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. (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, Boethius', 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