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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]].
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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]]
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| {{Monzo| -17 -6 9 2 }}
| {{Monzo| -17 -6 9 2 }}
| 2.7452
| 2.7452
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Pessoalisma]]
| [[Pessoalisma]]
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| {{Monzo| -20 7 -1 4 }}
| {{Monzo| -20 7 -1 4 }}
| 2.6749
| 2.6749
| [[User:Xenllium|Xenllium]] (2021)
| [[Xenllium]] (2021)
|-
|-
| [[Horwell comma]]
| [[Horwell comma]]
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| 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)
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| 24s171zM
| 24s171zM
|  
|  
| {{monzo| 62 -342 0 171 }}
| {{Monzo| 62 -342 0 171 }}
| 0.61971
| 0.61971
|  
|  
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| 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
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|
|
|  
|  
| {{monzo| 1603 0 0 -571 }}
| {{Monzo| 1603 0 0 -571 }}
| 0.40741
| 0.40741
|  
|  
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| 0.18904
| 0.18904
| [[Margo Schulter]] (2002)
| [[Margo Schulter]] (2002)
<!--
|-
|-
| laleruyo (171&1547&3125)
| laleruyo (171&1547&3125)
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| 0.18588
| 0.18588
|  
|  
-->
|-
|-
| 87-fold starling comma
| 87-fold starling comma
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| {{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
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| 0.023986
| 0.023986
|  
|  
-->
|-
|-
| [[Technologisma]]
| [[Technologisma]]
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| {{Monzo| 51 -13 -1 -10 }}
| {{Monzo| 51 -13 -1 -10 }}
| 0.012210
| 0.012210
| [[User:Godtone|Godtone]] (2024)
| [[Godtone]] (2024)
|-
|-
| Termite
| Termite
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