Unnoticeable comma

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Unnoticeable commas are very small intervals. These commas are called "unnoticeable" because, being equal to or less than 3.5 cents, they are smaller than the average peak JND (just-noticeable difference) of human pitch perception, as illustrated by the research of Aaron Andrew Hunt. It is improbable that even a trained listener would be able to notice these intervals, and as such they a prime target for psychoacoustically informed microtempering. (However, a considerably larger comma can be unnoticeable in an adaptive tuning context. Instead of one large pitch shift of the entire comma, there can be many small pitch shifts of a fraction of a comma, one per chord change.)

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 over 3.5 cents in size, see 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. Except for the 3-limit commas, the color name refers to both the comma and the temperament created when it is tempered out.

3-limit commas

Name(s) Color Name Monzo Cents
359-comma wa-359 comma w-359 [-569 359 1.8453
Sasktel comma wa-306 comma w-306 [485 -306 1.7697
Satanic comma wa-665 comma w-665 [-1054 665 0.075575
15601-comma wa-15601 comma w-15601 [24727 -15601 0.031499
31867-comma wa-31867 comma w-31867 [-50508 31867 0.012577

5-limit commas

Name(s) Color Name Ratio Monzo Cents
dodifo Quadla-sepquinyo [-67 -9 35 3.3850
vishnuzma, semisuper Sasepbigu 6115295232 / 6103515625 [23 6 -14 3.3380
enneadeca, 19-tone-comma Neyo 19073486328125 / 19042491875328 [-14 -19 19 2.8155
vavoom Quinla-seyo [-68 18 17 2.5232
tricot comma Quadsa-triyo 68719476736000 / 68630377364883 [39 -29 3 2.2461
schisma Layo 32805 / 32768 [-15 8 1 1.9537
counterschisma Tribilagu [-69 45 -1 1.6613
septendecima Lala-sebiyo [-52 -17 34 1.4313
hemithirds comma, lunama Sasa-quintrigu 274877906944 / 274658203125 [38 -2 -15 1.3843
minortonic comma, minortonma Trila-segu 50031545098999707 / 50000000000000000 [-16 35 -17 1.0919
ennealimmal Satritribiyo 7629394531250 / 7625597484987 [1 -27 18 0.86183
astro Tribisa-thirty-wegu [91 -12 -31 0.81486
kwazy Quadla-quadquadyo 9010162353515625 / 9007199254740992 [-53 10 16 0.56943
whoosh Saletrigu [37 25 -33 0.52246
egads Setriyo [-36 -52 51 0.33936
monzisma Quinsa-yoyo 450359962737049600 / 450283905890997363 [54 -37 2 0.29240
fortune Tritrila-sepbiyo [-107 47 14 0.27703
gross Quinbisa-forty-segu [144 -22 -47 0.24543
senior Quadla-sepquingu [-17 62 -35 0.23007
665&3684 comma Quintritrila-yo [-500 314 1 0.18399
raider Tritrisa-thirty-seyo [71 -99 37 0.062327
pirate Quinla-sepsepyo [-90 -15 49 0.046966
viking Nela-sixty-weyo [-251 69 61 0.031605
Kirnberger's atom Sepbisa-quadtrigu [161 -84 -12 0.015361
selenia [-433 -137 280 0.0047636
titania [2746 -521 -827 0.0031829
quark Twenty-thebila-sequinyo [-573 237 85 8.8361 × 10-4
scamp [-5836 4293 -417 3.3472 × 10-5
rover [1634 1502 -1729 2.7513 × 10-5
rascal [-7470 2791 1312 5.9596 × 10-6

7-limit commas

Name(s) Color Name Ratio Monzo Cents
44-septimal comma [-263 88 0 44 0.37996
571-7-comma [1603 0 0 -571 0.40741
horwell Lazoquinyo 65625 / 65536 [-16 1 5 1 2.3495
meter Latriru-asepyo 703125 / 702464 [-11 2 7 -3 1.6283
wizma Quinzo-ayoyo 420175 / 419904 [-6 -8 2 5 1.1170
breedsma Bizozogu 2401 / 2400 [-5 -1 -2 4 0.72120
ragisma Zoquadyo 4375 / 4374 [-1 -7 4 1 0.39576
akjaysma, 5\7 octave comma Trisa-sepruyo 140737488355328 / 140710042265625 [47 -7 -7 -7 0.33765
landscape Trizogugu 250047 / 250000 [-4 6 -6 3 0.32544
bapbo schismina 13841287201 / 13839609375 [0 -11 -7 12 0.20987
nanisma Quinbisaru [109 -67 0 -1 0.18904
laleruyo (171&1547&3125) Laleruyo 3955078125/3954653486 [-1 4 11 -11 0.18588
87-fold starling comma Twentynetri-zotrigu [86 174 -261 87 0.14469
starscape Latritriru-ayo 645700815 / 645657712 [-4 17 1 -9 0.11557
quinla-zoyoyo (12&53&612) Quinla-zoyoyo [-55 30 2 1 0.10336
euzenius Sabiruquinyo 78125000 / 78121827 [3 -13 10 -2 0.070314
171&1547&4973 comma Sa-twentythezo-atritribigu [1 -15 -18 23 0.023986
trisa-quinbiru-agu (441&1848&3125) Trisa-quinbiru-agu [51 -13 -1 -10 0.012210
termite Satritribiru-athirtyseyo [9 -28 37 -18 0.0010723
neutrino [1889 -2145 138 424 1.6361 × 10-10

11-limit commas

Name(s) Color Name Ratio Monzo Cents
11-cycle schisma, 37-11-comma [128 0 0 0 -37 1.2361
swetisma Lururuyo 540 / 539 [2 3 1 -2 -1 3.2090
wizardharry Triluyo 4000 / 3993 [5 -1 3 0 -3 3.0323
vishdel Saloquadgu 5632 / 5625 [9 -2 -4 0 1 2.1531
bilozogugu, undecimal hemifourths comma Bilozogugu 160083 / 160000 [-8 3 -4 2 2 0.89784
sesdecal Laquadlu-asepyo 234375 / 234256 [-4 1 7 0 -4 0.87923
hemigail Quadlo-atriru 43923 / 43904 [-7 1 0 -3 4 0.74905
lehmerisma Lolo-ruyoyo 3025 / 3024 [-4 -3 2 -1 2 0.57240
kalisma, Gauss' comma Bilorugu 9801 / 9800 [-3 4 -2 -2 2 0.17665
odiheim Luluquinzo-aquadgu 151263 / 151250 [-1 2 -4 5 -2 0.14879
parimo Satribilo-agu 1771561 / 1771470 [-1 -11 -1 0 6 0.088931
ultimo Quadlo-asepru-ayoyo 3294225 / 3294172 [-2 2 2 -7 4 0.027854

13-limit commas

Name Color Name Ratio Monzo Cents
bean Sathuquinlu 2097152 / 2093663 | 21 0 0 0 -5 -1 > 2.8826
tunbarsma Thuquadyo 625 / 624 [-4 -1 4 0 0 -1 2.7722
island comma Bithogu 676 / 675 [2 -3 -2 0 0 2 2.5629
squbema Lathuru 729 / 728 [-3 6 0 -1 0 -1 2.3764
petrma Trithu-aloyoyo 2200 / 2197 [3 0 2 0 1 -3 2.3624
nicola Thululuzoyoyo 1575 / 1573 [0 2 2 1 -2 -1 2.1998
sinbadma Tholozotrigu 1001 / 1000 [-3 0 -3 1 1 1 1.7303
cantonisma Trithoru-ayo 10985 / 10976 [-5 0 1 -3 0 3 1.4190
lummic Tholotriru-agu 1716 / 1715 [2 1 -1 -3 1 1 1.0092
ibnsinma Tholuruyo 2080 / 2079 [5 -3 1 -1 -1 1 0.83252
schismina Sathurugu 4096 / 4095 [12 -2 -1 -1 0 -1 0.42272
leprechaun comma Thotholuyoyo 4225 / 4224 [-7 -1 2 0 -1 2 0.40981
jacobin Thotrilu-agu 6656 / 6655 [9 0 -1 0 -3 1 0.26012
harmonisma Thuthutrilo-aru 10648 / 10647 [3 -2 0 -1 3 -2 0.16260
chalmersima Lathotholurugugu 123201 / 123200 [-6 6 -2 -1 -1 2 0.014052

17-limit commas

Name Color Name Ratio Monzo Cents
xenisma Sululutrizo 2058 / 2057 [1 1 0 3 -2 0 -1 0.84143
flashma Sotholuzotrigu 12376 / 12375 [3 -2 -3 1 -1 1 1 0.13989
sparkisma Sululuruyoyo 14400 / 14399 [6 2 2 -1 -2 0 -1 0.12023
scintillisma Lasuthuluquadzo-agu 194481 / 194480 [-4 4 -1 4 -1 -1 -1 0.0089018

19-limit commas

Name Color Name Ratio Monzo Cents
undevicesimal comma, undevicesimal schisma[1], Boethius' comma, Hunt 19-minor mediant comma Lano 513 / 512 [-9 3 0 0 0 0 0 1 3.3781
password Sanogu 1216 / 1215 [6 -5 -1 0 0 0 0 1 1.4243
Blumeyer comma Nosuthulu 2432 / 2431 [7 0 0 0 -1 -1 -1 1 0.71200
BMO schismina Sabinothu 369664 / 369603 [10 -7 0 0 0 -2 0 2 0.2857
frouggie comma Nusuquinthu-aquadlo 119939072 / 119927639 [13 0 0 0 4 -5 -1 -1 0.165035
pollar comma Nunusuquintho-alulu 742586 / 742577 [1 0 0 0 -2 5 -1 -2 0.020982
19-limit decimill Nosorurutrigu 165376 / 165375 [9 -3 -3 -2 0 0 1 1 0.010469