Unnoticeable comma: Difference between revisions

'''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]].

== 3-limit commas ==

! Name(s)

! Ratio

! Monzo

! Cents

| Sasktel comma, 51-Pythagorean comma

|

| {{Monzo|485 -306}}

| 1.7697

| [[Satanic comma]]

|

| {{Monzo|-1054 665}}

| 0.075575

== 5-limit commas ==

! Name(s)

! Ratio

! Monzo

! Cents

| dodifo

|

| {{Monzo|-67 -9 35}}

| 3.3850

| [[vishnuzma]], semisuper

| 6115295232 / 6103515625

| {{Monzo|23 6 -14}}

| 3.3380

| [[enneadeca]], 19-tone-comma

| 19073486328125 / 19042491875328

| {{Monzo|-14 -19 19}}

| 2.8155

| vavoom

|  

| {{Monzo|-68 18 17}}

| 2.5232

| tricot comma

| 68719476736000 / 68630377364883

| {{Monzo|39 -29 3}}

| 2.2461

| schisma

| 32805 / 32768

| {{Monzo|-15 8 1}}

| 1.9537

| counterschisma

|  

| {{Monzo|-69 45 -1}}

| 1.6613

| ? (schisma minus the 306–comma, tempered out in [[665edo]])

|

| {{Monzo|-500 314 1}}

| 1.000106

| septendecima

|  

| {{Monzo|-52 -17 34}}

| 1.4313

| hemithirds comma, lunama

| 274877906944 / 274658203125

| {{Monzo|38 -2 -15}}

| 1.3843

| minortone comma

| 50031545098999707 / 50000000000000000

| {{Monzo|-16 35 -17}}

| 1.0919

| [[Ennealimmal]]

| 7629394531250 / 7625597484987

| {{Monzo|1 -27 18}}

| 0.86183

| astro

|  

| {{Monzo|91 -12 -31}}

| 0.81486

| kwazy

| 9010162353515625 / 9007199254740992  

| {{Monzo|-53 10 16}}

| 0.56943

| whoosh

|  

| {{Monzo|37 25 -33}}

| 0.52246

| egads

|  

| {{Monzo|-36 -52 51}}

| 0.33936

| monzisma

| 450359962737049600 / 450283905890997363

| {{Monzo|54 -37 2}}

| 0.29240

| fortune

|  

| {{Monzo|-107 47 14}}

| 0.27703

| gross

|  

| {{Monzo|144 -22 -47}}

| 0.24543

| senior

|  

| {{Monzo|-17 62 -35}}

| 0.23007

| raider

|  

| {{Monzo|71 -99 37}}

| 0.062327

| pirate

|  

| {{Monzo|-90 -15 49}}

| 0.046966

| viking

|  

| {{Monzo|-251 69 61}}

| 0.031605

| atom

|  

| {{Monzo|161 -84 -12}}

| 0.015361

| selenia

|  

| {{Monzo|-433 -137 280}}

| 0.0047636

| titania

|  

| {{Monzo|2746 -521 -827}}

| 0.0031829

| quark

|  

| {{Monzo|-573 237 85}}

| 8.8361 × 10^-4

| scamp

|  

| {{Monzo|-5836 4293 -417}}

| 3.3472 × 10^-5

| rover

|  

| {{Monzo|1634 1502 -1729}}

| 2.7513 × 10^-5

| rascal

|  

| {{Monzo|-7470 2791 1312}}

| 5.9596 × 10^-6

== 7-limit commas ==

! Name(s)

! Ratio

! Monzo

! Cents

| 44-septimal comma

|  

| {{Monzo|-263 88 0 44}}

| 0.37996

| horwell

| 65625 / 65536

| {{Monzo|-16 1 5 1}}

| 2.3495

| meter

| 703125 / 702464

| {{Monzo|-11 2 7 -3}}

| 1.6283

| wizma

| 420175 / 419904

| {{Monzo|-6 -8 2 5}}

| 1.1170

| breedsma

| [[2401/2400|2401 / 2400]]

| {{Monzo|-5 -1 -2 4}}

| 0.72120

| ragisma

| 4375 / 4374

| {{Monzo|-1 -7 4 1}}

| 0.39576

| akjaysma, 5\7 octave comma

| 140737488355328 / 140710042265625

| {{Monzo|47 -7 -7 -7}}

| 0.33765

| landscape

| 250047 / 250000

| {{Monzo|-4 6 -6 3}}

| 0.32544

| starscape

| 645700815 / 645657712

| {{Monzo|-4 17 1 -9}}

| 0.11557

| euzenius

| 78125000 / 78121827

| {{Monzo|3 -13 10 -2}}

| 0.070314

| termite

|  

| {{Monzo|9 -28 37 -18}}

| 0.0010723

| neutrino

|  

| {{Monzo|1889 -2145 138 424}}

| 1.6361 × 10^-10

== 11-limit commas ==

! Name(s)

! Ratio

! Monzo

! Cents

| 11-cycle schisma, 37-11-comma

|  

| {{Monzo|128 0 0 0 -37}}

| 1.2361

| [[swetismic_chords|swetisma]]

| 540 / 539

| {{Monzo|2 3 1 -2 -1}}

| 3.2090

| wizardharry

| 4000 / 3993

| {{Monzo|5 -1 3 0 -3}}

| 3.0323

| vishdel

| 5632 / 5625

| {{Monzo|9 -2 -4 0 1}}

| 2.1531

| sesdecal

| 234375 / 234256

| {{Monzo|-4 1 7 0 -4}}

| 0.87923

| hemigail

| 43923 / 43904

| {{Monzo|-7 1 0 -3 4}}

| 0.74905

| lehmerisma

| 3025 / 3024

| {{Monzo|-4 -3 2 -1 2}}

| 0.57240

| kalisma, Gauss' comma

| 9801 / 9800

| {{Monzo|-3 4 -2 -2 2}}

| 0.17665

| odiheim

| 151263 / 151250

| {{Monzo|-1 2 -4 5 -2}}

| 0.14879

| parimo

| 1771561 / 1771470

| {{Monzo|-1 -11 -1 0 6}}

| 0.088931

| ultimo

| 3294225 / 3294172

| {{Monzo|-2 2 2 -7 4}}

| 0.027854

== 13-limit commas ==

! Name

! Ratio

! Monzo

! Cents

| tunbarsma

| 625 / 624

| {{Monzo|-4 -1 4 0 0 -1}}

| 2.7722

| [[The_Archipelago|island comma]]

| 676 / 675

| {{Monzo|2 -3 -2 0 0 2}}

| 2.5629

| [[squbemic_chords|squbema]]

| 729 / 728

| {{Monzo|-3 6 0 -1 0 -1}}

| 2.3764

| [[petrmic_triad|petrma]]

| 2200 / 2197

| {{Monzo|3 0 2 0 1 -3}}

| 2.3624

| [[nicolic_tetrad|nicola]]

| 1575 / 1573

| {{Monzo|0 2 2 1 -2 -1}}

| 2.1998

| [[sinbadmic_tetrad|sinbadma]]

| 1001 / 1000

| {{Monzo|-3 0 -3 1 1 1}}

| 1.7303

| cantonisma

| 10985 / 10976

| {{Monzo|-5 0 1 -3 0 3}}

| 1.4190

| lummic

| 1716 / 1715

| {{Monzo|2 1 -1 -3 1 1}}

| 1.0092

| ibnsinma

| 2080 / 2079

| {{Monzo|5 -3 1 -1 -1 1}}

| 0.83252

| schismina

| 4096 / 4095

| {{Monzo|12 -2 -1 -1 0 -1}}

| 0.42272

| leprechaun comma

| 4225 / 4224

| {{Monzo|-7 -1 2 0 -1 2}}

| 0.40981

| jacobin

| 6656 / 6655

| {{Monzo|9 0 -1 0 -3 1}}

| 0.26012

| harmonisma

| 10648 / 10647

| {{Monzo|3 -2 0 -1 3 -2}}

| 0.16260

| chalmersima

| 123201 / 123200

| {{Monzo|-6 6 -2 -1 -1 2}}

| 0.014052

== 17-limit commas ==

! Name

! Ratio

! Monzo

! Cents

| xenisma

| 2058 / 2057

| {{Monzo|1 1 0 3 -2 0 -1}}

| 0.84143

| flashma

| 12376 / 12375

| {{Monzo|3 -2 -3 1 -1 1 1}}

| 0.13989

| sparkisma

| 14400 / 14399

| {{Monzo|6 2 2 -1 -2 0 -1}}

| 0.12023

| scintillisma

| 194481 / 194480

| {{Monzo|-4 4 -1 4 -1 -1 -1}}

| 0.0089018

== 19-limit commas ==

! Name

! Ratio

! Monzo

! Cents

| Hunt 19-minor mediant comma

| 513 / 512

| {{Monzo|-9 3 0 0 0 0 0 1}}

| 3.3781

| password

| 1216 / 1215

| {{Monzo|6 -5 -1 0 0 0 0 1}}

| 1.4243

| Blumeyer comma

| 2432 / 2431

| {{Monzo|7 0 0 0 -1 -1 -1 1}}

| 0.71200

| 19-limit decimill

| 165376 / 165375

| {{Monzo|9 -3 -3 -2 0 0 1 1}}

| 0.010469