Revision as of 12:39, 25 October 2018
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.
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.
3-limit commas
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| Sasktel comma, 51-Pythagorean comma
|
|
[485 -306⟩
|
1.7697
|
| Satanic comma
|
|
[-1054 665⟩
|
0.075575
|
5-limit commas
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| dodifo
|
|
[-67 -9 35⟩
|
3.3850
|
| vishnuzma, semisuper
|
6115295232 / 6103515625
|
[23 6 -14⟩
|
3.3380
|
| enneadeca, 19-tone-comma
|
19073486328125 / 19042491875328
|
[-14 -19 19⟩
|
2.8155
|
| vavoom
|
|
[-68 18 17⟩
|
2.5232
|
| tricot comma
|
68719476736000 / 68630377364883
|
[39 -29 3⟩
|
2.2461
|
| schisma
|
32805 / 32768
|
[-15 8 1⟩
|
1.9537
|
| counterschisma
|
|
[-69 45 -1⟩
|
1.6613
|
| ? (schisma minus the 306–comma, tempered out in 665edo)
|
|
[-500 314 1⟩
|
1.000106
|
| septendecima
|
|
[-52 -17 34⟩
|
1.4313
|
| hemithirds comma, lunama
|
274877906944 / 274658203125
|
[38 -2 -15⟩
|
1.3843
|
| minortone comma
|
50031545098999707 / 50000000000000000
|
[-16 35 -17⟩
|
1.0919
|
| Ennealimmal
|
7629394531250 / 7625597484987
|
[1 -27 18⟩
|
0.86183
|
| astro
|
|
[91 -12 -31⟩
|
0.81486
|
| kwazy
|
9010162353515625 / 9007199254740992
|
[-53 10 16⟩
|
0.56943
|
| whoosh
|
|
[37 25 -33⟩
|
0.52246
|
| egads
|
|
[-36 -52 51⟩
|
0.33936
|
| monzisma
|
450359962737049600 / 450283905890997363
|
[54 -37 2⟩
|
0.29240
|
| fortune
|
|
[-107 47 14⟩
|
0.27703
|
| gross
|
|
[144 -22 -47⟩
|
0.24543
|
| senior
|
|
[-17 62 -35⟩
|
0.23007
|
| raider
|
|
[71 -99 37⟩
|
0.062327
|
| pirate
|
|
[-90 -15 49⟩
|
0.046966
|
| viking
|
|
[-251 69 61⟩
|
0.031605
|
| atom
|
|
[161 -84 -12⟩
|
0.015361
|
| selenia
|
|
[-433 -137 280⟩
|
0.0047636
|
| titania
|
|
[2746 -521 -827⟩
|
0.0031829
|
| quark
|
|
[-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)
|
Ratio
|
Monzo
|
Cents
|
| 44-septimal comma
|
|
[-263 88 0 44⟩
|
0.37996
|
| horwell
|
65625 / 65536
|
[-16 1 5 1⟩
|
2.3495
|
| meter
|
703125 / 702464
|
[-11 2 7 -3⟩
|
1.6283
|
| wizma
|
420175 / 419904
|
[-6 -8 2 5⟩
|
1.1170
|
| breedsma
|
2401 / 2400
|
[-5 -1 -2 4⟩
|
0.72120
|
| ragisma
|
4375 / 4374
|
[-1 -7 4 1⟩
|
0.39576
|
| akjaysma, 5\7 octave comma
|
140737488355328 / 140710042265625
|
[47 -7 -7 -7⟩
|
0.33765
|
| landscape
|
250047 / 250000
|
[-4 6 -6 3⟩
|
0.32544
|
| starscape
|
645700815 / 645657712
|
[-4 17 1 -9⟩
|
0.11557
|
| euzenius
|
78125000 / 78121827
|
[3 -13 10 -2⟩
|
0.070314
|
| termite
|
|
[9 -28 37 -18⟩
|
0.0010723
|
| neutrino
|
|
[1889 -2145 138 424⟩
|
1.6361 × 10-10
|
11-limit commas
| Name(s)
|
Ratio
|
Monzo
|
Cents
|
| 11-cycle schisma, 37-11-comma
|
|
[128 0 0 0 -37⟩
|
1.2361
|
| swetisma
|
540 / 539
|
[2 3 1 -2 -1⟩
|
3.2090
|
| wizardharry
|
4000 / 3993
|
[5 -1 3 0 -3⟩
|
3.0323
|
| vishdel
|
5632 / 5625
|
[9 -2 -4 0 1⟩
|
2.1531
|
| sesdecal
|
234375 / 234256
|
[-4 1 7 0 -4⟩
|
0.87923
|
| hemigail
|
43923 / 43904
|
[-7 1 0 -3 4⟩
|
0.74905
|
| lehmerisma
|
3025 / 3024
|
[-4 -3 2 -1 2⟩
|
0.57240
|
| kalisma, Gauss' comma
|
9801 / 9800
|
[-3 4 -2 -2 2⟩
|
0.17665
|
| odiheim
|
151263 / 151250
|
[-1 2 -4 5 -2⟩
|
0.14879
|
| parimo
|
1771561 / 1771470
|
[-1 -11 -1 0 6⟩
|
0.088931
|
| ultimo
|
3294225 / 3294172
|
[-2 2 2 -7 4⟩
|
0.027854
|
13-limit commas
| Name
|
Ratio
|
Monzo
|
Cents
|
| tunbarsma
|
625 / 624
|
[-4 -1 4 0 0 -1⟩
|
2.7722
|
| island comma
|
676 / 675
|
[2 -3 -2 0 0 2⟩
|
2.5629
|
| squbema
|
729 / 728
|
[-3 6 0 -1 0 -1⟩
|
2.3764
|
| petrma
|
2200 / 2197
|
[3 0 2 0 1 -3⟩
|
2.3624
|
| nicola
|
1575 / 1573
|
[0 2 2 1 -2 -1⟩
|
2.1998
|
| sinbadma
|
1001 / 1000
|
[-3 0 -3 1 1 1⟩
|
1.7303
|
| cantonisma
|
10985 / 10976
|
[-5 0 1 -3 0 3⟩
|
1.4190
|
| lummic
|
1716 / 1715
|
[2 1 -1 -3 1 1⟩
|
1.0092
|
| ibnsinma
|
2080 / 2079
|
[5 -3 1 -1 -1 1⟩
|
0.83252
|
| schismina
|
4096 / 4095
|
[12 -2 -1 -1 0 -1⟩
|
0.42272
|
| leprechaun comma
|
4225 / 4224
|
[-7 -1 2 0 -1 2⟩
|
0.40981
|
| jacobin
|
6656 / 6655
|
[9 0 -1 0 -3 1⟩
|
0.26012
|
| harmonisma
|
10648 / 10647
|
[3 -2 0 -1 3 -2⟩
|
0.16260
|
| chalmersima
|
123201 / 123200
|
[-6 6 -2 -1 -1 2⟩
|
0.014052
|
17-limit commas
| Name
|
Ratio
|
Monzo
|
Cents
|
| xenisma
|
2058 / 2057
|
[1 1 0 3 -2 0 -1⟩
|
0.84143
|
| flashma
|
12376 / 12375
|
[3 -2 -3 1 -1 1 1⟩
|
0.13989
|
| sparkisma
|
14400 / 14399
|
[6 2 2 -1 -2 0 -1⟩
|
0.12023
|
| scintillisma
|
194481 / 194480
|
[-4 4 -1 4 -1 -1 -1⟩
|
0.0089018
|
19-limit commas
| Name
|
Ratio
|
Monzo
|
Cents
|
| Hunt 19-minor mediant comma
|
513 / 512
|
[-9 3 0 0 0 0 0 1⟩
|
3.3781
|
| password
|
1216 / 1215
|
[6 -5 -1 0 0 0 0 1⟩
|
1.4243
|
| Blumeyer comma
|
2432 / 2431
|
[7 0 0 0 -1 -1 -1 1⟩
|
0.71200
|
| 19-limit decimill
|
165376 / 165375
|
[9 -3 -3 -2 0 0 1 1⟩
|
0.010469
|