Unnoticeable comma

Revision as of 04:44, 16 August 2023 by Xenllium (talk | contribs)

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

Name(s) Color Name Monzo Cents Named by
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 Marc Jones (1990)
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

Name(s) Color Name Ratio Monzo Cents Named by
Dodifo comma Quadla-sepquinyo L4y35-9 [-67 -9 35 3.3850
Vishnuzma, semisuper comma Sasepbigu sg144 6115295232/6103515625 [23 6 -14 3.3380 Gene Ward Smith (2002)
Enneadeca, 19-tone-comma Neyo y19-4 19073486328125/19042491875328 [-14 -19 19 2.8155 Gene Ward Smith (2002)
Vavoom comma Quinla-seyo L5y17-7 [-68 18 17 2.5232 Paul Erlich (2002)
Tricot comma Quadsa-triyo s4y33 68719476736000/68630377364883 [39 -29 3 2.2461 Paul Erlich (2002)
Schisma Layo Ly-2 32805/32768 [-15 8 1 1.9537 Hermann von Helmholtz, Alexander Ellis (1875)
Counterschisma Tribilagu L6g-5 [-69 45 -1 1.6613 Gene Ward Smith (2003)
Septendecima Lala-sebiyo LLy34-8 [-52 -17 34 1.4313
Luna comma, hemithirds comma Sasa-quintrigu ssg155 274877906944/274658203125 [38 -2 -15 1.3843 Gene Ward Smith (2002)
Minortone comma, minortonma Trila-segu L3g172 [-16 35 -17 1.0919 Gene Ward Smith (2002)
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 Paul Erlich (2002)
Gaster comma Quadbila-negu L8g19-3 [-70 72 -19 0.79950 Xenllium (2022)
Kwazy Quadla-quadquadyo L4y16-6 [-53 10 16 0.56943 Paul Erlich, Gene Ward Smith (2002)
Whoosh Saletrigu sg337 [37 25 -33 0.52246 Paul Erlich (2002)
Egads Setriyo y51-9 [-36 -52 51 0.33936 Paul Erlich (2002)
Monzisma Quinsa-yoyo s5yy4 [54 -37 2 0.29240 Margo Schulter (2001)
Fortune Tritrila-sepbiyo L9y14-9 [-107 47 14 0.27703 Paul Erlich (2002)
Gross Quinbisa-fosegu s10g4715 [144 -22 -47 0.24543 Paul Erlich (2002)
Senior Quadla-sepquingu L4g354 [-17 62 -35 0.23007 Paul Erlich (2002)
Counterquectisma, deltapion Quintritrilayo L45y-31 [-500 314 1 0.18399 Eliora (2023)
Quectisma [554 -351 1 0.10841 CompactStar (2023)
Raider Tritrisa-thiseyo s9y371 [71 -99 37 0.062327 Gene Ward Smith (2002)
Pirate Quinla-sepsepyo L5y49-12 [-90 -15 49 0.046966 Paul Erlich (2002)
Viking Nela-siweyo L19y61-23 [-251 69 61 0.031605 Gene Ward Smith (2002)
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 Named by
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 Sasa-tribiru-agugu ssr6gg-2 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 comma Lazoquinyo Lzy5-2 65625/65536 [-16 1 5 1 2.3495
Forge comma Lala-trizo-aquingu LLz3g52 1640558367/1638400000 [-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 Aaron Krister Johnson (2011)
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 Margo Schulter (2002)
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
Nommisma Quinla-zoyoyo L5zzy-4 [-55 30 2 1 0.10336 Flora Canou (2023)
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 Named by
Swetisma Lururuyo 1urry-2 540/539 [2 3 1 -2 -1 3.2090 Manuel Op de Coul (2004)
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 22876792454961 / 22866405883904 [-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
Syntonisma Trisa-lusepyo s31uy72 83886080000000 / 83881572334857 [30 -27 7 0 -1 0.093031 Xenllium (2023)
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 2541867610898 / 2541865828329 [1 -26 0 2 10 0.0012141

13-limit commas

Name(s) Color Name Ratio Monzo Cents Named by
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 Mike Battaglia (2011)
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 Margo Schulter (2013)
Punctisma Sathutrizogu s3uz3g33 43904/43875 [7 -3 -3 3 0 -1 1.1439 Jerdle, Aura (2023)
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 Gene Ward Smith (2014)
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)
Grossmisma septholo-azogu 3o71o7zg2 [-30 -13 -1 1 7 7 0.016410 Xenllium (2023)
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 Named by
Monardisma, tsaharuk comma Solorugu 17o1org1 561/560 [-4 1 -1 -1 1 0 1 3.0887 Scott Dakota (2023) for monardisma
Dakotisma Soluzoyo 17o1uzy2 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)
Ainisma, ainic comma Sutholugu 17u3o1ug1 936/935 [3 2 -1 0 -1 1 -1 1.8506 Aura (2020)
Fidesma Susuruyoyo 17uuryy-3 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)
Cimbrisma Sothubiruyo 17o3urryy-2 1275/1274 [-1 1 2 -2 0 -1 1 1.3584 Xenllium (2023)
Palingenetic comma, palingenesis Suzogugu 17uzgg1 1701/1700 [-2 5 -2 1 0 0 -1 1.0181 Aura (2021)
Laser comma Lasorutriyo L17ory3-2 57375/57344 [-13 3 3 -1 0 0 1 0.93564 Jerdle (2023)
Xenisma Sululutrizo 17u1uuz32 2058/2057 [1 1 0 3 -2 0 -1 0.84143 Margo Schulter (2000)
Cyclops comma Sothululuru 17o3u1uur1 11016/11011 [3 4 0 -1 -2 -1 1 0.78596 Eliora (2022)
Sperasma Subiruyoyo 17urry4-3 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)
Galileisma Lalesu-agu L17u11g-7 [14 21 -1 0 0 0 -11 0.23180 Xenllium (2023)
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)
Insanobromisma Sepquinsuyoyo 17u35y70-29 [36 -35 70 0 0 0 -35 0.095608 Eliora (2023)
Neuseisma Suquadtho-arugu 17u3o4rg1 28561/28560 [-4 -1 -1 -1 0 4 -1 0.060616 Budjarn Lambeth (2023)
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 Named by
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)[1]
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)
Heartlandisma Nonoloruru 19oo1orr1 3971/3969 [0 -4 0 -2 1 0 0 2 0.87216 Xenllium (2023)
Crawma Nuquadso-atrithu 19u17o43u32 83521/83486 [-1 0 0 0 0 -3 4 -1 0.72564 ground fault (2023)
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
Lakisma Saquadnoso-agu s19o417o4g5 10884540241/10883911680 [-12 -12 -1 0 0 0 4 4 0.09998 +merlan #flirora (2021)
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
Devicisma Nunusothutrilo-azogu 19uu17o3u1o3zg1 633556/633555 [2 -3 -1 1 3 -1 1 -2 0.0027326 Xenllium (2023)

23-limit commas

Name(s) Color Name Ratio Monzo Cents Named by
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 Named by
Lily comma 7936/7921 2.31.89 [8 1 -2 3.27534 Budjarn Lambeth (2023)
Marmosarubra Twenutwethonu 29u23o19u1 552/551 2.3.19.23.29 [3 1 -1 1 -1 3.13914 Budjarn Lambeth (2023)
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)
Molar comma 704969/704000 2.5.11.89 [-9 -3 -1 3 2.38127 Budjarn Lambeth (2023)
Ancient Chinese tempering comma 750/749 2.3.5.7.107 [1 1 3 -1 -1 2.3099
Shaftesburisma Bifowutweno 41uu29oo2 1682/1681 2.29.41 [1 2 -2 1.02958 Budjarn Lambeth (2023)
Misericorde Thisuthulozoyoyo 37u3u1ozyy-2 1925/1924 2.5.7.11.13.37 [-2 2 1 1 -1 -1 0.89958 Kaiveran (2023)
Helevenisma Bitwenosu-alo 29oo17uu1o-2 9251/9248 2.11.17.29 [-5 1 -2 2 0.56151 Zhea Erose (2023)
Yunzee comma Lathiwuzozo L31uzz2 3969/3968 2.3.7.31 [-7 4 2 -1 0.43624 Kaiveran (2021)
Bullionisma 5292/5291 2.3.7.11.13.37 [2 3 2 -1 -1 -1 0.32717 Eliora (2023)
Pulsar comma 101o1oz2 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)
Zudilisma 68630377364883/68630356164608 2.3.7.23.397 [-30 29 -1 -1 -1 0.00053479 Budjarn Lambeth (2023)

Notes