Unnoticeable comma: Difference between revisions

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clarification of unnoticeable comma
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'''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 [http://musictheory.zentral.zone/huntsystem2.html#2 JND] (just-noticeable difference) of human pitch perception, as illustrated by the research of [[Aaron_Andrew_Hunt|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|microtempering]].
'''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 [http://musictheory.zentral.zone/huntsystem2.html#2 JND] (just-noticeable difference) of human pitch perception, as illustrated by the research of [[Aaron_Andrew_Hunt|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|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 [[Comma|Commas]].
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 [[Comma|Commas]].

Revision as of 06:31, 1 September 2020

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
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