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 comma; for commas in between 30 and 100 cents in size, see Medium comma; and for commas over 3.5 cents in size, see Small comma.

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.

List of commas, by prime limit

3-limit commas

See also: Table of 3-limit commas

Name(s)	Color Name		Monzo	Cents	Denomination
359-comma	Wa-359	w-359	[-569 359⟩	1.8453
Sasktel comma	Wa-306	w-306	[485 -306⟩	1.7697
Satanic comma	Wa-665	w-665	[-1054 665⟩	0.075575
15601-comma	Wa-15601	w-15601	[24727 -15601⟩	0.031499
31867-comma	Wa-31867	w-31867	[-50508 31867⟩	0.012577
Archangelic comma	Wa-190537 comma	w-190537	[301994 -190537⟩	0.000112	Aura (2022)

5-limit commas

See also: Table of 5-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents	Denomination
Dodifo comma	Quadla-sepquinyo	L4y35-9		[-67 -9 35⟩	3.3850
Vishnuzma, semisuper comma	Sasepbigu	sg144	6115295232/6103515625	[23 6 -14⟩	3.3380
Enneadeca, 19-tone-comma	Neyo	y19-4	19073486328125/19042491875328	[-14 -19 19⟩	2.8155
Vavoom comma	Quinla-seyo	L5y17-7		[-68 18 17⟩	2.5232
Tricot comma	Quadsa-triyo	s4y33	68719476736000/68630377364883	[39 -29 3⟩	2.2461
Schisma	Layo	Ly-2	32805/32768	[-15 8 1⟩	1.9537
Counterschisma	Tribilagu	L6g-5		[-69 45 -1⟩	1.6613
Septendecima	Lala-sebiyo	LLy34-8		[-52 -17 34⟩	1.4313
Luna comma, hemithirds comma	Sasa-quintrigu	ssg155	274877906944/274658203125	[38 -2 -15⟩	1.3843
Minortone comma, minortonma	Trila-segu	L3g172		[-16 35 -17⟩	1.0919
Ennealimma	Satritribiyo	sy18-3	7629394531250/7625597484987	[1 -27 18⟩	0.86183	Paul Erlich, Gene Ward Smith (2001)
Astro comma	Tribisa-thiwegu	s6g3110		[91 -12 -31⟩	0.81486
Gaster	Quadbila-negu	L8g19-3		[-70 72 -19⟩	0.79950
Kwazy	Quadla-quadquadyo	L4y16-6		[-53 10 16⟩	0.56943
Whoosh	Saletrigu	sg337		[37 25 -33⟩	0.52246
Egads	Setriyo	y51-9		[-36 -52 51⟩	0.33936
Monzisma	Quinsa-yoyo	s5yy4		[54 -37 2⟩	0.29240	Margo Schulter (2001)
Fortune	Tritrila-sepbiyo	L9y14-9		[-107 47 14⟩	0.27703
Gross	Quinbisa-fosegu	s10g4715		[144 -22 -47⟩	0.24543
Senior	Quadla-sepquingu	L4g354		[-17 62 -35⟩	0.23007
665&3684 comma	Quintritrilayo	L45y-31		[-500 314 1⟩	0.18399
Raider	Tritrisa-thiseyo	s9y371		[71 -99 37⟩	0.062327
Pirate	Quinla-sepsepyo	L5y49-12		[-90 -15 49⟩	0.046966
Viking	Nela-siweyo	L19y61-23		[-251 69 61⟩	0.031605
Kirnberger's atom	Sepbisa-quadtrigu	s14g1212		[161 -84 -12⟩	0.015361
Selenia				[-433 -137 280⟩	0.0047636
Titania				[2746 -521 -827⟩	0.0031829
Quark	Twethebila-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	Denomination
Decovulture comma	Sasa-birugugu	ssrrg42	67108864/66976875	[26 -7 -4 -2⟩	3.4083	Xenllium (2021)
Rainy comma	Laquinzo-atriyo	Lz5y32	2100875/2097152	[-21 0 3 5⟩	3.0706	+merlan #flirora (2020)
Pontiqak comma	Lazozotritriyo	Lzzy9-2	95703125/95551488	[-17 -6 9 2⟩	2.7452	Xenllium (2021)
Pessoalisma			2147483648/2144153025	[31 -6 -2 -6⟩	2.6871	Aura (2023)
Mitonisma	Laquadzo-agu	Lz4g2	5250987/5242880	[-20 7 -1 4⟩	2.6749	Xenllium (2021)
Horwell	Lazoquinyo	Lzy5-2	65625/65536	[-16 1 5 1⟩	2.3495
Forge comma			1640558367/163840000	[-19 14 -5 3⟩	2.2792	Aura (2022)
Neptunisma	Laruruleyo	Lrry11-4	48828125/48771072	[-12 -5 11 -2⟩	2.0240	Xenllium (2021)
Septiennealimma	Tritrizo	z95	40353607/40310784	[-11 -9 0 9⟩	1.8382	Eliora, Flora Canou (2021)
Meter	Latriru-asepyo	Lr3y7-4	703125/702464	[-11 2 7 -3⟩	1.6283
Skeetsma	Lala-rutrigu	LLrg3-2	14348907/14336000	[-14 15 -3 -1⟩	1.5580	Jerdle (2021)
Wizma	Quinzo-ayoyo	z5yy3	420175/419904	[-6 -8 2 5⟩	1.1170
Supermatertisma	Lasepru-atritriyo	Lr7y9-6	52734375/52706752	[-6 3 9 -7⟩	0.90708	Xenllium (2021)
Trienstonisma	Laquinru-agu	Lr5g-4	43046721/43025920	[-9 16 -1 -5⟩	0.83677	Xenllium (2021)
Breedsma	Bizozogu	z4gg3	2401/2400	[-5 -1 -2 4⟩	0.72120
171-9/7-comma	Quadtribisa-netritrizo			[62 -342 0 171⟩	0.61971
Supermasesquartisma	Laquadbiru-aquinyo	Lr8y5-6	184528125/184473632	[-5 10 5 -8⟩	0.51133	Xenllium (2021)
571-7-comma				[1603 0 0 -571⟩	0.40741
Ragisma	Zoquadyo	zy41	4375/4374	[-1 -7 4 1⟩	0.39576
Septiruthenia	Nela-lequadzo	L19z448		[-263 88 0 44⟩	0.37996	Eliora (2022)
Akjaysma	Trisa-seprugu	s3r7g71		[47 -7 -7 -7⟩	0.33765
Landscape comma	Trizogugu	z3g63	250047/250000	[-4 6 -6 3⟩	0.32544
Izar comma, bapbo schismina	Saquadtrizo-asepgu	sz12g78	13841287201/13839609375	[0 -11 -7 12⟩	0.20987
Nanisma	Quinbisaru	s10r7		[109 -67 0 -1⟩	0.18904
laleruyo (171&1547&3125)	Laleruyo	Lr11y11-8	3955078125/3954653486	[-1 4 11 -11⟩	0.18588
87-fold starling comma	Twenetri-zotrigu			[86 174 -261 87⟩	0.14469
Starscape comma	Latritriru-ayo	Lr9y-6	645700815/645657712	[-4 17 1 -9⟩	0.11557
quinla-zoyoyo (12&53&612)	Quinla-zoyoyo	L5zzy-4		[-55 30 2 1⟩	0.10336
Euzenius comma	Sabiruquinyo	srry10-3	78125000/78121827	[3 -13 10 -2⟩	0.070314
171&1547&4973 comma	Satwethezo-atritribigu	sz23g1815		[1 -15 -18 23⟩	0.023986
trisa-quinbiru-agu (441&1848&3125)	Trisa-quinbiru-agu	s3r10g-3		[51 -13 -1 -10⟩	0.012210
Termite	Satritribiru-athiseyo	sr18y37-14		[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	Denomination
Swetisma	Lururuyo	1urry-2	540/539	[2 3 1 -2 -1⟩	3.2090
Wizardharry	Triluyo	1u3y31	4000/3993	[5 -1 3 0 -3⟩	3.0323
Symbiotic comma	Salozo	s1oz2	19712/19683	[8 -9 0 1 1⟩	2.5488	Aura (2020)
Vishdel	Saloquadgu	s1og42	5632/5625	[9 -2 -4 0 1⟩	2.1531
Nexus comma, nexisma	Tribilo	1o6-2	1771561/1769472	[-16 -3 0 0 6⟩	2.0427	Aura (2020)
Tinge	Lolotrizo	1ooz32	41503/41472	[-9 -4 0 3 2⟩	1.2936	Gayle Young (2018), Todd Harrop (2020)
Olympia	Salururu	s1urr1	131072/130977	[17 -5 0 -2 -1⟩	1.2552	Flora Canou (2021)
11-cycle schisma, 37-11-comma	Quinsa-thiselu	s51u379		[128 0 0 0 -37⟩	1.2361
Undecimal hemifourths comma	Bilozogugu	1oozzg42	160083/160000	[-8 3 -4 2 2⟩	0.89784
Sesdecal	Laquadlu-asepyo	L1u4y7-2	234375/234256	[-4 1 7 0 -4⟩	0.87923
Frameshift comma	Quadla-trilu	L41u3-3		[-34 28 0 0 -3⟩	0.78620	Aura (2021)
Hemigail	Quadlo-atriru	1o4r3-3	43923/43904	[-7 1 0 -3 4⟩	0.74905
Lehmerisma	Loloruyoyo	1ooryy-2	3025/3024	[-4 -3 2 -1 2⟩	0.57240
Quartisma	Saquinlu-azo	s1u5z3	117440512/117406179	[24 -6 0 1 -5⟩	0.50619	Aura (2020)
Kalisma, Gauss' comma	Bilorugu	1oorrgg-2	9801/9800	[-3 4 -2 -2 2⟩	0.17665	Margo Schulter (2000)
Odiheim	Luluquinzo-aquadgu	1uuz5g44	151263/151250	[-1 2 -4 5 -2⟩	0.14879
Parimo	Satribilo-agu	s1o6g1	1771561/1771470	[-1 -11 -1 0 6⟩	0.088931
Parisma	Laquadlu-arurugu	L1u4rrg-2	14348907/14348180	[-2 15 -1 -2 -4⟩	0.087717
Ultimo	Quadlo-asepru-ayoyo	1o4r7yy-5	3294225/3294172	[-2 2 2 -7 4⟩	0.027854
Parismina	Sasa-quinbilo-azozo	ss1o10zz2		[1 -26 0 2 10⟩	0.0012141

13-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents	Denomination
Wilschisma	Sathoyo	s3oy2	532480/531441	[13 -12 1 0 0 1⟩	3.3814	Flora Canou (2021)
Bean	Sathuquinlu	s3u1u52	2097152/2093663	[21 0 0 0 -5 -1⟩	2.8826
Tunbarsma	Thuquadyo	3uy4-2	625/624	[-4 -1 4 0 0 -1⟩	2.7722
Island comma	Bithogu	3oogg2	676/675	[2 -3 -2 0 0 2⟩	2.5629
Squbema	Lathuru	L3ur-2	729/728	[-3 6 0 -1 0 -1⟩	2.3764
Petrma	Trithu-aloyoyo	3u31oyy-2	2200/2197	[3 0 2 0 1 -3⟩	2.3624
Nicola	Thululuzoyoyo	3u1uuzyy1	1575/1573	[0 2 2 1 -2 -1⟩	2.1998
Sinbadma	Tholozotrigu	3o1ozg32	1001/1000	[-3 0 -3 1 1 1⟩	1.7303
Cantonisma	Trithoru-ayo	3o3r3y-2	10985/10976	[-5 0 1 -3 0 3⟩	1.4190
Lummic comma	Tholotriru-agu	3o1or3g-2	1716/1715	[2 1 -1 -3 1 1⟩	1.0092
Ibnsinma	Tholuruyo	3o1ury1	2080/2079	[5 -3 1 -1 -1 1⟩	0.83252	Margo Schulter (2012)
Phaotic comma, phaotisma	Sathotriyo	s3uy31	256000/255879	[11 -9 3 0 0 -1⟩	0.81847	Aura (2021)
Schismina	Sathurugu	s3urg1	4096/4095	[12 -2 -1 -1 0 -1⟩	0.42272
Leprechaun comma	Thotholuyoyo	3oo1uyy1	4225/4224	[-7 -1 2 0 -1 2⟩	0.40981	Margo Schulter (2012)
Jacobin comma	Thotrilu-agu	3o1u3g2	6656/6655	[9 0 -1 0 -3 1⟩	0.26012
Harmonisma	Thuthutrilo-aru	3uu1o3r-2	10648/10647	[3 -2 0 -1 3 -2⟩	0.16260	Margo Schulter (2002)
Pentonisma	Saquinthuzogu	s3u5z5g54		[24 -5 -5 5 0 -5⟩	0.14765	Xenllium (2022)
Chalmersia	Lathotholurugugu	L3oo1urgg1	123201/123200	[-6 6 -2 -1 -1 2⟩	0.014052	Gene Ward Smith (2003)

17-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents	Denomination
Dakotisma			595/594	[-1 -3 1 1 -1 0 1⟩	2.9121	Praveen Venkataramana (2022)
September comma	Sutholoruyo	17u3o1ory-2	715/714	[-1 -1 1 -1 1 1 -1⟩	2.4230	Scott Dakota (2021)
Horizma, horizon comma	Sothuzozo	17o3uzz2	833/832	[-6 0 0 2 0 -1 1⟩	2.0796	Jerdle (2021)
Ainos comma, ainma	Sutholugu	17u3o1ug1	936/935	[3 2 -1 0 -1 1 -1⟩	1.8506	Aura (2020)
Fidesma			2025/2023	[0 4 2 -1 0 0 -2⟩	1.7107	Aura (2023)
Twosquare comma	Sulolo	17u1oo-2	1089/1088	[-6 2 0 0 2 0 -1⟩	1.5905	Kaiveran (2018)
Quadrantonisma	Sosolurugu	17oo1urg2	1156/1155	[2 -1 -1 -1 -1 0 2⟩	1.4983	Flora Canou (2023)
Noellisma	Subizoyo	17uzzyy1	1225/1224	[-3 -2 2 2 0 0 -1⟩	1.4138	Flora Canou (2022)
Palingenetic comma, palingenesis			1701/1700	[-2 5 -2 1 0 0 -1⟩	1.0181	Aura (2021)
Xenisma	Sululutrizo	17u1uuz32	2058/2057	[1 1 0 3 -2 0 -1⟩	0.84143	Margo Schulter (2000)
Cyclops comma			11016/11011	[3 4 0 -1 -2 -1 1⟩	0.78596	Eliora (2022)
Sperasma			2500/2499	[2 -1 4 -2 0 0 -1⟩	0.69263	Aura (2023)
Sextantonisma	Sosothugugu	17oo3ugg2	2601/2600	[-3 2 -2 0 0 -1 2⟩	0.66573	Flora Canou (2023)
Chlorisma	Sutriru	17ur3-3	5832/5831	[3 6 0 -3 0 0 -1⟩	0.29688	Jerdle (2021)
(18/17)11(16/15) comma	Lalesu-agu	L17u11g-7		[14 21 -1 0 0 0 -11⟩	0.23180
Flashma	Sotholuzotrigu	17o3o1uzg33	12376/12375	[3 -2 -3 1 -1 1 1⟩	0.13989	Kaiveran (2016)
Sparkisma	Sululuruyoyo	17u1uuryy-2	14400/14399	[6 2 2 -1 -2 0 -1⟩	0.12023	Kaiveran (2016)
Scintillisma	Lasuthuluquadzo-agu	L17u3u1uz4g2	194481/194480	[-4 4 -1 4 -1 -1 -1⟩	0.0089018	Margo Schulter (2012)

19-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents	Denomination
Undevicesimal comma, undevicesimal schisma, Boethius' comma, Hunt 19-minor mediant comma	Lano	L19o1	513/512	[-9 3 0 0 0 0 0 1⟩	3.3780	Plainsound Music Edition (2020)
Password, Eratosthenes' comma	Sanogu	s19og2	1216/1215	[6 -5 -1 0 0 0 0 1⟩	1.4243
Aureusma	Nunusosoyo	19uu17ooy1	1445/1444	[-2 0 1 0 0 0 2 -2⟩	1.1985	Flora Canou (2021)
Pinkanberry	Nuthothogu	19u3o3og1	1521/1520	[-4 2 -1 0 0 2 0 -1⟩	1.1386	Kaiveran (2021)
Ramanujanisma	Nothozo	19o3oz2	1729/1728	[-6 -3 0 1 0 1 0 1⟩	1.0016	Frédéric Gagné (2021)
Blumeyer comma	Nosuthulu	19o17u3u1u1	2432/2431	[7 0 0 0 -1 -1 -1 1⟩	0.71200	Douglas Blumeyer (2015)
BMO schismina	Sabinothu	s19oo3uu2	369664/369603	[10 -7 0 0 0 -2 0 2⟩	0.28570
Frouggie comma	Nusuquinthu-aquadlo	19u17u3u51o4-3	119939072/119927639	[13 0 0 0 4 -5 -1 -1⟩	0.16503
Pollar comma	Nunusuquintho-alulu	19uu17u3o51uu1	742586/742577	[1 0 0 0 -2 5 -1 -2⟩	0.020982
Decimillisma, 19-limit decimill	Sanosorurutrigu	s19o17orrg32	165376/165375	[9 -3 -3 -2 0 0 1 1⟩	0.010469

23-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents	Denomination
Worcester comma	Twethugugu	23ugg1	576/575	[6 2 -2 0 0 0 0 0 -1⟩	3.00823	Kaiveran (2023)
Kaifsma	Twethunosutholuzozogu	23u19o17u3o1uzzg2	193648/193545	[4 -2 -1 2 -1 1 -1 1 -1⟩	0.92108	Kaiveran (2022)

Higher-limit commas

Name(s)	Color Name		Ratio	Monzo	Cents	Denomination
Cmloegcmluinisma (/ˈʃmlɛg.ʃmlɪ.nɪs.mə/)	Twenutwethonu	29u23o19u1	552/551	2.3.19.23.29 [3 1 -1 1 -1⟩	3.13914	Douglas Blumeyer (2021)
Owowhatsthisma	Thiwutwethogu	31u23og2	621/620	2.3.5.23.31 [-2 3 -1 1 -1⟩	2.79006	HEHEHE I AM A SUPAHSTAR SAGA (2021)
Minimyna	Thisunulo	37u19u1o-2	704/703	2.11.19.37 [6 1 -1 -1⟩	2.46088	Kaiveran (2023)
Eroğluisma	Bifowutweno	41uu29oo2	1682/1681	2.29.41 [1 2 -2⟩	1.02958	Douglas Blumeyer (2021)
Misericorde	Thisuthulozoyoyo	37u3u1ozyy-2	1925/1924	2.5.7.11.13.37 [-2 2 1 1 -1 -1⟩	0.89958	Kaiveran (2023)
Yunzee comma	Lathiwuzozo	L31uzz2	3969/3968	2.3.7.31 [-7 4 2 -1⟩	0.43624	Kaiveran (2021)
Pulsar comma			7777/7776	2.3.7.11.101 [-5 -5 1 1 1⟩	0.22262	Eliora (2022)
Palimilli		1003001o23o1u1	23069023/23068672	2.11.23.1003001 [-21 -1 1 1⟩	0.026341	Kaiveran (2021)