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Line 2: Line 2:
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.
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]]; for commas in between 30 and 100 cents in size, see [[Medium 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 [[conventions|convention]] elsewhere on the wiki.
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 [[conventions|convention]] elsewhere on the wiki.
Line 16: Line 16:
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
|-
| limma, Pythagorean minor second
| small wa 2nd
| sw2
| [[256/243|256 / 243]]
| {{Monzo| 8 -5 }}
| 90.225
|-
|-
| [[Pythagorean comma]]
| [[Pythagorean comma]]
Line 30: Line 23:
| {{Monzo| -19 12 }}
| {{Monzo| -19 12 }}
| 23.460
| 23.460
|-
| [[17-comma]]
| wa-17 comma
| ssw3
| 134217728 / 129140163
| {{Monzo| 27 -17 }}
| 66.765
|-
| [[29-comma]]
| wa-29 comma
| s<sup>4</sup>w4
| 70368744177664 / 68630377364883
| {{Monzo| 46 -29 }}
| 43.305
|-
|-
| [[41-comma]]
| [[41-comma]]
Line 58: Line 37:
| {{Monzo| -84 53 }}
| {{Monzo| -84 53 }}
| 3.6150
| 3.6150
|-
| 70-comma
| wa-70 comma
| s<sup>10</sup>w8
|
| {{Monzo| 111 -70 }}
| 63.150
|-
| 77-comma
| wa-77 comma
| L<sup>11</sup>w-8
|
| {{Monzo| -122 77 }}
| 50.535
|-
|-
| 200-comma, Pythagorean integer cents comma <!-- the meaning of "integer cents" is ambiguous, because this comma is both near an integer in cents and involves integer cent fifths (702 cents), causing that term to be inconsistently used for one or the other -->
| 200-comma, Pythagorean integer cents comma <!-- the meaning of "integer cents" is ambiguous, because this comma is both near an integer in cents and involves integer cent fifths (702 cents), causing that term to be inconsistently used for one or the other -->
Line 89: Line 54:
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
|-
| double large yoyo negative 2nd
| lala-yoyo
| LLyy-2
| 4428675 / 4194304
| {{Monzo| -22 11 2 }}
| 94.132
|-
| major chroma, major limma, pelogic comma
| layobi
| Ly1
| [[135/128|135 / 128]]
| {{Monzo| -7 3 1 }}
| 92.179
|-
| double small gu 3rd
| sasagu
| ssg3
| 8388608 / 7971615
| {{Monzo| 23 -13 -1 }}
| 88.271
|-
| bohpier, [[13edt]] comma
| satheyo
| sy<sup>13</sup>-2
| 1220703125 / 1162261467
| {{Monzo| 0 -19 13 }}
| 84.933
|-
| ripple
| quingu
| g<sup>5</sup>2
| 6561 / 6250
| {{Monzo| -1 8 -5 }}
| 84.071
|-
| doublewide
| quadbiyo
| y<sup>8</sup>-2
| 390625 / 373248
| {{Monzo| -9 -6 8 }}
| 78.780
|-
| sevond
| sasepyo
| sy<sup>7</sup>1
| 5000000 / 4782969
| {{Monzo| 6 -14 7 }}
| 76.826
|-
| nusecond
| legu
| g<sup>11</sup>3
| 51018336 / 48828125
| {{Monzo| 5 13 -11 }}
| 75.964
|-
| sentinel
| trila-quadyo
| L<sup>3</sup>y<sup>4</sup>-3
| 8968066875 / 8589934592
| {{Monzo| -33 15 4 }}
| 74.580
|-
| large triyo negative 2nd
| latriyo
| Ly<sup>3</sup>-2
| 273375 / 262144
| {{Monzo| -18 7 3 }}
| 72.626
|-
| chromatic semitone
| yoyo
| yy1
| [[25/24|25 / 24]]
| {{Monzo| -3 -1 2 }}
| 70.672
|-
| superpyth, grave minor second
| sayo
| sy2
| 20480 / 19683
| {{Monzo| 12 -9 1 }}
| 68.719
|-
| major diesis, diminished comma
| quadgu
| g<sup>4</sup>2
| [[648/625|648 / 625]]
| {{Monzo| 3 4 -4 }}
| 62.565
|-
| passion
| saquingu
| sg<sup>5</sup>3
| 262144 / 253125
| {{Monzo| 18 -4 -5 }}
| 60.611
|-
| shibboleth
| tritriyo
| y<sup>9</sup>-2
| 1953125 / 1889568
| {{Monzo| -5 -10 9 }}
| 57.273
|-
| mynic
| quinbigu
| g<sup>10</sup>3
| 10077696 / 9765625
| {{Monzo| 9 9 -10 }}
| 54.458
|-
| tritonic
| lala-quinyo
| LLy<sup>5</sup>-3
| 553584375 / 536870912
| {{Monzo| -29 11 5 }}
| 53.074
|-
| [[negri comma]], double augmentation diesis
| laquadyo
| Ly<sup>4</sup>-2
| 16875 / 16384
| {{Monzo| -14 3 4 }}
| 51.120
|-
| maximal diesis, porcupine
| triyo
| y<sup>3</sup>1
| [[250/243|250 / 243]]
| {{Monzo| 1 -5 3 }}
| 49.166
|-
| mowgli, [[15edt]] comma
| laquintrigu
| Lg<sup>15</sup>3
| 31381059609 / 30517578125
| {{Monzo| 0 22 -15 }}
| 48.304
|-
| immunity
| sasa-yoyo
| ssyy2
| 1638400 / 1594323
| {{Monzo| 16 -13 2 }}
| 47.212
|-
| double large green comma
| lalagu
| LLg-2
| 43046721 / 41943040
| {{Monzo| -23 16 -1 }}
| 44.966
|-
| diesis, augmented comma
| trigu
| g<sup>3</sup>2
| [[128/125|128 / 125]]
| {{Monzo| 7 0 -3 }}
| 41.059
|-
| wizard
| lala-quadtriyo
| LLy<sup>12</sup>-4
| 2197265625 / 2147483648
| {{Monzo| -31 2 12 }}
| 39.675
|-
| sycamore
| laleyo
| Ly<sup>11</sup>-3
| 48828125 / 47775744
| {{Monzo| -16 -6 11 }}
| 37.721
|-
| absurdity
| lala-sepgu
| LLg<sup>7</sup>1
| 10460353203 / 10240000000
| {{Monzo| -17 21 -7 }}
| 36.859
|-
| fifive
| saquinbiyo
| sy<sup>10</sup>-2
| 9765625 / 9565938
| {{Monzo| -1 -14 10 }}
| 35.767
|-
| unicorn
| laquadbigu
| Lg<sup>8</sup>2
| 1594323 / 1562500
| {{Monzo| -2 13 -8 }}
| 34.905
|-
| valentine comma
| satritrigu
| sg<sup>9</sup>3
| 1990656 / 1953125
| {{Monzo| 13 5 -9 }}
| 32.952
|-
| [[ampersand]], Ampersand's comma
| lala-tribiyo
| LLy<sup>6</sup>-3
| 34171875 / 33554432
| {{Monzo| -25 7 6 }}
| 31.567
|-
| mabila comma
| sasa-quinbigu
| ssg<sup>10</sup>4
| 268435456 / 263671875
| {{Monzo| 28 -3 -10 }}
| 30.998
|-
|-
| small diesis, [[magic comma]]
| small diesis, [[magic comma]]
Line 509: Line 257:
| {{Monzo| 77 -31 -12 }}
| {{Monzo| 77 -31 -12 }}
| 3.6304
| 3.6304
|-
| 10-15-comma
| trila-quinbiyo
| L<sup>3</sup>y<sup>10</sup>-4
| 576650390625 / 549755813888
| {{Monzo| -39 10 10 }}
| 82.687
|-
|-
| 11-15-comma, undecatonic comma
| 11-15-comma, undecatonic comma
Line 523: Line 264:
| {{Monzo| 43 -11 -11 }}
| {{Monzo| 43 -11 -11 }}
| 29.044
| 29.044
|-
| 21-15-comma
|tribila-septriyo
|L<sup>6</sup>y<sup>21</sup>-8
|
| {{Monzo| -82 21 21 }}
| 53.643
|-
| Twenty-two thirds limma
| trila-lebiyo
| L<sup>3</sup>y<sup>22</sup>-6
| 2384185791015625 / 2251799813685248
| {{Monzo| -51 0 22 }}
| 98.902
|-
| 23-3/5-comma
| twenty-thegu
| g<sup>23</sup>5
| 12339534735212544 / 11920928955078125
| {{Monzo| 17 23 -23 }}
| 59.750
|-
| sibbolet
| quadla-quinquinyo
| L<sup>4</sup>y<sup>25</sup>-7
| 298023223876953125 / 288230376151711744
| {{Monzo| -58 0 25 }}
| 57.843
|-
| Hunt 5-cycle comma
| quadla-sepquadyo
| L<sup>4</sup>y<sup>28</sup>-8
| 37252902984619140625 / 36893488147419103232
| {{Monzo| -65 0 28 }}
| 16.784
|-
| acute thirds comma
|quadsa-thirty-wegu
| s<sup>4</sup>g<sup>31</sup>9
|
| {{Monzo| 72 0 -31 }}
| 24.275
|-
| 32-15-comma
|tritrila-quadquadbiyo
|L<sup>9</sup>y<sup>32</sup>-12
|
| {{Monzo| -125 32 32 }}
| 24.599
|-
| 34-5-comma
|quinsa-sebigu
| s<sup>5</sup>g<sup>34</sup>10
|
| {{Monzo| 79 0 -34 }}
| 65.334
|-
| 34-3/5-comma
| sebiyo
| y<sup>34</sup>3
|
| {{Monzo| -25 -34 34 }}
| 68.196
|-
|-
| Huntian 15-cycle comma
| Huntian 15-cycle comma
Line 593: Line 271:
| {{Monzo| 168 -43 -43 }}
| {{Monzo| 168 -43 -43 }}
| 4.4453
| 4.4453
|-
| Schismic thirds chromatic semitone
|
|
|
| {{Monzo| -123 0 53 }}
| 74.627
|-
| 53-15-comma
|
|
|
| {{Monzo| -207 53 53 }}
| 78.242
|-
| 53-3/5-comma
| fifty-theyo
| y<sup>53</sup>7
|
| {{Monzo| -39 -53 53 }}
| 71.012
|-
| 54-15-comma
|
|
|
| {{Monzo| 211 -54 -54 }}
| 33.489
|-
|-
| 56-syntonic comma
| 56-syntonic comma
Line 635: Line 285:
| {{Monzo| 137 0 -59 }}
| {{Monzo| 137 0 -59 }}
| 7.4909
| 7.4909
|-
| 76-15-comma
|
|
|
| {{Monzo| 297 -76 -76 }}
| 91.578
|}
|}


Line 652: Line 295:
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
|-
| minor semitone
| zogu
| zg2
| 21 / 20
| {{Monzo| -2 1 -1 1 }}
| 84.467
|-
| laruru negative 2nd
| laruru
| Lrr-2
| 6561 / 6272
| {{Monzo| -7 8 0 -2 }}
| 77.988
|-
| bapbo
| rurugu
| rrg1
| 256 / 245
| {{Monzo| 8 0 -1 -2 }}
| 76.034
|-
| Archytas' 1/3-tone
| zo
| z2
| 28 / 27
| {{Monzo| 2 -3 0 1 }}
| 62.961
|-
| greenwoodma
| ruruyo
| rry-2
| 405 / 392
| {{Monzo| -3 4 1 -2 }}
| 56.482
|-
| Harrison's comma
| laru
| Lr-2
| [[59049/57344|59049 / 57344]]
| {{Monzo| -13 10 0 -1 }}
| 50.724
|-
| keega
| trizogu
| z<sup>3</sup>g<sup>3</sup>3
| 1029 / 1000
| {{Monzo| -3 1 -3 3 }}
| 49.492
|-
| septimal quarter tone
| rugu
| rg1
| [[36/35|36 / 35]]
| {{Monzo| 2 2 -1 -1 }}
| 48.770
|-
| 5-21-comma
| saquinru
| sr<sup>5</sup>-2
| 4194304 / 4084101
| {{Monzo| 22 -5 0 -5 }}
| 46.095
|-
| cloudy
| laquinzo
| Lz<sup>5</sup>3
| 16807 / 16384
| {{Monzo| -14 0 0 5 }}
| 44.130
|-
| Avicenna, Avicenna's enharmonic diesis
| lazoyoyo
| Lzyy1
| 525 / 512
| {{Monzo| -9 1 2 1 }}
| 43.408
|-
| slendro diesis
| zozo
| zz2
| [[49/48|49 / 48]]
| {{Monzo| -4 -1 0 2 }}
| 35.697
|-
| tritonic diesis, jubilisma
| biruyo
| rryy-2
| [[50/49|50 / 49]]
| {{Monzo| 1 0 2 -2 }}
| 34.976
|-
| eric
| sepru
| r<sup>7</sup>-4
| 839808 / 823543
| {{Monzo| 7 8 0 -7 }}
| 33.859
|-
|-
| senga
| senga
Line 967: Line 512:
| {{Monzo| 22 -32 16 -3 }}
| {{Monzo| 22 -32 16 -3 }}
| 11.982
| 11.982
|-
| 8-35-comma
| lala-quadbizoyo
| LLz<sup>8</sup>y<sup>8</sup>2
| 2251875390625 / 2199023255552
| {{Monzo| -41 0 8 8 }}
| 41.117
|-
| 15-35-comma
|
|
|
| {{Monzo| 77 0 -15 -15 }}
| 72.906
|-
| hexadecatone comma, 16-7-comma
| sasa-quadquadrubi
| ssr<sup>16</sup>-6
| 35184372088832 / 33232930569601
| {{Monzo| 45 0 0 -16 }}
| 98.785
|-
| 18-21-comma
|
|
|
| {{Monzo| -79 18 0 18 }}
| 74.056
|-
| 21-7-comma
|
|
| 576460752303423488 / 558545864083284007
| {{Monzo| 59 0 0 -21 }}
| 54.656
|-
|-
| 23-21-comma
| 23-21-comma
Line 1,037: Line 547:
| {{Monzo| 123 -28 0 -28 }}
| {{Monzo| 123 -28 0 -28 }}
| 18.135
| 18.135
|-
| 29-7/5-comma
|
|
|
| {{Monzo| -14 0 -29 29 }}
| 92.854
|-
| German sixth comma
|
|
|
| {{Monzo| -87 0 0 31 }}
| 33.603
|-
| 31-7/5-comma
|
|
|
| {{Monzo| -15 0 -31 31 }}
| 57.878
|-
|-
| 31-35-comma
| 31-35-comma
Line 1,093: Line 582:
| {{Monzo| -101 0 0 36 }}
| {{Monzo| -101 0 0 36 }}
| 77.733
| 77.733
|-
| 37-7/5-comma
|
|
|
| {{Monzo| 18 0 37 -37 }}
| 47.049
|-
| 39-7/5-comma
|
|
|
| {{Monzo| 19 0 39 -39 }}
| 82.024
|-
| 39-35-comma
|
|
|
| {{Monzo| -200 0 39 39 }}
| 50.445
|-
| 47-7-comma
|
|
|
| {{Monzo| 132 0 0 -47 }}
| 65.182
|-
| 47-35-comma
|
|
|
| {{Monzo| -241 0 47 47 }}
| 91.562
|-
|-
| Huntian 35-cycle comma
| Huntian 35-cycle comma
Line 1,149: Line 603:
| {{Monzo| -33 0 -68 68 }}
| {{Monzo| -33 0 -68 68 }}
| 10.829
| 10.829
|-
| <strike>slendro integer cents comma</strike>
|
|
|
| {{Monzo| 1123 0 0 -400 }}
| 69.637
|}
|}


Line 1,166: Line 613:
! Monzo
! Monzo
! Cents
! Cents
|-
| undecimal minor semitone
| loru
| 1or1
| 22 / 21
| {{Monzo| 1 -1 0 -1 1 }}
| 80.537
|-
| lalu unison
| lalu
| L1u1
| 729 / 704
| {{Monzo| -6 6 0 0 -1 }}
| 60.412
|-
| undecimal comma, al-Farabi's 1/4-tone
| ilo
| 1o1
| 33 / 32
| {{Monzo| -5 1 0 0 1 }}
| 53.273
|-
| Hunt flat 5 comma
| salu
| s1u2
| 8192 / 8019
| {{Monzo| 13 -6 0 0 -1 }}
| 36.952
|-
| sterno
| lotriru
| 1or<sup>3</sup>-2
| 352 / 343
| {{Monzo| 5 0 0 -3 1 }}
| 44.840
|-
| 1/5-tone
| luyo
| 1uy1
| 45 / 44
| {{Monzo| -2 2 1 0 -1 }}
| 38.906
|-
| undecimal diesis
| luzogu
| 1uzg2
| 56 / 55
| {{Monzo| 3 0 -1 1 -1 }}
| 31.194
|-
| telepathma
| loyo
| 1oy1
| 55 / 54
| {{Monzo| -1 -3 1 0 1 }}
| 31.767
|-
|-
| thuja comma
| thuja comma
Line 1,341: Line 732:
| {{Monzo| -2 0 3 -3 1 }}
| {{Monzo| -2 0 3 -3 1 }}
| 3.7814
| 3.7814
|-
| 11-cycle chroma, 11-11-comma
| lala-lelo
| LL1o<sup>11</sup>-3
| 285311670611 / 274877906944
| {{Monzo| -38 0 0 0 11 }}
| 64.497
|-
| the Igs boson, 13-11-comma
| sasa-thelu
| ss1u<sup>13</sup>4
| 35184372088832 / 34522712143931
| {{Monzo| 45 0 0 0 -13 }}
| 32.867
|-
| Hunt 11-cycle comma
|
|
|
| {{Monzo| -83 0 0 0 24 }}
| 31.631
|-
| 11-cycle major seventh prote, 35-11-comma
|
|
|
| {{Monzo| -121 0 0 0 35 }}
| 96.128
|}
|}


Line 1,379: Line 742:
! Monzo
! Monzo
! Cents
! Cents
|-
| tridecimal comma
| thu
| 3u1
| 27 / 26
| {{Monzo| -1 3 0 0 0 -1 }}
| 65.337
|-
| tridecimal 1/3-tone
| thogu
| 3og2
| 26 / 25
| {{Monzo| 1 0 -2 0 0 1 }}
| 67.900
|-
| Hunt minor submediant comma
| latho
| L3o1
| 1053 / 1024
| {{Monzo| -10 4 0 0 0 1 }}
| 48.348
|-
| tridecimal minor diesis
| thuyo
| 3uy1
| 40 / 39
| {{Monzo| 3 -1 1 0 0 -1 }}
| 43.831
|-
| astburyp
| latribitho
| L3o<sup>6</sup>2
| 4826809 / 4718592
| {{Monzo| -19 -2 0 0 0 6 }}
| 39.256
|-
|-
| wilsorma
| wilsorma
Line 1,561: Line 889:
| {{Monzo| -37 0 0 0 0 10 }}
| {{Monzo| -37 0 0 0 0 10 }}
| 5.2766
| 5.2766
|-
| <strike>silver half cents comma</strike>
|
|
|
| {{Monzo| -8881 0 0 0 0 2400 }}
| 66.388
|}
|}


Line 1,578: Line 899:
! Monzo
! Monzo
! Cents
! Cents
|-
| Arabic lute index finger
| su
| 17u1
| 18 / 17
| {{Monzo| 1 2 0 0 0 0 -1 }}
| 98.955
|-
| septendecimal 1/4-tone
| suzoyo
| 17uzy1
| 35 / 34
| {{Monzo| -1 0 1 1 0 0 -1 }}
| 50.184
|-
|solu 2nd
| solu
| 17o1u2
| 34 / 33
| {{Monzo| 1 -1 0 0 -1 0 1 }}
| 51.682
|-
| 17th-partial chroma
| sogugu
| 17ogg2
| 51 / 50
| {{Monzo| -1 1 -2 0 0 0 1 }}
| 34.283
|-
|sutho unison
| sutho
| 17u3o1
| 52 / 51
| {{Monzo| 2 -1 0 0 0 1 -1 }}
| 33.617
|-
|-
|soruyo unison
|soruyo unison
Line 1,662: Line 948:
| {{Monzo| -5 -2 0 0 0 0 2 }}
| {{Monzo| -5 -2 0 0 0 0 2 }}
| 6.0008
| 6.0008
|-
| 11 semitone comma
|
|
| 35184372088832 / 34271896307633
| {{Monzo| 45 0 0 0 0 0 -11 }}
| 45.490
|-
| 12 semitone comma
|
|
| 582622237229761 / 562949953421312
| {{Monzo| -49 0 0 0 0 0 12 }}
| 59.465
|-
|-
| 23 semitone comma
| 23 semitone comma
Line 1,683: Line 955:
| {{Monzo| -94 0 0 0 0 0 23 }}
| {{Monzo| -94 0 0 0 0 0 23 }}
| 13.974
| 13.974
|-
| Hunt 17-cycle comma
|
|
|
| {{Monzo| 139 0 0 0 0 0 -34 }}
| 31.516
|-
|-
| 17-ripple <strike>integer cents</strike> comma
| 17-ripple <strike>integer cents</strike> comma
Line 1,707: Line 972:
! Monzo
! Monzo
! Cents
! Cents
|-
| undevicesimal semitone
| ino
| 19o2
| 19 / 18
| {{Monzo| -1 -2 0 0 0 0 0 1 }}
| 93.603
|-
| small undevicesimal semitone
| nuyo
| 19uy1
| 20 / 19
| {{Monzo| 2 0 1 0 0 0 0 -1 }}
| 88.801
|-
|nutho unison
| nutho
| 19u3o1
| 39 / 38
| {{Monzo| -1 1 0 0 0 1 0 -1 }}
| 44.970
|-
|noru unison
| noru
| 19or1
| 57 / 56
| {{Monzo| -3 1 0 -1 0 0 0 1 }}
| 30.642
|-
|-
|nuruyo comma
|nuruyo comma
Retrieved from "https://en.xen.wiki/w/Small_comma"