Punctisma - Revision history

FloraC: More commatic relations

2026-03-12T11:01:54Z

More commatic relations

← Older revision		Revision as of 11:01, 12 March 2026
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	}}		}}

	The '''punctisma''', with a [[ratio]] of '''43904/43875''', is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] (specifically [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]]) [[comma]] measuring about 1.14 [[cent]]s. It is the difference between three [[15/14]] semitones and a [[16/13]] neutral third. It factors into ([[2401/2400]])⋅([[4096/4095]]).		The '''punctisma''', with a [[ratio]] of '''43904/43875''', is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] (specifically [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]]) [[comma]] measuring about 1.14 [[cent]]s. It is the difference between three [[15/14]] semitones and a [[16/13]] neutral third.

			In terms of other commas, it is the difference between [[196/195]] and [[225/224]]. It factors into ([[2401/2400]])⋅([[4096/4095]]). In the [[19-limit]] it further factors into ([[2926/2925]])⋅([[3136/3135]]).

	== Temperaments ==		== Temperaments ==

FloraC: Rework on intro. + temp data

2026-03-12T10:54:09Z

Rework on intro. + temp data

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 }}
-The '''punctisma''', with a [[ratio]] of '''43904/43875''', is the difference between three [[15/14]] semitones and a [[16/13]] neutral third. It factors into ([[2401/2400]])([[4096/4095]]).
+The '''punctisma''', with a [[ratio]] of '''43904/43875''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (specifically [[2.3.5.7.13 subgroup|2.3.5.7.13-]][[subgroup]]) [[comma]] measuring about 1.14 [[cent]]s. It is the difference between three [[15/14]] semitones and a [[16/13]] neutral third. It factors into ([[2401/2400]])⋅([[4096/4095]]).
 == Temperaments ==
-Tempering out this comma is characteristic of the [[10edo|10''n'']] family of [[edo]]s, including [[decoid]] tunings [[130edo]], [[140edo]], and [[270edo]], which approximate both 15/14 and 16/13 to within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[31edo]], [[41edo]], [[99edo]], [[171edo]], [[311edo]], and [[441edo]]. Perhaps surprisingly, [[111edo]] and [[159edo]] temper it out as well.
+[[Tempering out]] this comma in the full 13-limit leads to the rank-5 '''punctismic''' temperament, or in the 2.3.5.17.13 subgroup, the rank-4 '''punctic''' temperament. It is characteristic of the [[10edo|10''n'']] family of [[edo]]s, including [[decoid]] tunings [[130edo]], [[140edo]], and [[270edo]], which approximate both 15/14 and 16/13 to within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[31edo]], [[41edo]], [[99edo]], [[171edo]], [[311edo]], and [[441edo]]. Perhaps surprisingly, [[111edo]] and [[159edo]] temper it out as well.
 == Etymology ==

Recentlymaterialized at 21:37, 14 January 2025

2025-01-14T21:37:23Z

← Older revision		Revision as of 21:37, 14 January 2025
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma is characteristic of the 10''n'' family of [[edo]]s, which approximate both 15/14 and 16/13 to within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[41edo]], [[171edo]], and [[~~311edo~~]]. Perhaps surprisingly, [[159edo]] ~~tempers~~ it out as well.		Tempering out this comma is characteristic of the [[10edo\|10''n'']] family of [[edo]]s, including [[decoid]] tunings [[130edo]], [[140edo]], and [[270edo]], which approximate both 15/14 and 16/13 to within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[31edo]], [[41edo]], [[99edo]], [[171edo]], [[311edo]], and [[441edo]]. Perhaps surprisingly, [[111edo]] and [[159edo]] temper it out as well.

	== Etymology ==		== Etymology ==

BudjarnLambeth at 03:24, 4 November 2024

2024-11-04T03:24:31Z

← Older revision		Revision as of 03:24, 4 November 2024
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	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]
	[[Category:Commas named after their interval size]]		[[Category:Commas named after their interval size]]
			[[Category:Commas named by translating something into another language]]

BudjarnLambeth at 03:23, 4 November 2024

2024-11-04T03:23:54Z

← Older revision		Revision as of 03:23, 4 November 2024
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	[[Category:Punctismic]]		[[Category:Punctismic]]
			[[Category:Commas named for their periods per equave]]
			[[Category:Commas named after their interval size]]

Aura at 15:39, 9 September 2023

2023-09-09T15:39:20Z

← Older revision		Revision as of 15:39, 9 September 2023
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma is characteristic of the 10''n'' family of [[edo]]s, which approximate both 15/14 and 16/13 within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[41edo]], [[171edo]], and [[311edo]]. Perhaps surprisingly, [[159edo]] tempers it out as well.		Tempering out this comma is characteristic of the 10''n'' family of [[edo]]s, which approximate both 15/14 and 16/13 to within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[41edo]], [[171edo]], and [[311edo]]. Perhaps surprisingly, [[159edo]] tempers it out as well.

	== Etymology ==		== Etymology ==

FloraC: +category

2023-09-09T13:17:38Z

+category

← Older revision		Revision as of 13:17, 9 September 2023
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	== Etymology ==		== Etymology ==
	This comma was named by [[User:Jerdle\|Jerdle]] and [[Aura]] in 2023, from Latin [[Wiktionary: punctum #Latin\|''pūnctum'']] ("point") based on both its relation to the 10''n'' family of edos as well as its small size.		This comma was named by [[User:Jerdle\|Jerdle]] and [[Aura]] in 2023, from Latin [[Wiktionary: punctum #Latin\|''pūnctum'']] ("point") based on both its relation to the 10''n'' family of edos as well as its small size.

			[[Category:Punctismic]]

FloraC: Note the factorization; 41edo as an example; year of naming

2023-09-09T13:17:09Z

Note the factorization; 41edo as an example; year of naming

← Older revision		Revision as of 13:17, 9 September 2023
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	}}		}}

	The '''punctisma''', with a ratio of '''43904/43875''', is the difference between three [[15/14]] semitones and a [[16/13]] neutral third. ~~Its tempering~~ out is characteristic of the ~~10n~~ family of ~~edos~~, which approximate both ~~of these intervals~~ within a fraction of a cent. ~~Surprisingly, it~~ is also tempered out in [[~~159edo~~]], [[171edo]], and [[311edo]]. It was named by [[User:Jerdle\|Jerdle]] and [[Aura]] from Latin [[Wiktionary: punctum #Latin\|''pūnctum'']] ("point") based on both its relation to the ~~10n~~ family of ~~EDOs~~ as well as its small size.		The '''punctisma''', with a [[ratio]] of '''43904/43875''', is the difference between three [[15/14]] semitones and a [[16/13]] neutral third. It factors into ([[2401/2400]])([[4096/4095]]).

			== Temperaments ==
			Tempering out this comma is characteristic of the 10''n'' family of [[edo]]s, which approximate both 15/14 and 16/13 within a fraction of a cent. It is also tempered out by any temperament which tempers out both 2401/2400 and 4096/4095, such as [[41edo]], [[171edo]], and [[311edo]]. Perhaps surprisingly, [[159edo]] tempers it out as well.

			== Etymology ==
			This comma was named by [[User:Jerdle\|Jerdle]] and [[Aura]] in 2023, from Latin [[Wiktionary: punctum #Latin\|''pūnctum'']] ("point") based on both its relation to the 10''n'' family of edos as well as its small size.

Fredg999: Add ratio in infobox (after page move)

2023-06-05T21:18:22Z

Add ratio in infobox (after page move)

← Older revision		Revision as of 21:18, 5 June 2023
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	{{Infobox Interval		{{Infobox Interval
			\| Ratio = 43904/43875
	\| Name = punctisma		\| Name = punctisma
	\| Color name = s3uz<sup>3</sup>g<sup>3</sup>3, sathutrizogu 3rd		\| Color name = s3uz<sup>3</sup>g<sup>3</sup>3, sathutrizogu 3rd

Fredg999: Fredg999 moved page 43904/43875 to Punctisma: Denominator is >9999

2023-06-05T21:17:46Z

Fredg999 moved page 43904/43875 to Punctisma: Denominator is >9999

← Older revision	Revision as of 21:17, 5 June 2023
(No difference)