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]].
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| [[Petr Pařízek]] (2011)
| [[Petr Pařízek]] (2011)
|-
|-
| [[Vishnuzma]], semisuper comma
| [[Vishnu comma]], semisuper comma
| Sasepbiguma
| Sasepbiguma
| s14gM
| s14gM
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| [[Gene Ward Smith]] (2001), for ''semisuper comma''
| [[Gene Ward Smith]] (2001), for ''semisuper comma''
|-
|-
| [[Enneadeca]], 19-tone-comma
| [[Enneadeca]]
| Neyoma
| Neyoma
| 19yM
| 19yM
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| [[Gene Ward Smith]] (2002)
| [[Gene Ward Smith]] (2002)
|-
|-
| [[Minortone comma]], minortonma
| [[Minortone comma]]
| Trila-seguma
| Trila-seguma
| 3L17gM
| 3L17gM
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| [[Paul Erlich]], [[Gene Ward Smith]] (2001)
| [[Paul Erlich]], [[Gene Ward Smith]] (2001)
|-
|-
| Astro comma
| [[Astro comma]]
| Tribisa-thiweguma
| Tribisa-thiweguma
| 6s31gM
| 6s31gM
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| {{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
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| [[Paul Erlich]] (2002)
| [[Paul Erlich]] (2002)
|-
|-
| Viking
| Viking comma
| Nela-siweyoma
| Nela-siweyoma
| 19L61yM
| 19L61yM
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| 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]]
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| 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