Unnoticeable comma

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.

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.

3-limit commas

Name(s)	Ratio	Monzo	Cents
Sasktel comma, 51-Pythagorean comma		[485 -306⟩	1.7697
Satanic comma		[-1054 665⟩	0.075575

5-limit commas

Name(s)	Ratio	Monzo	Cents
dodifo		[-67 -9 35⟩	3.3850
vishnuzma, semisuper	6115295232 / 6103515625	[23 6 -14⟩	3.3380
enneadeca, 19-tone-comma	19073486328125 / 19042491875328	[-14 -19 19⟩	2.8155
vavoom		[-68 18 17⟩	2.5232
tricot comma	68719476736000 / 68630377364883	[39 -29 3⟩	2.2461
schisma	32805 / 32768	[-15 8 1⟩	1.9537
counterschisma		[-69 45 -1⟩	1.6613
septendecima		[-52 -17 34⟩	1.4313
hemithirds comma, lunama	274877906944 / 274658203125	[38 -2 -15⟩	1.3843
minortone comma	50031545098999707 / 50000000000000000	[-16 35 -17⟩	1.0919
ennealimmal	7629394531250 / 7625597484987	[1 -27 18⟩	0.86183
astro		[91 -12 -31⟩	0.81486
kwazy	9010162353515625 / 9007199254740992	[-53 10 16⟩	0.56943
whoosh		[37 25 -33⟩	0.52246
egads		[-36 -52 51⟩	0.33936
monzisma	450359962737049600 / 450283905890997363	[54 -37 2⟩	0.29240
fortune		[-107 47 14⟩	0.27703
gross		[144 -22 -47⟩	0.24543
senior		[-17 62 -35⟩	0.23007
665&3684 comma		[-500 314 1⟩	0.18399
raider		[71 -99 37⟩	0.062327
pirate		[-90 -15 49⟩	0.046966
viking		[-251 69 61⟩	0.031605
Kirnberger's_atom		[161 -84 -12⟩	0.015361
selenia		[-433 -137 280⟩	0.0047636
titania		[2746 -521 -827⟩	0.0031829
quark		[-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)	Ratio	Monzo	Cents
44-septimal comma		[-263 88 0 44⟩	0.37996
571-7-comma		[1603 0 0 -571⟩	0.40741
horwell	65625 / 65536	[-16 1 5 1⟩	2.3495
meter	703125 / 702464	[-11 2 7 -3⟩	1.6283
wizma	420175 / 419904	[-6 -8 2 5⟩	1.1170
breedsma	2401 / 2400	[-5 -1 -2 4⟩	0.72120
ragisma	4375 / 4374	[-1 -7 4 1⟩	0.39576
akjaysma, 5\7 octave comma	140737488355328 / 140710042265625	[47 -7 -7 -7⟩	0.33765
landscape	250047 / 250000	[-4 6 -6 3⟩	0.32544
nanisma		[109 -67 0 -1⟩	0.18904
large r11y11 comma	3955078125/3954653486	[-1 4 11 -11⟩	0.18588
starscape	645700815 / 645657712	[-4 17 1 -9⟩	0.11557
quintuple-large zuyoyo comma		[-55 30 2 1⟩	0.10336
euzenius	78125000 / 78121827	[3 -13 10 -2⟩	0.070314
small z23g18 comma		[1 -15 -18 23⟩	0.023986
triple-small r10g comma		[51 -13 -1 -10⟩	0.012210
termite		[9 -28 37 -18⟩	0.0010723
neutrino		[1889 -2145 138 424⟩	1.6361 × 10-10

11-limit commas

Name(s)	Ratio	Monzo	Cents
11-cycle schisma, 37-11-comma		[128 0 0 0 -37⟩	1.2361
swetisma	540 / 539	[2 3 1 -2 -1⟩	3.2090
wizardharry	4000 / 3993	[5 -1 3 0 -3⟩	3.0323
vishdel	5632 / 5625	[9 -2 -4 0 1⟩	2.1531
sesdecal	234375 / 234256	[-4 1 7 0 -4⟩	0.87923
hemigail	43923 / 43904	[-7 1 0 -3 4⟩	0.74905
lehmerisma	3025 / 3024	[-4 -3 2 -1 2⟩	0.57240
kalisma, Gauss' comma	9801 / 9800	[-3 4 -2 -2 2⟩	0.17665
odiheim	151263 / 151250	[-1 2 -4 5 -2⟩	0.14879
parimo	1771561 / 1771470	[-1 -11 -1 0 6⟩	0.088931
ultimo	3294225 / 3294172	[-2 2 2 -7 4⟩	0.027854

13-limit commas

Name	Ratio	Monzo	Cents
tunbarsma	625 / 624	[-4 -1 4 0 0 -1⟩	2.7722
island comma	676 / 675	[2 -3 -2 0 0 2⟩	2.5629
squbema	729 / 728	[-3 6 0 -1 0 -1⟩	2.3764
petrma	2200 / 2197	[3 0 2 0 1 -3⟩	2.3624
nicola	1575 / 1573	[0 2 2 1 -2 -1⟩	2.1998
sinbadma	1001 / 1000	[-3 0 -3 1 1 1⟩	1.7303
cantonisma	10985 / 10976	[-5 0 1 -3 0 3⟩	1.4190
lummic	1716 / 1715	[2 1 -1 -3 1 1⟩	1.0092
ibnsinma	2080 / 2079	[5 -3 1 -1 -1 1⟩	0.83252
schismina	4096 / 4095	[12 -2 -1 -1 0 -1⟩	0.42272
leprechaun comma	4225 / 4224	[-7 -1 2 0 -1 2⟩	0.40981
jacobin	6656 / 6655	[9 0 -1 0 -3 1⟩	0.26012
harmonisma	10648 / 10647	[3 -2 0 -1 3 -2⟩	0.16260
chalmersima	123201 / 123200	[-6 6 -2 -1 -1 2⟩	0.014052

17-limit commas

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

19-limit commas

Name	Ratio	Monzo	Cents
undevicesimal, Boethius', Hunt 19-minor mediant comma	513 / 512	[-9 3 0 0 0 0 0 1⟩	3.3781
password	1216 / 1215	[6 -5 -1 0 0 0 0 1⟩	1.4243
Blumeyer comma	2432 / 2431	[7 0 0 0 -1 -1 -1 1⟩	0.71200
19-limit decimill	165376 / 165375	[9 -3 -3 -2 0 0 1 1⟩	0.010469