Comma

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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; 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 convention elsewhere on the wiki.

List of commas, by prime limit

3-limit commas

Name(s) Color Name Ratio Monzo Cents
Pythagorean comma wa comma LLw-2 531441 / 524288 | -19 12 > 23.460
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
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
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
tertiosec comma laquadtribiyo L6y24-9 | -89 21 24 > 12.584
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
11-15-comma, undecatonic comma trisa-legu s3g115 8796093022208 / 8649755859375 | 43 -11 -11 > 29.044
Huntian 15-cycle comma | 168 -43 -43 > 4.4453
56-syntonic comma | -225 224 -56 > 4.3522
59-5-comma | 137 0 -59 > 7.4909

7-limit commas

Name(s) Color Name Ratio Monzo Cents
senga trizo-agugu z3gg3 686 / 675 | 1 -3 -2 3 > 27.985
septimal / Archytas' comma, Leipziger Komma ru r1 64 / 63 | 6 -2 0 -1 > 27.264
mandos birugugu rrg41 31104 / 30625 | 7 5 -4 -2 > 26.868
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 triru-agu 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 latritrizo-ayo 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-aquadquadyo s3r3y16-3 640000000000000000 / 635585924776181463 | 22 -32 16 -3 > 11.982
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
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
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

11-limit commas

Name(s) Color Name Ratio Monzo Cents
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 biluzo-ayo 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 trilu-azo 1u3z2 1344 / 1331 | 6 1 0 1 -3 > 16.827
biyatisma lologu 1oog1 121 / 120 | -3 -1 -1 0 2 > 14.367
aphrowe trilo-aruru 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

13-limit commas

Name(s) Color Name Ratio Monzo Cents
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 bithulo-azogu 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

17-limit commas

Name(s) Color Name Ratio Monzo Cents
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
23 semitone comma | -94 0 0 0 0 0 23 > 13.974
17-ripple integer cents comma | 327 0 0 0 0 0 -80 > 3.5672

19-limit commas

Name(s) Color Name Ratio Monzo Cents
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