |||
| 31-35-comma | [-159 0 31 31⟩ | 9.3282 | |||
| 33-7/5-comma | [-16 0 -33 33⟩ | 22.902 | |||
| 33-21-comma | [145 -33 0 -33⟩ | 64.230 | |||
| 35-7/5-comma | [17 0 35 -35⟩ | 12.073 | |||
| 36-7-comma | [-101 0 0 36⟩ | 77.733 | |||
| 37-7/5-comma | [18 0 37 -37⟩ | 47.049 | |||
| 39-7/5-comma | [19 0 39 -39⟩ | 82.024 | |||
| 39-35-comma | [-200 0 39 39⟩ | 50.445 | |||
| 47-7-comma | [132 0 0 -47⟩ | 65.182 | |||
| 47-35-comma | [-241 0 47 47⟩ | 91.562 | |||
| Huntian 35-cycle comma | [277 0 -54 -54⟩ | 22.461 | |||
| slendro 34-comma | [-137 -34 0 68⟩ | 13.692 | |||
| 34-jubilismic comma | [-33 0 -68 68⟩ | 10.829 | |||
| [1123 0 0 -400⟩ | 69.637 | ||||
11-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| undecimal minor semitone | loru | 1or1 | 22 / 21 | [1 -1 0 -1 1⟩ | 80.537 |
| lalu unison | lalu | L1u1 | 729 / 704 | [-6 6 0 0 -1⟩ | 60.412 |
| undecimal comma, al-Farabi's 1/4-tone | ilo | 1o1 | 33 / 32 | [-5 1 0 0 1⟩ | 53.273 |
| Hunt flat 5 comma | salu | s1u2 | 8192 / 8019 | [13 -6 0 0 -1⟩ | 36.952 |
| sterno | lotriru | 1or3-2 | 352 / 343 | [5 0 0 -3 1⟩ | 44.840 |
| 1/5-tone | luyo | 1uy1 | 45 / 44 | [-2 2 1 0 -1⟩ | 38.906 |
| undecimal diesis | luzogu | 1uzg2 | 56 / 55 | [3 0 -1 1 -1⟩ | 31.194 |
| telepathma | loyo | 1oy1 | 55 / 54 | [-1 -3 1 0 1⟩ | 31.767 |
| thuja comma | saquinlu'ayo | s1u5y2 | 163840 / 161051 | [15 0 1 0 -5⟩ | 29.724 |
| sensmus | salozogu | s1ozg2 | 1232 / 1215 | [4 -5 -1 1 1⟩ | 24.055 |
| sevnothrush | loquingu | 1og52 | 3168 / 3125 | [5 2 -5 0 1⟩ | 23.659 |
| cassacot | biluzoayo | 1uuzzy2 | 245 / 242 | [-1 0 1 2 -2⟩ | 21.330 |
| mothwellsma | loruru | 1orr-2 | 99 / 98 | [-1 2 0 -2 1⟩ | 17.576 |
| ptolemisma | luyoyo | 1uyy1 | 100 / 99 | [2 -2 2 0 -1⟩ | 17.399 |
| hemimin | triluazo | 1u3z2 | 1344 / 1331 | [6 1 0 1 -3⟩ | 16.827 |
| biyatisma | lologu | 1oog1 | 121 / 120 | [-3 -1 -1 0 2⟩ | 14.367 |
| aphrowe | triloaruru | 1o3rr-2 | 1331 / 1323 | [0 -3 0 -2 3⟩ | 10.437 |
| valinorsma | lorugugu | 1orgg1 | 176 / 175 | [4 0 -2 -1 1⟩ | 9.8646 |
| pentacircle | saluzo | s1uz2 | 896 / 891 | [7 -4 0 1 -1⟩ | 9.6880 |
| orgonisma | satrilu'aruru | s1u3rr1 | 65536 / 65219 | [16 0 0 -2 -3⟩ | 8.3944 |
| rastma | lulu | 1uu1 | 243 / 242 | [-1 5 0 0 -2⟩ | 7.1391 |
| myhemiwell | lolozotrigu | 1oozg32 | 3388 / 3375 | [2 -3 -3 1 2⟩ | 6.6556 |
| keenanisma | lozoyo | 1ozy1 | 385 / 384 | [-7 -1 1 1 1⟩ | 4.5026 |
| werckisma | luzozogu | 1uzzg2 | 441 / 440 | [-3 2 -1 2 -1⟩ | 3.9302 |
| moctdel | lotriruyo | 1or3y3-3 | 1375 / 1372 | [-2 0 3 -3 1⟩ | 3.7814 |
| 11-cycle chroma, 11-11-comma | lalalelo | LL1o11-3 | 285311670611 / 274877906944 | [-38 0 0 0 11⟩ | 64.497 |
| the Igs boson, 13-11-comma | sasathelu | ss1u134 | 35184372088832 / 34522712143931 | [45 0 0 0 -13⟩ | 32.867 |
| Hunt 11-cycle comma | [-83 0 0 0 24⟩ | 31.631 | |||
| 11-cycle major seventh prote, 35-11-comma | [-121 0 0 0 35⟩ | 96.128 | |||
13-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| tridecimal comma | thu | 3u1 | 27 / 26 | [-1 3 0 0 0 -1⟩ | 65.337 |
| tridecimal 1/3-tone | thogu | 3og2 | 26 / 25 | [1 0 -2 0 0 1⟩ | 67.900 |
| Hunt minor submediant comma | latho | L3o1 | 1053 / 1024 | [-10 4 0 0 0 1⟩ | 48.348 |
| tridecimal minor diesis | thuyo | 3uy1 | 40 / 39 | [3 -1 1 0 0 -1⟩ | 43.831 |
| astburyp | latribitho | L3o62 | 4826809 / 4718592 | [-19 -2 0 0 0 6⟩ | 39.256 |
| wilsorma | thoyo | 3oy1 | 65 / 64 | [-6 0 1 0 0 1⟩ | 26.841 |
| winmeanma | thulogu | 3u1og1 | 66 / 65 | [1 1 -1 0 1 -1⟩ | 26.432 |
| negustma | tholuru | 3o1ur1 | 78 / 77 | [1 1 0 -1 -1 1⟩ | 22.339 |
| superleap | thozogu | 3ozg2 | 91 / 90 | [-1 -2 -1 1 0 1⟩ | 19.130 |
| animist | thuzoyo | 3uzy1 | 105 / 104 | [-3 1 1 1 0 -1⟩ | 16.567 |
| secorian | sathuzo | s3uz2 | 28672 / 28431 | [12 -7 0 1 0 -1⟩ | 14.613 |
| mosaic | lathoruru | L3orr-2 | 3159 / 3136 | [-6 5 0 -2 0 1⟩ | 12.651 |
| gassorma | thuloruyoyo | 3u1oryy-2 | 275 / 273 | [0 -1 2 -1 1 -1⟩ | 12.637 |
| grossma | thulu | 3u1u1 | 144 / 143 | [4 2 0 0 -1 -1⟩ | 12.064 |
| buzurgisma, dhanvantarisma | thothoru | 3oor1 | 169 / 168 | [-3 -1 0 -1 0 2⟩ | 10.274 |
| catadictma | thologu | 3o1og1 | 1287 / 1280 | [-8 2 -1 0 1 1⟩ | 9.4419 |
| mynucuma | thuzozogu | 3uzzg2 | 196 / 195 | [2 -1 -1 2 0 -1⟩ | 8.8554 |
| huntma, nelindic comma | thururuyo | 3urry-2 | 640 / 637 | [7 0 1 -2 0 -1⟩ | 8.1342 |
| threedie | satritho | s3o32 | 2197 / 2187 | [0 -7 0 0 0 3⟩ | 7.8980 |
| kestrel comma | thuthuloru | 3uu1or-2 | 1188 / 1183 | [2 3 0 -1 1 -2⟩ | 7.3017 |
| marveltwin | thoyoyo | 3oyy1 | 325 / 324 | [-2 -4 2 0 0 1⟩ | 5.3351 |
| ratwolfsma | thorugugu | 3orgg1 | 351 / 350 | [-1 3 -2 -1 0 1⟩ | 4.9393 |
| minthma | thulo | 3u1o1 | 352 / 351 | [5 -3 0 0 1 -1⟩ | 4.9253 |
| gentle comma | tholuluzo | 3o1uuz2 | 364 / 363 | [2 -1 0 1 -2 1⟩ | 4.7627 |
| cuthbert | bithuloazogu | 3uu1oozg1 | 847 / 845 | [0 0 -1 1 2 -2⟩ | 4.0928 |
| Hunt 13-cycle comma | laquinbitho | L3o102 | 137858491849 / 137438953472 | [-37 0 0 0 0 10⟩ | 5.2766 |
| [-8881 0 0 0 0 2400⟩ | 66.388 | ||||
17-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| Arabic lute index finger | su | 17u1 | 18 / 17 | [1 2 0 0 0 0 -1⟩ | 98.955 |
| septendecimal 1/4-tone | suzoyo | 17uzy1 | 35 / 34 | [-1 0 1 1 0 0 -1⟩ | 50.184 |
| solu 2nd | solu | 17o1u2 | 34 / 33 | [1 -1 0 0 -1 0 1⟩ | 51.682 |
| 17th-partial chroma | sogugu | 17ogg2 | 51 / 50 | [-1 1 -2 0 0 0 1⟩ | 34.283 |
| sutho unison | sutho | 17u3o1 | 52 / 51 | [2 -1 0 0 0 1 -1⟩ | 33.617 |
| soruyo unison | soruyo | 17ory1 | 85 / 84 | [-2 -1 1 -1 0 0 1⟩ | 20.488 |
| Hunt flat 2 comma | laso | L17o1 | 4131 / 4096 | [-12 5 0 0 0 0 1⟩ | 14.730 |
| suruyo comma | suruyo | 17ury-2 | 120 / 119 | [3 1 1 -1 0 0 -1⟩ | 14.487 |
| Blume comma | sololo | 17o1oo1 | 2057 / 2048 | [-11 0 0 0 2 0 1⟩ | 7.5913 |
| septendecimal kleisma | sugu | 17ug1 | 256 / 255 | [8 -1 -1 0 0 0 -1⟩ | 6.7759 |
| tannisma | suthozo | 17u3oz1 | 273 / 272 | [-4 1 0 1 0 1 -1⟩ | 6.3532 |
| septendecimal integer cents comma | soso | 17oo2 | 289 / 288 | [-5 -2 0 0 0 0 2⟩ | 6.0008 |
| 11 semitone comma | 35184372088832 / 34271896307633 | [45 0 0 0 0 0 -11⟩ | 45.490 | ||
| 12 semitone comma | 582622237229761 / 562949953421312 | [-49 0 0 0 0 0 12⟩ | 59.465 | ||
| 23 semitone comma | [-94 0 0 0 0 0 23⟩ | 13.974 | |||
| Hunt 17-cycle comma | [139 0 0 0 0 0 -34⟩ | 31.516 | |||
| 17-ripple |
[327 0 0 0 0 0 -80⟩ | 3.5672 | |||
19-limit commas
| Name(s) | Color Name | Ratio | Monzo | Cents | |
|---|---|---|---|---|---|
| undevicesimal semitone | ino | 19o2 | 19 / 18 | [-1 -2 0 0 0 0 0 1⟩ | 93.603 |
| small undevicesimal semitone | nuyo | 19uy1 | 20 / 19 | [2 0 1 0 0 0 0 -1⟩ | 88.801 |
| nutho unison | nutho | 19u3o1 | 39 / 38 | [-1 1 0 0 0 1 0 -1⟩ | 44.970 |
| noru unison | noru | 19or1 | 57 / 56 | [-3 1 0 -1 0 0 0 1⟩ | 30.642 |
| nuruyo comma | nuruyo | 19ury-2 | 135 / 133 | [0 3 1 -1 0 0 0 -1⟩ | 25.840 |
| nogugu 2nd | nogugu | 19ogg2 | 76 / 75 | [2 -1 -2 0 0 0 0 1⟩ | 22.931 |
| approximation to Pyth 53-comma | nulozo | 19u1oz1 | 77 / 76 | [-2 0 0 1 1 0 0 -1⟩ | 22.631 |
| 19th-partial chroma | nugu | 19ug1 | 96 / 95 | [5 1 -1 0 0 0 0 -1⟩ | 18.128 |
| noluzo 2nd | noluzo | 19o1uz2 | 133 / 132 | [-2 -1 0 1 -1 0 0 1⟩ | 13.066 |
| Ganassi's comma | nuso | 19u17o1 | 153 / 152 | [-3 2 0 0 0 0 1 -1⟩ | 11.352 |
| nosugu unison | nosugu | 19o17ug1 | 171 / 170 | [-1 2 -1 0 0 0 -1 1⟩ | 10.154 |
| Hunt 19-cycle comma | saquadnu | s19u4-2 | 131072 / 130321 | [17 0 0 0 0 0 0 -4⟩ | 9.9479 |
| spleen comma | nuluzoyo | 19u1uzy1 | 210 / 209 | [1 1 1 1 -1 0 0 -1⟩ | 8.2637 |
| nusu comma | nusu | 19u17u-2 | 324 / 323 | [2 4 0 0 0 0 -1 -1⟩ | 5.3516 |
| go comma | nonogu | 19oog2 | 361 / 360 | [-3 -2 -1 0 0 0 0 2⟩ | 4.8023 |