Summary[edit]
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.
List of commas, by prime limit[edit]
3-limit commas[edit]
| name(s)
|
ratio
|
monzo
|
cents
|
| Sasktel comma, 51-Pythagorean comma
|
|
| 485 -306 >
|
1.7697
|
| Satanic comma
|
|
| -1054 665 >
|
0.075575
|
5-limit commas[edit]
| 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 >
|
0.18399
|
| 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
|
| ennealimma
|
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 >
|
0.00088361
|
| scamp
|
|
| -5836 4293 -417 >
|
0.000033472
|
| rover
|
|
| 1634 1502 -1729 >
|
0.000027513
|
| rascal
|
|
| -7470 2791 1312 >
|
0.0000059596
|
7-limit commas[edit]
| 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 >
|
0.00000000016361
|
11-limit commas[edit]
| 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[edit]
| name(s)
|
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[edit]
| name(s)
|
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[edit]
| name(s)
|
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
|