Unnoticeable comma: Difference between revisions

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→7-limit commas: incoporate the neologisms
→17-limit commas: +595/594, +1701/1700
Line 806: Line 806:
! Monzo
! Monzo
! Cents
! Cents
|-
| dakotisma
|
|
| [[595/594]]
| {{monzo| -1 -3 1 1 -1 0 1 }}
| 2.9121
|-
|-
| september comma, septendecimal bridge comma
| september comma, septendecimal bridge comma
| Sutholoruyo
| Sutholoruyo
|17u3o1ory-2
| 17u3o1ory-2
| [[715/714]]
| [[715/714]]
| {{monzo| -1 -1 1 -1 1 1 -1 }}
| {{monzo| -1 -1 1 -1 1 1 -1 }}
Line 816: Line 823:
| horizon comma
| horizon comma
| Sothuzozo
| Sothuzozo
|17o3uzz2
| 17o3uzz2
| [[833/832]]
| [[833/832]]
| {{monzo| -6 0 0 2 0 -1 1 }}
| {{monzo| -6 0 0 2 0 -1 1 }}
Line 823: Line 830:
| ainos comma, ainma
| ainos comma, ainma
| Sutholugu
| Sutholugu
|17u3o1ug1
| 17u3o1ug1
| [[936/935]]
| [[936/935]]
| {{monzo| 3 2 -1 0 -1 1 -1 }}
| {{monzo| 3 2 -1 0 -1 1 -1 }}
Line 830: Line 837:
| twosquare comma
| twosquare comma
| Sulolo
| Sulolo
|17u1oo-2
| 17u1oo-2
| [[1089/1088]]
| [[1089/1088]]
| {{monzo| -6 2 0 0 2 0 -1 }}
| {{monzo| -6 2 0 0 2 0 -1 }}
Line 837: Line 844:
| septendecimal quartertones comma
| septendecimal quartertones comma
| Sosolurugu
| Sosolurugu
|17oo1urg2
| 17oo1urg2
| [[1156/1155]]
| [[1156/1155]]
| {{monzo| 2 -1 -1 -1 -1 0 2 }}
| {{monzo| 2 -1 -1 -1 -1 0 2 }}
Line 844: Line 851:
| noellisma
| noellisma
| Subizoyo
| Subizoyo
|17uzzyy1
| 17uzzyy1
| [[1225/1224]]
| [[1225/1224]]
| {{monzo| -3 -2 2 2 0 0 -1 }}
| {{monzo| -3 -2 2 2 0 0 -1 }}
Line 851: Line 858:
|  
|  
| Sothubiruyo
| Sothubiruyo
|17o3urryy-2
| 17o3urryy-2
| 1275/1274
| 1275/1274
| {{monzo| -1 1 2 -2 0 -1 1 }}
| {{monzo| -1 1 2 -2 0 -1 1 }}
| 1.3584
| 1.3584
|-
| palingenetic comma
|
|
| [[1701/1700]]
| {{monzo| -2 5 -2 1 0 0 1 }}
| 1.0181
|-
|-
| xenisma
| xenisma
| Sululutrizo
| Sululutrizo
|17u1uuz<sup>3</sup>2
| 17u1uuz<sup>3</sup>2
| 2058/2057
| 2058/2057
| {{monzo| 1 1 0 3 -2 0 -1 }}
| {{monzo| 1 1 0 3 -2 0 -1 }}
Line 865: Line 879:
|
|
| Sothologu
| Sothologu
|17o3o1og2
| 17o3o1og2
| 2431/2430
| 2431/2430
| {{monzo| -1 -5 -1 0 1 1 1 }}
| {{monzo| -1 -5 -1 0 1 1 1 }}
Line 872: Line 886:
| septendecimal six-tones comma
| septendecimal six-tones comma
| Sosothugugu
| Sosothugugu
|17oo3ugg2
| 17oo3ugg2
| [[2601/2600]]
| [[2601/2600]]
| {{monzo| -3 2 -2 0 0 -1 2 }}
| {{monzo| -3 2 -2 0 0 -1 2 }}
Line 879: Line 893:
| chlorisma
| chlorisma
| Sutriru
| Sutriru
|17ur<sup>3</sup>-3
| 17ur<sup>3</sup>-3
| [[5832/5831]]
| [[5832/5831]]
| {{monzo| 3 6 0 -3 0 0 -1 }}
| {{monzo| 3 6 0 -3 0 0 -1 }}
| 0.29688
| 0.29688
|-
|-
| (18/17)<sup>11</sup>(16/15) comma
| (18/17)<sup>11</sup>(16/15) comma
| Lalesu-agu
| Lalesu-agu
|L17u<sup>11</sup>g-7
| L17u<sup>11</sup>g-7
|  
|  
| {{monzo| 14 21 -1 0 0 0 -11 }}
| {{monzo| 14 21 -1 0 0 0 -11 }}
| 0.23180
| 0.23180
|-
|-
| flashma
| [[flashma]]
| Sotholuzotrigu
| Sotholuzotrigu
|17o3o1uzg<sup>3</sup>3
| 17o3o1uzg<sup>3</sup>3
| 12376/12375
| 12376/12375
| {{monzo| 3 -2 -3 1 -1 1 1 }}
| {{monzo| 3 -2 -3 1 -1 1 1 }}
Line 901: Line 914:
| [[sparkisma]]
| [[sparkisma]]
| Sululuruyoyo
| Sululuruyoyo
|17u1uuryy-2
| 17u1uuryy-2
| 14400/14399
| 14400/14399
| {{monzo| 6 2 2 -1 -2 0 -1 }}
| {{monzo| 6 2 2 -1 -2 0 -1 }}
Line 908: Line 921:
| scintillisma
| scintillisma
| Lasuthuluquadzo-agu
| Lasuthuluquadzo-agu
|L17u3u1uz<sup>4</sup>g2
| L17u3u1uz<sup>4</sup>g2
| 194481/194480
| 194481/194480
| {{monzo| -4 4 -1 4 -1 -1 -1 }}
| {{monzo| -4 4 -1 4 -1 -1 -1 }}

Revision as of 11:49, 11 November 2022

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.

3-limit commas

Name(s) Color name Monzo Cents
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

5-limit commas

Name(s) Color name Ratio Monzo Cents
dodifo Quadla-sepquinyo L4y35-9 [-67 -9 35⟩ 3.3850
vishnuzma, semisuper 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
hemithirds comma, lunama 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
astro Tribisa-thiwegu s6g3110 [91 -12 -31⟩ 0.81486
gaster comma 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
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
decovulture Sasa-birugugu ssrrg42 67108864/66976875 [26 -7 -4 -2⟩ 3.4083
lux Sasa-quinru-ayoyo ssr5yy-2 26843545600/26795786661 [30 -13 2 -5⟩ 3.0829
rainy Laquinzo-atriyo Lz5y32 2100875/2097152 [-21 0 3 5⟩ 3.0706
pontiqak Lazozotritriyo Lzzy9-2 95703125/95551488 [-17 -6 9 2⟩ 2.7452
mitonisma Laquadzo-agu Lz4g2 5250987/5242880 [-20 7 -1 4⟩ 2.6749
horwell Lazoquinyo Lzy5-2 65625/65536 [-16 1 5 1⟩ 2.3495
forge comma 1640558367/163840000 [-19 14 -5 3⟩ 2.2792
neptunisma Laruruleyo Lrry11-4 48828125/48771072 [-12 -5 11 -2⟩ 2.0240
septiennealimma Tritrizo z95 40353607/40310784 [-11 -9 0 9⟩ 1.8382
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
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
trienstonisma Laquinru-agu Lr5g-4 43046721/43025920 [-9 16 -1 -5⟩ 0.83677
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
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
akjaysma, 5\7 octave comma Trisa-seprugu s3r7g71 [47 -7 -7 -7⟩ 0.33765
landscape Trizogugu z3g63 250047/250000 [-4 6 -6 3⟩ 0.32544
izar, 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 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 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
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, symbiosma Salozo s1oz2 19712/19683 [8 -9 0 1 1⟩ 2.5488
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⟩ 2.04265
tinge Lolotrizo 1ooz32 41503/41472 [-9 -4 0 3 2⟩ 1.29360
olympia Salururu s1urr1 131072/130977 [17 -5 0 -2 -1⟩ 1.25524
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
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
kalisma, Gauss' comma Bilorugu 1oorrgg-2 9801/9800 [-3 4 -2 -2 2⟩ 0.17665
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 Color name Ratio Monzo Cents
wilschisma Sathoyo s3oy2 532480/531441 [13 -12 1 0 0 1⟩ 3.3814
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 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
phaotic, phaotisma Sathotriyo s3uy31 256000/255879 [11 -9 3 0 0 -1⟩ 0.81847
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
jacobin 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
pentonisma Saquinthuzogu s3u5z5g54 [24 -5 -5 5 0 -5⟩ 0.14765
chalmersia Lathotholurugugu L3oo1urgg1 123201/123200 [-6 6 -2 -1 -1 2⟩ 0.014052

17-limit commas

Name Color name Ratio Monzo Cents
dakotisma 595/594 [-1 -3 1 1 -1 0 1⟩ 2.9121
september comma, septendecimal bridge comma Sutholoruyo 17u3o1ory-2 715/714 [-1 -1 1 -1 1 1 -1⟩ 2.4230
horizon comma Sothuzozo 17o3uzz2 833/832 [-6 0 0 2 0 -1 1⟩ 2.0796
ainos comma, ainma Sutholugu 17u3o1ug1 936/935 [3 2 -1 0 -1 1 -1⟩ 1.8506
twosquare comma Sulolo 17u1oo-2 1089/1088 [-6 2 0 0 2 0 -1⟩ 1.5905
septendecimal quartertones comma Sosolurugu 17oo1urg2 1156/1155 [2 -1 -1 -1 -1 0 2⟩ 1.4983
noellisma Subizoyo 17uzzyy1 1225/1224 [-3 -2 2 2 0 0 -1⟩ 1.4138
Sothubiruyo 17o3urryy-2 1275/1274 [-1 1 2 -2 0 -1 1⟩ 1.3584
palingenetic comma 1701/1700 [-2 5 -2 1 0 0 1⟩ 1.0181
xenisma Sululutrizo 17u1uuz32 2058/2057 [1 1 0 3 -2 0 -1⟩ 0.84143
Sothologu 17o3o1og2 2431/2430 [-1 -5 -1 0 1 1 1⟩ 0.71230
septendecimal six-tones comma Sosothugugu 17oo3ugg2 2601/2600 [-3 2 -2 0 0 -1 2⟩ 0.66573
chlorisma Sutriru 17ur3-3 5832/5831 [3 6 0 -3 0 0 -1⟩ 0.29688
(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
sparkisma Sululuruyoyo 17u1uuryy-2 14400/14399 [6 2 2 -1 -2 0 -1⟩ 0.12023
scintillisma Lasuthuluquadzo-agu L17u3u1uz4g2 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 L19o1 513/512 [-9 3 0 0 0 0 0 1⟩ 3.3780
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
pinkanberry Nuthothogu 19u3o3og1 1521/1520 [-4 2 -1 0 0 2 0 -1⟩ 1.1386
ramanujanisma Nothozo 19o3oz2 1729/1728 [-6 -3 0 1 0 1 0 1⟩ 1.0016
Blumeyer comma Nosuthulu 19o17u3u1u1 2432/2431 [7 0 0 0 -1 -1 -1 1⟩ 0.71200
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

Higher-limit commas

Name Color name Ratio Monzo Cents
cmloegcmluinisma (/ˈʃmlɛg.ʃmlɪ.nɪs.mə/) Twenutwethonu 29u23o19u1 552/551 [3 1 0 0 0 0 0 -1 1 -1⟩ 3.139138
owowhatsthisma Thiwutwethogu 31u23og2 621/620 [-2 3 -1 0 0 0 0 0 1 0 -1⟩ 2.79006
eroğluisma Bifowutweno 41uu29oo2 1682/1681 [1 0 0 0 0 0 0 0 0 2 0 0 -2⟩ 1.029577
kaifsma Twethunosutholuzozogu 23u19o17u3o1uzzg2 193648/193545 [4 -2 -1 2 -1 1 -1 1 -1⟩ 0.92108
yunzee comma Lathiwuzozo L31uzz2 3969/3968 [-7 4 0 2 0 0 0 0 0 0 -1⟩ 0.43624
palimilli 1003001o23o1u1 23069023/23068672 2-21 * 11-1 * 23 * 1003001 0.026341
  1. ↑ The Helmholtz-Ellis JI Pitch Notation (HEJI)
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