Unnoticeable comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
updated color names
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
updated the color names
Line 45: Line 45:
|-
|-
| [[vishnuzma]], semisuper
| [[vishnuzma]], semisuper
| sa-sepbigu
| sasepbigu
| 6115295232 / 6103515625
| 6115295232 / 6103515625
| {{Monzo|23 6 -14}}
| {{Monzo|23 6 -14}}
Line 75: Line 75:
|-
|-
| counterschisma
| counterschisma
| tribila-gu
| tribilagu
|  
|  
| {{Monzo|-69 45 -1}}
| {{Monzo|-69 45 -1}}
Line 99: Line 99:
|-
|-
| [[ennealimmal]]
| [[ennealimmal]]
| sa-tritribiyo
| satritribiyo
| 7629394531250 / 7625597484987
| 7629394531250 / 7625597484987
| {{Monzo|1 -27 18}}
| {{Monzo|1 -27 18}}
Line 242: Line 242:
|-
|-
| horwell
| horwell
| la-zoquinyo
| lazoquinyo
| 65625 / 65536
| 65625 / 65536
| {{Monzo|-16 1 5 1}}
| {{Monzo|-16 1 5 1}}
Line 248: Line 248:
|-
|-
| meter
| meter
| la-triru-asepyo
| latriru-asepyo
| 703125 / 702464
| 703125 / 702464
| {{Monzo|-11 2 7 -3}}
| {{Monzo|-11 2 7 -3}}
Line 284: Line 284:
|-
|-
| nanisma
| nanisma
| quinbisa-ru
| quinbisaru
|  
|  
| {{Monzo|109 -67 0 -1}}
| {{Monzo|109 -67 0 -1}}
Line 290: Line 290:
|-
|-
| 171&1547&3125 comma
| 171&1547&3125 comma
| la-leruyo
| laleruyo
| 3955078125/3954653486
| 3955078125/3954653486
| {{Monzo|-1 4 11 -11}}
| {{Monzo|-1 4 11 -11}}
Line 296: Line 296:
|-
|-
| starscape
| starscape
| la-tritriru-ayo
| latritriru-ayo
| 645700815 / 645657712
| 645700815 / 645657712
| {{Monzo|-4 17 1 -9}}
| {{Monzo|-4 17 1 -9}}
Line 308: Line 308:
|-
|-
| euzenius
| euzenius
| sa-biruquinyo
| sabiruquinyo
| 78125000 / 78121827
| 78125000 / 78121827
| {{Monzo|3 -13 10 -2}}
| {{Monzo|3 -13 10 -2}}
Line 367: Line 367:
|-
|-
| vishdel
| vishdel
| sa-loquadgu
| saloquadgu
| 5632 / 5625
| 5632 / 5625
| {{Monzo|9 -2 -4 0 1}}
| {{Monzo|9 -2 -4 0 1}}
Line 373: Line 373:
|-
|-
| sesdecal
| sesdecal
| la-quadlu-asepyo
| laquadlu-asepyo
| 234375 / 234256
| 234375 / 234256
| {{Monzo|-4 1 7 0 -4}}
| {{Monzo|-4 1 7 0 -4}}
Line 397: Line 397:
|-
|-
| odiheim
| odiheim
| lulu-quinzo-aquadgu
| luluquinzo-aquadgu
| 151263 / 151250
| 151263 / 151250
| {{Monzo|-1 2 -4 5 -2}}
| {{Monzo|-1 2 -4 5 -2}}
Line 403: Line 403:
|-
|-
| parimo
| parimo
| sa-tribilo-agu
| satribilo-agu
| 1771561 / 1771470
| 1771561 / 1771470
| {{Monzo|-1 -11 -1 0 6}}
| {{Monzo|-1 -11 -1 0 6}}
Line 450: Line 450:
|-
|-
| [[nicolic_tetrad|nicola]]
| [[nicolic_tetrad|nicola]]
| thululu-zoyoyo
| thululuzoyoyo
| 1575 / 1573
| 1575 / 1573
| {{Monzo|0 2 2 1 -2 -1}}
| {{Monzo|0 2 2 1 -2 -1}}
Line 456: Line 456:
|-
|-
| [[sinbadmic_tetrad|sinbadma]]
| [[sinbadmic_tetrad|sinbadma]]
| tholozo-trigu
| tholozotrigu
| 1001 / 1000
| 1001 / 1000
| {{Monzo|-3 0 -3 1 1 1}}
| {{Monzo|-3 0 -3 1 1 1}}
Line 468: Line 468:
|-
|-
| lummic
| lummic
| tholo-triru-agu
| tholotriru-agu
| 1716 / 1715
| 1716 / 1715
| {{Monzo|2 1 -1 -3 1 1}}
| {{Monzo|2 1 -1 -3 1 1}}
Line 480: Line 480:
|-
|-
| schismina
| schismina
| sa-thurugu
| sathurugu
| 4096 / 4095
| 4096 / 4095
| {{Monzo|12 -2 -1 -1 0 -1}}
| {{Monzo|12 -2 -1 -1 0 -1}}
Line 486: Line 486:
|-
|-
| leprechaun comma
| leprechaun comma
| thotho-luyoyo
| thotholuyoyo
| 4225 / 4224
| 4225 / 4224
| {{Monzo|-7 -1 2 0 -1 2}}
| {{Monzo|-7 -1 2 0 -1 2}}
Line 498: Line 498:
|-
|-
| harmonisma
| harmonisma
| thuthu-trilo-aru
| thuthutrilo-aru
| 10648 / 10647
| 10648 / 10647
| {{Monzo|3 -2 0 -1 3 -2}}
| {{Monzo|3 -2 0 -1 3 -2}}
Line 504: Line 504:
|-
|-
| chalmersima
| chalmersima
| lathotho-luru-gugu
| lathotholurugugu
| 123201 / 123200
| 123201 / 123200
| {{Monzo|-6 6 -2 -1 -1 2}}
| {{Monzo|-6 6 -2 -1 -1 2}}
Line 521: Line 521:
|-
|-
| xenisma
| xenisma
| sululu-trizo
| sululutrizo
| 2058 / 2057
| 2058 / 2057
| {{Monzo|1 1 0 3 -2 0 -1}}
| {{Monzo|1 1 0 3 -2 0 -1}}
Line 527: Line 527:
|-
|-
| flashma
| flashma
| sotho-luzo-trigu
| sotholuzotrigu
| 12376 / 12375
| 12376 / 12375
| {{Monzo|3 -2 -3 1 -1 1 1}}
| {{Monzo|3 -2 -3 1 -1 1 1}}
Line 533: Line 533:
|-
|-
| sparkisma
| sparkisma
| sululu-ruyoyo
| sululuruyoyo
| 14400 / 14399
| 14400 / 14399
| {{Monzo|6 2 2 -1 -2 0 -1}}
| {{Monzo|6 2 2 -1 -2 0 -1}}
Line 539: Line 539:
|-
|-
| scintillisma
| scintillisma
| la-suthulu-quadzo-agu
| lasuthuluquadzo-agu
| 194481 / 194480
| 194481 / 194480
| {{Monzo|-4 4 -1 4 -1 -1 -1}}
| {{Monzo|-4 4 -1 4 -1 -1 -1}}
Line 568: Line 568:
|-
|-
| Blumeyer comma
| Blumeyer comma
| nosu-thulu
| nosuthulu
| 2432 / 2431
| 2432 / 2431
| {{Monzo|7 0 0 0 -1 -1 -1 1}}
| {{Monzo|7 0 0 0 -1 -1 -1 1}}
Line 574: Line 574:
|-
|-
| 19-limit decimill
| 19-limit decimill
| noso-ruru-trigu
| nosorurutrigu
| 165376 / 165375
| 165376 / 165375
| {{Monzo|9 -3 -3 -2 0 0 1 1}}
| {{Monzo|9 -3 -3 -2 0 0 1 1}}

Revision as of 04:22, 23 January 2019

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.

For commas over 100 cents in size, see Large 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 Ratio Monzo Cents
Sasktel comma, 51-Pythagorean comma wa-306 comma [485 -306⟩ 1.7697
Satanic comma wa-665 comma [-1054 665⟩ 0.075575

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 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 [144 -22 -47⟩ 0.24543
senior quadla-sepquingu [-17 62 -35⟩ 0.23007
665&3684 comma quintritrila-yo [-500 314 1⟩ 0.18399
raider [71 -99 37⟩ 0.062327
pirate [-90 -15 49⟩ 0.046966
viking [-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 [-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
nanisma quinbisaru [109 -67 0 -1⟩ 0.18904
171&1547&3125 comma laleruyo 3955078125/3954653486 [-1 4 11 -11⟩ 0.18588
starscape latritriru-ayo 645700815 / 645657712 [-4 17 1 -9⟩ 0.11557
12&53&612 comma quinla-zoyoyo [-55 30 2 1⟩ 0.10336
euzenius sabiruquinyo 78125000 / 78121827 [3 -13 10 -2⟩ 0.070314
171&1547&4973 comma [1 -15 -18 23⟩ 0.023986
441&1848&3125 comma trisa-quinbiru-agu [51 -13 -1 -10⟩ 0.012210
termite [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
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
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
19-limit decimill nosorurutrigu 165376 / 165375 [9 -3 -3 -2 0 0 1 1⟩ 0.010469
Retrieved from "https://en.xen.wiki/index.php?title=Unnoticeable_comma&oldid=39712"