Unnoticeable comma - Revision history

FloraC: /* 7-limit commas */ + aristoschisma

2026-08-30T07:51:54Z

7-limit commas: + aristoschisma

← Older revision		Revision as of 07:51, 30 August 2026
Line 457:		Line 457:
	\| 1.9659		\| 1.9659
	\| [[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]]

FloraC: /* 7-limit commas */ cleanup

2026-08-30T07:47:16Z

7-limit commas: cleanup

← Older revision		Revision as of 07:47, 30 August 2026
Line 384:		Line 384:
	\| {{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
Line 454:		Line 454:
	\| 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)
	\|-		\|-
	\| [[Septimal ennealimma]]		\| [[Septimal ennealimma]]
Line 480:		Line 480:
	\| {{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]]
Line 504:		Line 504:
	\| {{Monzo\| -6 3 9 -7 }}		\| {{Monzo\| -6 3 9 -7 }}
	\| 0.90708		\| 0.90708
	\| [[~~User:Xenllium\|~~Xenllium]] (2021)		\| [[Xenllium]] (2021)
	\|-		\|-
	\| [[Trienstonisma]]		\| [[Trienstonisma]]
Line 510:		Line 510:
	\| 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]]
Line 518:		Line 518:
	\| 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)
Line 526:		Line 526:
	\| 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 534:
	\| 24s171zM		\| 24s171zM
	\|		\|
	\| {{~~monzo~~\| 62 -342 0 171 }}		\| {{Monzo\| 62 -342 0 171 }}
	\| 0.61971		\| 0.61971
	\|		\|
Line 542:		Line 542:
	\| 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)
Line 609:		Line 610:
	\| 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
Line 673:		Line 676:
	\| 0.023986		\| 0.023986
	\|		\|
			-->
	\|-		\|-
	\| [[Technologisma]]		\| [[Technologisma]]
Line 680:		Line 684:
	\| {{Monzo\| 51 -13 -1 -10 }}		\| {{Monzo\| 51 -13 -1 -10 }}
	\| 0.012210		\| 0.012210
	\| [[~~User:Godtone\|~~Godtone]] (2024)		\| [[Godtone]] (2024)
	\|-		\|-
	\| Termite		\| Termite

Tonwood: brevity

2026-07-20T02:06:07Z

brevity

← Older revision		Revision as of 02:06, 20 July 2026
Line 1:		Line 1:
	'''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]].

FloraC: /* 19-limit commas */ +1

2026-06-30T11:37:13Z

19-limit commas: +1

← Older revision		Revision as of 11:37, 30 June 2026
Line 1,837:		Line 1,837:
	\| 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

FilterNashi: /* 13-limit commas */+1 comma (Tendoartisma)

2026-06-25T06:21:38Z

13-limit commas: +1 comma (Tendoartisma)

← Older revision		Revision as of 06:21, 25 June 2026
Line 1,247:		Line 1,247:
	\| 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]]

FloraC: /* List of commas, by prime limit */ less absurdities

2026-06-18T08:12:33Z

List of commas, by prime limit: less absurdities

← Older revision		Revision as of 08:12, 18 June 2026
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]]
Line 215:		Line 215:
	\| [[Paul Erlich]], [[Gene Ward Smith]] (2002)		\| [[Paul Erlich]], [[Gene Ward Smith]] (2002)
	\|-		\|-
	\| Whoosh		\| [[Whoosh comma]]
	\| Saletriguma		\| Saletriguma
	\| s33gM		\| s33gM
Line 223:		Line 223:
	\| [[Paul Erlich]] (2002)		\| [[Paul Erlich]] (2002)
	\|-		\|-
	\| Egads		\| [[Egads comma]]
	\| Setriyoma		\| Setriyoma
	\| 51yM		\| 51yM
Line 239:		Line 239:
	\| [[Margo Schulter]] (2001)		\| [[Margo Schulter]] (2001)
	\|-		\|-
	\| Fortune		\| [[Fortune comma]]
	\| Tritrila-sepbiyoma		\| Tritrila-sepbiyoma
	\| 9L14yM		\| 9L14yM
Line 247:		Line 247:
	\| [[Paul Erlich]] (2002)		\| [[Paul Erlich]] (2002)
	\|-		\|-
	\| Gross		\| [[Gross comma]]
	\| Quinbisa-foseguma		\| Quinbisa-foseguma
	\| 10s47gM		\| 10s47gM
Line 255:		Line 255:
	\| [[Paul Erlich]] (2002)		\| [[Paul Erlich]] (2002)
	\|-		\|-
	\| Senior		\| [[Senior comma]]
	\| Quadla-sepquinguma		\| Quadla-sepquinguma
	\| 4L35gM		\| 4L35gM
Line 263:		Line 263:
	\| [[Paul Erlich]] (2002)		\| [[Paul Erlich]] (2002)
	\|-		\|-
	\| [[Counterquectisma]], deltapion		\| [[Counterquectisma]], deltapion comma
	\| Quintritrilayoma		\| Quintritrilayoma
	\| 45LyM		\| 45LyM
Line 277:		Line 277:
	\| {{Monzo\| 73 77 -84 }}		\| {{Monzo\| 73 77 -84 }}
	\| 0.18310		\| 0.18310
	\| [[~~User:Xenllium\|~~Xenllium]] (2026)		\| [[Xenllium]] (2026)
	\|-		\|-
	\| [[Quectisma]]		\| [[Quectisma]]
Line 287:		Line 287:
	\| [[User:CompactStar\|CompactStar]] (2023)		\| [[User:CompactStar\|CompactStar]] (2023)
	\|-		\|-
	\| Raider		\| Raider comma
	\| Tritrisa-thiseyoma		\| Tritrisa-thiseyoma
	\| 9s37yM		\| 9s37yM
Line 295:		Line 295:
	\| [[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

Overthink: Please don't mass remove established content without discussion

2026-05-13T00:09:29Z

Please don't mass remove established content without discussion

Show changes

Domin: Musically irrelevant gunk removed.

2026-05-12T23:59:57Z

Musically irrelevant gunk removed.

Show changes

Domin: Musically irrelevant gunk removed.

2026-05-12T23:43:46Z

Musically irrelevant gunk removed.

@@ Line 8: / Line 8: @@
 == List of commas, by prime limit ==
 === 5-limit commas ===
 {| class="wikitable"

FloraC: /* 13-limit commas */ + eufalesma

2026-05-06T09:28:31Z

13-limit commas: + eufalesma

← Older revision		Revision as of 09:28, 6 May 2026
Line 1,071:		Line 1,071:
	\| 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 1,230:
	\| {{Monzo\| 5 -9 -2 1 0 3 }}		\| {{Monzo\| 5 -9 -2 1 0 3 }}
	\| 0.18646		\| 0.18646
	\| ~~[[User:Recentlymaterialized\|Recentlymaterialized]] (2024)~~		\|
	\|-		\|-
	\| [[Harmonisma]]		\| [[Harmonisma]]