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Unnoticeable comma: Difference between revisions

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'''Unnoticeable commas''' are very small intervals. These [[comma]]s 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]]. It is improbable that even a trained listener would be able to notice these intervals, and as such they are a prime target for psychoacoustically informed [[microtempering]]. (However, a considerably larger comma can be unnoticeable in an [[adaptive just intonation|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. Given this, a noticeable 3-limit comma that arguably deserves inclusion is the [[mercator comma]], corresponding to using [[53edo]] for the circle of fifths.)  
'''Unnoticeable commas''' are very small intervals. These [[comma]]s are called "unnoticeable" because, being equal to or less than 3.5 cents, they are smaller than the average peak [[just-noticeable difference]] (JND) of human pitch perception, as illustrated by the research of [[Aaron Andrew Hunt]]<ref>[http://musictheory.zentral.zone/huntsystem2.html#2 H-Pi Instruments | ''Hunt System Scale §The JND'']</ref>. It is improbable that even a trained listener would be able to notice these intervals, and as such they are a prime target for psychoacoustically informed [[microtempering]]. (However, a considerably larger comma can be unnoticeable in an [[adaptive just intonation|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. Given this, a noticeable 3-limit comma that arguably deserves inclusion is the [[mercator comma]], corresponding to using [[53edo]] for the circle of fifths.)  


For commas over 100 cents in size, see [[Large comma]]; for commas in between 30 and 100 cents in size, see [[Medium comma]]; and for commas over 3.5 cents in size, see [[Small comma]].
For commas over 100 cents in size, see [[Large comma]]; for commas in between 30 and 100 cents in size, see [[Medium comma]]; and for commas over 3.5 cents in size, see [[Small comma]].
Line 77: Line 77:
| Quadla-sepquinyo
| Quadla-sepquinyo
| 4L35y-9
| 4L35y-9
|
| <abbr title="2910383045673370361328125 / 2904698108822600835661824">(50 digits)</abbr>
| {{Monzo| -67 -9 35 }}
| {{Monzo| -67 -9 35 }}
| 3.3850
| 3.3850
Line 101: Line 101:
| Quinla-seyo
| Quinla-seyo
| 5L17y-7
| 5L17y-7
|  
| <abbr title="295578376007080078125 / 295147905179352825856">(42 digits)</abbr>
| {{Monzo| -68 18 17 }}
| {{Monzo| -68 18 17 }}
| 2.5232
| 2.5232
Line 120: Line 120:
| {{Monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
| 1.9537
| 1.9537
| Hermann von Helmholtz, Alexander Ellis (1875)
| [[Hermann von Helmholtz]], [[Alexander Ellis]] (1875)
|-
|-
| [[Aluminium comma]]
| [[Aluminium comma]]
| Sepsa-thegu
| Sepsa-thegu
| 7s13g8
| 7s13g8
|
| <abbr title="4951760157141521099596496896 / 4946966739525117513427734375">(56 digits)</abbr>
| {{Monzo| 92 -39 -13 }}
| {{Monzo| 92 -39 -13 }}
| 1.6767
| 1.6767
Line 133: Line 133:
| Tribilagu
| Tribilagu
| 6Lg-5
| 6Lg-5
|  
| <abbr title="2954312706550833698643 / 2951479051793528258560">(44 digits)</abbr>
| {{Monzo| -69 45 -1 }}
| {{Monzo| -69 45 -1 }}
| 1.6613
| 1.6613
Line 140: Line 140:
| [[Neon comma]]
| [[Neon comma]]
| Laquinquinbigu
| Laquinquinbigu
|
| L50g8
|
| <abbr title="88900702359186211632409599176343552 / 88817841970012523233890533447265625">(70 digits)</abbr>
| {{monzo| 21 60 -50 }}
| {{monzo| 21 60 -50 }}
| 1.6144
| 1.6144
Line 149: Line 149:
| Lala-sebiyo
| Lala-sebiyo
| LL34y-8
| LL34y-8
|  
| <abbr title="582076609134674072265625 / 581595589965365114830848">(48 digits)</abbr>
| {{Monzo| -52 -17 34 }}
| {{Monzo| -52 -17 34 }}
| 1.4313
| 1.4313
Line 165: Line 165:
| Trila-segu
| Trila-segu
| 3L17g2
| 3L17g2
|  
| <abbr title="50031545098999707 / 50000000000000000">(34 digits)</abbr>
| {{Monzo| -16 35 -17 }}
| {{Monzo| -16 35 -17 }}
| 1.0919
| 1.0919
Line 181: Line 181:
| Tribisa-thiwegu
| Tribisa-thiwegu
| 6s31g10
| 6s31g10
|  
| <abbr title="2475880078570760549798248448 / 2474715001881122589111328125">(56 digits)</abbr>
| {{Monzo| 91 -12 -31 }}
| {{Monzo| 91 -12 -31 }}
| 0.81486
| 0.81486
Line 189: Line 189:
| Quadbila-negu
| Quadbila-negu
| 8L19g-3
| 8L19g-3
|  
| <abbr title="22528399544939174411840147874772641 / 22517998136852480000000000000000000">(70 digits)</abbr>
| {{Monzo| -70 72 -19 }}
| {{Monzo| -70 72 -19 }}
| 0.79950
| 0.79950
Line 205: Line 205:
| Quadla-quadquadyo
| Quadla-quadquadyo
| 4L16y-6
| 4L16y-6
|  
| <abbr title="9010162353515625 / 9007199254740992">(32 digits)</abbr>
| {{Monzo| -53 10 16 }}
| {{Monzo| -53 10 16 }}
| 0.56943
| 0.56943
Line 213: Line 213:
| Saletrigu
| Saletrigu
| s33g7
| s33g7
|  
| <abbr title="116450459770592056836096 / 116415321826934814453125">(48 digits)</abbr>
| {{Monzo| 37 25 -33 }}
| {{Monzo| 37 25 -33 }}
| 0.52246
| 0.52246
Line 221: Line 221:
| Setriyo
| Setriyo
| 51y-9
| 51y-9
|  
| <abbr title="444089209850062616169452667236328125 / 444002166576103304796646509039845376">(72 digits)</abbr>
| {{Monzo| -36 -52 51 }}
| {{Monzo| -36 -52 51 }}
| 0.33936
| 0.33936
Line 229: Line 229:
| Quinsa-yoyo
| Quinsa-yoyo
| 5syy4
| 5syy4
|  
| <abbr title="450359962737049600 / 450283905890997363">(36 digits)</abbr>
| {{Monzo| 54 -37 2 }}
| {{Monzo| 54 -37 2 }}
| 0.29240
| 0.29240
Line 237: Line 237:
| Tritrila-sepbiyo
| Tritrila-sepbiyo
| 9L14y-9
| 9L14y-9
|  
| <abbr title="162285243890121480027996826171875 / 162259276829213363391578010288128">(66 digits)</abbr>
| {{Monzo| -107 47 14 }}
| {{Monzo| -107 47 14 }}
| 0.27703
| 0.27703
Line 245: Line 245:
| Quinbisa-fosegu
| Quinbisa-fosegu
| 10s47g15
| 10s47g15
|  
| <abbr title="22300745198530623141535718272648361505980416 / 22297583945629639856633730232715606689453125">(88 digits)</abbr>
| {{Monzo| 144 -22 -47 }}
| {{Monzo| 144 -22 -47 }}
| 0.24543
| 0.24543
Line 253: Line 253:
| Quadla-sepquingu
| Quadla-sepquingu
| 4L35g4
| 4L35g4
|  
| <abbr title="381520424476945831628649898809 / 381469726562500000000000000000">(60 digits)</abbr>
| {{Monzo| -17 62 -35 }}
| {{Monzo| -17 62 -35 }}
| 0.23007
| 0.23007
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| Tritrisa-thiseyo
| Tritrisa-thiseyo
| 9s37y1
| 9s37y1
|  
| <abbr title="171798691840000000000000000000000000000000000000 / 171792506910670443678820376588540424234035840667">(96 digits)</abbr>
| {{Monzo| 71 -99 37 }}
| {{Monzo| 71 -99 37 }}
| 0.062327
| 0.062327
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| Quinla-sepsepyo
| Quinla-sepsepyo
| 5L49y-12
| 5L49y-12
|  
| <abbr title="17763568394002504646778106689453125 / 17763086495282268024161967871623168">(70 digits)</abbr>
| {{Monzo| -90 -15 49 }}
| {{Monzo| -90 -15 49 }}
| 0.046966
| 0.046966
Line 301: Line 301:
| Sepbisa-quadtrigu
| Sepbisa-quadtrigu
| 14s12g12
| 14s12g12
|  
| <abbr title="2923003274661805836407369665432566039311865085952 / 2922977339492680612451840826835216578535400390625">(98 digits)</abbr>
| {{Monzo| 161 -84 -12 }}
| {{Monzo| 161 -84 -12 }}
| 0.015361
| 0.015361
Line 437: Line 437:
| [[User:Xenllium|Xenllium]] (2021)
| [[User:Xenllium|Xenllium]] (2021)
|-
|-
| [[Slendrisma]], slendric schisma
| [[Slendroschisma]], slendric schisma
| Sasa-quinbiru
| Sasa-quinbiru
| ss10r-4
| ss10r-4
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| {{monzo| 36 -5 0 -10 }}
| {{monzo| 36 -5 0 -10 }}
| 1.9659
| 1.9659
| [[User:Xenllium|Xenllium]] (2024)
| [[User:Xenllium|Xenllium]] (2024), <br>modified by [[Flora Canou]] (2025)
|-
|-
| [[Septimal ennealimma]]
| [[Septimal ennealimma]]
Line 584: Line 584:
| Quinbisaru
| Quinbisaru
| 10sr7
| 10sr7
|  
| <abbr title="649037107316853453566312041152512 / 648966242035284859600333477874109">(66 digits)</abbr>
| {{Monzo| 109 -67 0 -1 }}
| {{Monzo| 109 -67 0 -1 }}
| 0.18904
| 0.18904
Line 608: Line 608:
| Sasa-neru
| Sasa-neru
| ss19r-8
| ss19r-8
|  
| <abbr title="11399736556781568 / 11398895185373143">(34 digits)</abbr>
| {{Monzo| 47 4 0 -19 }}
| {{Monzo| 47 4 0 -19 }}
| 0.12778
| 0.12778
Line 624: Line 624:
| Quinla-zoyoyo
| Quinla-zoyoyo
| 5Lzzy-4
| 5Lzzy-4
|  
| <abbr title="36030948116563575 / 36028797018963968">(34 digits)</abbr>
| {{Monzo| -55 30 2 1 }}
| {{Monzo| -55 30 2 1 }}
| 0.10336
| 0.10336
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| Satwethezo-atritribigu
| Satwethezo-atritribigu
| s23za18g15
| s23za18g15
|  
| <abbr title="54737494680161832686 / 54736736297607421875">(40 digits)</abbr>
| {{Monzo| 1 -15 -18 23 }}
| {{Monzo| 1 -15 -18 23 }}
| 0.023986
| 0.023986
Line 648: Line 648:
| Trisa-quinbiru-agu
| Trisa-quinbiru-agu
| 3s10rag-3
| 3s10rag-3
|  
| <abbr title="2251799813685248 / 2251783932057135">(32 digits)</abbr>
| {{Monzo| 51 -13 -1 -10 }}
| {{Monzo| 51 -13 -1 -10 }}
| 0.012210
| 0.012210
Line 656: Line 656:
| Satritribiru-athiseyo
| Satritribiru-athiseyo
| s18ra37y-14
| s18ra37y-14
|  
| <abbr title="37252902984619140625000000000 / 37252879910233655318543787489">(58 digits)</abbr>
| {{Monzo| 9 -28 37 -18 }}
| {{Monzo| 9 -28 37 -18 }}
| 0.0010723
| 0.0010723
Line 715: Line 715:
| Twetheluzo
| Twetheluzo
| 23(1uz)14
| 23(1uz)14
| 896819112839771466727424 / <br> 895430243255237372246531
| <abbr title="896819112839771466727424 / 895430243255237372246531">(48 digits)</abbr>
| {{Monzo| 15 0 0 23 -23}}
| {{Monzo| 15 0 0 23 -23 }}
| 2.6832
| 2.6832
|  
|  
Line 779: Line 779:
| Quinsa-thiselu
| Quinsa-thiselu
| 5s37(1u)9
| 5s37(1u)9
|
| <abbr title="340282366920938463463374607431768211456 / 340039485861577398992406882305761986971">(78 digits)</abbr>
| {{Monzo| 128 0 0 0 -37 }}
| {{Monzo| 128 0 0 0 -37 }}
| 1.2361
| 1.2361
Line 816: Line 816:
| [[Dawson Berry]] (2021)
| [[Dawson Berry]] (2021)
|-
|-
| Hemigail
| Chrysia, hemigail
| Quadlo-atriru
| Quadlo-atriru
| 4(1o)3r-3
| 4(1o)3r-3
Line 827: Line 827:
| Trila-lusepruyoyo
| Trila-lusepruyoyo
| 3L1u7ryy-8
| 3L1u7ryy-8
| 9730975341796875 / 9726998192586752
| <abbr title="9730975341796875 / 9726998192586752">(32 digits)</abbr>
| {{Monzo| -30 13 14 -7 -1 }}
| {{Monzo| -30 13 14 -7 -1 }}
| 0.70772
| 0.70772
Line 896: Line 896:
| [[User:Eliora|Eliora]] (2023)
| [[User:Eliora|Eliora]] (2023)
|-
|-
| [[Syntonisma]]
| [[Syntonoschisma]]
| Trisa-lusepyo
| Trisa-lusepyo
| 3s1u7y2
| 3s1u7y2
Line 923: Line 923:
| Laquadquadlo-aquadtrizo
| Laquadquadlo-aquadtrizo
| L16(1o)12z4
| L16(1o)12z4
| 636003407850068828189211361 / <br> 635974777627126753067532288
| <abbr title="636003407850068828189211361 / 635974777627126753067532288">(54 digits)</abbr>
| {{Monzo| -51 -24 0 12 16 }}
| {{Monzo| -51 -24 0 12 16 }}
| 0.077935
| 0.077935
Line 1,035: Line 1,035:
|  
|  
|-
|-
| [[24192/24167|Navicular comma]]
| [[Navicular comma]]
| Trithu-aluzo
| Trithu-aluzo
| 3(3u)1uz1
| 3(3u)1uz1
Line 1,121: Line 1,121:
| {{Monzo| 5 -3 1 -1 -1 1 }}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| 0.83252
| 0.83252
| [[Margo Schulter]], [[Gene Ward Smith]] (2012)<br>[[Flora Canou]] (2023)
| [[Margo Schulter]], [[Gene Ward Smith]] (2012) <br>[[Flora Canou]] (2023)
|-
|-
| [[Phaotic comma]], phaotisma
| [[Phaotic comma]], phaotisma
Line 1,138: Line 1,138:
| 0.66993
| 0.66993
| [[User:原井玉葱郎|Misohito Nakai]] (2025)
| [[User:原井玉葱郎|Misohito Nakai]] (2025)
|-
| [[Barbadisma]]
| Quadla-thuyo
| 4L3uy-4
| 114383962274805 / 114349209288704
| {{Monzo| -43 28 1 0 0 -1 }}
| 0.52608
| [[User:Xenllium|Xenllium]] (2025)
|-
|-
| [[4096/4095|Schismina]]
| [[4096/4095|Schismina]]
Line 1,200: Line 1,208:
| 1990656/1990625
| 1990656/1990625
| {{Monzo| 13 5 -5 -2 0 -1 }}
| {{Monzo| 13 5 -5 -2 0 -1 }}
| 0.027
| 0.026960
| [[User:Recentlymaterialized|Recentlymaterialized]]
| [[User:Recentlymaterialized|Recentlymaterialized]] (2024)
|-
|-
| [[Grossmisma]]
| [[Grossmisma]]
| septholo-azogu
| septholo-azogu
| 7(3o1o)zg2
| 7(3o1o)zg2
|  
| <abbr title="8559537565427849 / 8559456430325760">(32 digits)</abbr>
| {{Monzo| -30 -13 -1 1 7 7 }}
| {{Monzo| -30 -13 -1 1 7 7 }}
| 0.016410
| 0.016410
Line 1,238: Line 1,246:
! Named by
! Named by
|-
|-
| [[1419857/1417176|Quinticular comma]]
| [[Quinticular comma]]
| Saquinso
| Saquinso
| s5(17o)4
| s5(17o)4
Line 1,386: Line 1,394:
| 17oo3ugg2
| 17oo3ugg2
| 2601/2600
| 2601/2600
| {{Monzo| -3 2 -2 0 0 1 3 }}
| {{Monzo| -3 2 -2 0 0 -1 2 }}
| 0.66573
| 0.66573
| [[Flora Canou]] (2023)
| [[Flora Canou]] (2023)
Line 1,533: Line 1,541:
| L19o1
| L19o1
| 513/512
| 513/512
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| 2.3.19 {{Monzo| -9 3 1 }}
| 3.3780
| 3.3780
| Plainsound Music Edition (2020)<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref> for ''undevicesimal schisma''
| Plainsound Music Edition (2020)<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref> for ''undevicesimal schisma''
Line 1,767: Line 1,775:
| {{Monzo| 2 0 1 3 0 0 0 -3 }}
| {{Monzo| 2 0 1 3 0 0 0 -3 }}
| 0.25238
| 0.25238
| [[User:Xenllium|Xenllium]] (2025)
|-
| [[Undevicesimal counterschisma]]
| Seplanu
| 7L19u-6
| <abbr title=" 717897987691852588770249 / 717799705396186072481792">(48 digits)</abbr>
| 2.3.19 {{Monzo| -75 50 -1 }}
| 0.23703
| [[User:Xenllium|Xenllium]] (2025)
| [[User:Xenllium|Xenllium]] (2025)
|-
|-
Line 1,932: Line 1,948:
| [[User:Xenllium|Xenllium]] (2023)
| [[User:Xenllium|Xenllium]] (2023)
|-
|-
| [[1197/1196|Rhodesisma]]
| [[7942/7935|Brigade comma]]
| Bitwethuno-alogu
| 23uu19oo1og1
| 7942/7935
| {{Monzo| 1 -1 -1 0 1 0 0 2 -2 }}
| 1.5266
| [[User:Xenllium|Xenllium]] (2025)
|-
| [[1197/1196|Rodessisma]]
| Twethunothuzo
| Twethunothuzo
| 23u19o3uz1
| 23u19o3uz1
Line 1,938: Line 1,962:
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
| 1.4469
| 1.4469
| [[User:Xenllium|Xenllium]] (2023)
| [[Lériendil]] (2025)
|-
|-
| [[1288/1287|Triaphonisma]], santisma
| [[1288/1287|Triaphonisma]], santisma
Line 2,152: Line 2,176:
| 23oozzg3
| 23oozzg3
| 25921/25920
| 25921/25920
| 2.3.5.7.23 {{monzo| 6 -4 -1 2 2 }}
| 2.3.5.7.23 {{monzo| -6 -4 -1 2 2 }}
| 0.066790
| 0.066790
| [[Flora Canou]] (2023), modified by [[Lériendil]] (2024)
| [[Flora Canou]] (2023), modified by [[Lériendil]] (2024)
Retrieved from "https://en.xen.wiki/w/Unnoticeable_comma"