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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{{cent}}, 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.) In [[Sagittal notation]], intervals in the smaller part of this category are [[schismina]]s, and intervals in the larger part of this category are [[schisma (interval region)|schismas]]<ref>[https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>.  
'''Unnoticeable commas''' are very small intervals. These [[comma]]s are called "unnoticeable" because they are smaller than 3.5{{cent}}, 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.) In [[Sagittal notation]], intervals in the smaller part of this category are [[schismina]]s, and intervals in the larger part of this category are [[schisma (interval region)|schismas]]<ref>[https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>.  


For commas over 100{{c}} in size, see [[Large comma]]; for commas in between 30–100{{c}} in size, see [[Medium comma]]; and for commas between 3.5–30{{c}} in size, see [[Small comma]].
For commas over 100{{c}} in size, see [[Large comma]]; for commas in between 30–100{{c}} in size, see [[Medium comma]]; and for commas between 3.5–30{{c}} in size, see [[Small comma]].
Line 87: Line 87:
| [[Petr Pařízek]] (2011)
| [[Petr Pařízek]] (2011)
|-
|-
| [[Vishnuzma]], semisuper comma
| [[Vishnu comma]], semisuper comma
| Sasepbiguma
| Sasepbiguma
| s14gM
| s14gM
Line 95: Line 95:
| [[Gene Ward Smith]] (2001), for ''semisuper comma''
| [[Gene Ward Smith]] (2001), for ''semisuper comma''
|-
|-
| [[Enneadeca]], 19-tone-comma
| [[Enneadeca]]
| Neyoma
| Neyoma
| 19yM
| 19yM
Line 167: Line 167:
| [[Gene Ward Smith]] (2002)
| [[Gene Ward Smith]] (2002)
|-
|-
| [[Minortone comma]], minortonma
| [[Minortone comma]]
| Trila-seguma
| Trila-seguma
| 3L17gM
| 3L17gM
Line 183: Line 183:
| [[Paul Erlich]], [[Gene Ward Smith]] (2001)
| [[Paul Erlich]], [[Gene Ward Smith]] (2001)
|-
|-
| Astro comma
| [[Astro comma]]
| Tribisa-thiweguma
| Tribisa-thiweguma
| 6s31gM
| 6s31gM
Line 197: Line 197:
| {{Monzo| -70 72 -19 }}
| {{Monzo| -70 72 -19 }}
| 0.79950
| 0.79950
| [[User:Xenllium|Xenllium]] (2022)
| [[Xenllium]] (2022)
|-
|-
| [[Niobium comma]]
| [[Niobium comma]]
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| [[Paul Erlich]], [[Gene Ward Smith]] (2002)
| [[Paul Erlich]], [[Gene Ward Smith]] (2002)
|-
|-
| Whoosh
| [[Whoosh comma]]
| Saletriguma
| Saletriguma
| s33gM
| s33gM
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| [[Paul Erlich]] (2002)
| [[Paul Erlich]] (2002)
|-
|-
| Egads
| [[Egads comma]]
| Setriyoma
| Setriyoma
| 51yM
| 51yM
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| [[Margo Schulter]] (2001)
| [[Margo Schulter]] (2001)
|-
|-
| Fortune
| [[Fortune comma]]
| Tritrila-sepbiyoma
| Tritrila-sepbiyoma
| 9L14yM
| 9L14yM
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| [[Paul Erlich]] (2002)
| [[Paul Erlich]] (2002)
|-
|-
| Gross
| [[Gross comma]]
| Quinbisa-foseguma
| Quinbisa-foseguma
| 10s47gM
| 10s47gM
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| [[Paul Erlich]] (2002)
| [[Paul Erlich]] (2002)
|-
|-
| Senior
| [[Senior comma]]
| Quadla-sepquinguma
| Quadla-sepquinguma
| 4L35gM
| 4L35gM
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| [[Paul Erlich]] (2002)
| [[Paul Erlich]] (2002)
|-
|-
| [[Counterquectisma]], deltapion
| [[Counterquectisma]], deltapion comma
| Quintritrilayoma
| Quintritrilayoma
| 45LyM
| 45LyM
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| {{Monzo| 73 77 -84 }}
| {{Monzo| 73 77 -84 }}
| 0.18310
| 0.18310
| [[User:Xenllium|Xenllium]] (2026)
| [[Xenllium]] (2026)
|-
|-
| [[Quectisma]]
| [[Quectisma]]
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| [[User:CompactStar|CompactStar]] (2023)
| [[User:CompactStar|CompactStar]] (2023)
|-
|-
| Raider
| Raider comma
| Tritrisa-thiseyoma
| Tritrisa-thiseyoma
| 9s37yM
| 9s37yM
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| [[Gene Ward Smith]] (2002)
| [[Gene Ward Smith]] (2002)
|-
|-
| Pirate
| Pirate comma
| Quinla-sepsepyoma
| Quinla-sepsepyoma
| 5L49yM
| 5L49yM
Line 303: Line 303:
| [[Paul Erlich]] (2002)
| [[Paul Erlich]] (2002)
|-
|-
| Viking
| Viking comma
| Nela-siweyoma
| Nela-siweyoma
| 19L61yM
| 19L61yM
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| {{Monzo| 26 -7 -4 -2 }}
| {{Monzo| 26 -7 -4 -2 }}
| 3.4083
| 3.4083
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Rainy comma]]
| [[Rainy comma]]
Line 400: Line 400:
| {{Monzo| -17 -6 9 2 }}
| {{Monzo| -17 -6 9 2 }}
| 2.7452
| 2.7452
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Pessoalisma]]
| [[Pessoalisma]]
Line 416: Line 416:
| {{Monzo| -20 7 -1 4 }}
| {{Monzo| -20 7 -1 4 }}
| 2.6749
| 2.6749
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Horwell comma]]
| [[Horwell comma]]
Line 446: Line 446:
| Lrr11yM
| Lrr11yM
| 48828125 / 48771072
| 48828125 / 48771072
| {{monzo| -12 -5 11 -2 }}
| {{Monzo| -12 -5 11 -2 }}
| 2.0240
| 2.0240
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Slendroschisma]], slendric schisma
| [[Slendroschisma]], slendric schisma
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| ss10rM
| ss10rM
| 68719476736 / 68641485507
| 68719476736 / 68641485507
| {{monzo| 36 -5 0 -10 }}
| {{Monzo| 36 -5 0 -10 }}
| 1.9659
| 1.9659
| [[User:Xenllium|Xenllium]] (2024), <br>modified by [[Flora Canou]] (2025)
| [[Xenllium]] (2024), <br>modified by [[Flora Canou]] (2025)
|-
| [[Aristoschisma]]
|
|
| 1 099 511 627 776 / 1 098 337 086 315
| {{Monzo| 40 -22 -1 -1 }}
| 1.8504
| [[Flora Canou]] (2026)
|-
|-
| [[Septimal ennealimma]]
| [[Septimal ennealimma]]
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| {{Monzo| -14 15 -3 -1}}
| {{Monzo| -14 15 -3 -1}}
| 1.5580
| 1.5580
| [[User:Jerdle|Jerdle]] (2021)
| {{U|Jerdle}} (2021)
|-
|-
| [[Breeze comma]]
| [[Breeze comma]]
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| {{Monzo| -6 3 9 -7 }}
| {{Monzo| -6 3 9 -7 }}
| 0.90708
| 0.90708
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Trienstonisma]]
| [[Trienstonisma]]
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| L5ragM
| L5ragM
| 43046721 / 43025920
| 43046721 / 43025920
| {{monzo| -9 16 -1 -5 }}
| {{Monzo| -9 16 -1 -5 }}
| 0.83677
| 0.83677
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[2401/2400|Breedsma]]
| [[2401/2400|Breedsma]]
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| 2zzgM
| 2zzgM
| 2401/2400
| 2401/2400
| {{monzo| -5 -1 -2 4 }}
| {{Monzo| -5 -1 -2 4 }}
| 0.72120
| 0.72120
| [[Gene Ward Smith]] (2004)
| [[Gene Ward Smith]] (2004)
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| 15L6zM
| 15L6zM
|  
|  
| {{monzo| -169 96 0 6 }}
| {{Monzo| -169 96 0 6 }}
| 0.63552
| 0.63552
| [[Tristan Bay]] (2023)
| [[Tristan Bay]] (2023)
Line 534: Line 542:
| 24s171zM
| 24s171zM
|  
|  
| {{monzo| 62 -342 0 171 }}
| {{Monzo| 62 -342 0 171 }}
| 0.61971
| 0.61971
|  
|  
Line 542: Line 550:
| L8ra5yM
| L8ra5yM
| 184528125 / 184473632
| 184528125 / 184473632
| {{monzo| -5 10 5 -8 }}
| {{Monzo| -5 10 5 -8 }}
| 0.51133
| 0.51133
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| 571-7-comma
| 571-7-comma
Line 550: Line 558:
|
|
|  
|  
| {{monzo| 1603 0 0 -571 }}
| {{Monzo| 1603 0 0 -571 }}
| 0.40741
| 0.40741
|  
|  
Line 601: Line 609:
| 0.18904
| 0.18904
| [[Margo Schulter]] (2002)
| [[Margo Schulter]] (2002)
<!--
|-
|-
| laleruyo (171&1547&3125)
| laleruyo (171&1547&3125)
Line 609: Line 618:
| 0.18588
| 0.18588
|  
|  
-->
|-
|-
| 87-fold starling comma
| 87-fold starling comma
Line 664: Line 674:
| {{Monzo| -7 30 -9 -7 }}
| {{Monzo| -7 30 -9 -7 }}
| 0.045256
| 0.045256
| [[User:Xenllium|Xenllium]] (2026)
| [[Xenllium]] (2026)
<!--
|-
|-
| 171&1547&4973 comma
| 171&1547&4973 comma
Line 673: Line 684:
| 0.023986
| 0.023986
|  
|  
-->
|-
|-
| [[Technologisma]]
| [[Technologisma]]
Line 680: Line 692:
| {{Monzo| 51 -13 -1 -10 }}
| {{Monzo| 51 -13 -1 -10 }}
| 0.012210
| 0.012210
| [[User:Godtone|Godtone]] (2024)
| [[Godtone]] (2024)
|-
|-
| Termite
| Termite
Line 1,071: Line 1,083:
| 2.1998
| 2.1998
|  
|  
|-
| [[Eufalesma]]
|
|
| 35035/34992
| {{Monzo| -4 -7 1 2 1 1 }}
| 2.1261
| [[Eufalesio]] (2026)
|-
|-
| [[Navicular comma]]
| [[Navicular comma]]
Line 1,222: Line 1,242:
| {{Monzo| 5 -9 -2 1 0 3 }}
| {{Monzo| 5 -9 -2 1 0 3 }}
| 0.18646
| 0.18646
| [[User:Recentlymaterialized|Recentlymaterialized]] (2024)
|  
|-
|-
| [[Harmonisma]]
| [[Harmonisma]]
Line 1,239: Line 1,259:
| 0.14765
| 0.14765
| [[User:Xenllium|Xenllium]] (2022)
| [[User:Xenllium|Xenllium]] (2022)
|-
| [[Tendoartisma]]
| sasa-sethoguma
| ss17(3o)17gM
| <abbr title="8650415919381337933 / 8649755859375000000">(38 digits)</abbr>
| {{Monzo| -6 -11 -17 0 0 17 }}
| 0.13210
| [[User:FilterNashi|FilterNashi]] (2026)
|-
|-
| [[Pontigailimma]]
| [[Pontigailimma]]
Line 1,821: Line 1,849:
| 0.23703
| 0.23703
| [[Xenllium]] (2025)
| [[Xenllium]] (2025)
|-
| [[10241/10240|Tinisma]]
|
|
| 10241/10240
| {{Monzo| -11 0 -1 2 1 0 0 1 }}
| 0.16906
| [[Eufalesio]] (2026)
|-
|-
| Frouggie comma
| Frouggie comma
Retrieved from "https://en.xen.wiki/w/Unnoticeable_comma"