1729/1728 - Revision history

BudjarnLambeth at 02:18, 16 November 2024

2024-11-16T02:18:29Z

← Older revision		Revision as of 02:18, 16 November 2024
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	[[Category:Ramanujanismic]]		[[Category:Ramanujanismic]]
			[[Category:Commas named after mathematicians]]
			[[Category:Commas referencing a famous use of a number]]

Dummy index: /* Commatic relations */ mark the subgroup-strict decomposition

2024-05-10T16:12:09Z

Commatic relations: mark the subgroup-strict decomposition

← Older revision		Revision as of 16:12, 10 May 2024
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	* [[361/360]] and [[456/455]]		* [[361/360]] and [[456/455]]
	* [[385/384]] and [[495/494]]		* [[385/384]] and [[495/494]]
	* [[513/512]] and [[729/728]]		* [[513/512]] and [[729/728]] *
	* [[1001/1000]] and [[2376/2375]]		* [[1001/1000]] and [[2376/2375]]
	* [[1216/1215]] and [[4096/4095]]		* [[1216/1215]] and [[4096/4095]]
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	* [[1701/1700]] and [[104976/104975]]		* [[1701/1700]] and [[104976/104975]]
	* [[1716/1715]] and [[228096/228095]]		* [[1716/1715]] and [[228096/228095]]
			<nowiki>*</nowiki> all is within the 2.3.7.13.19 subgroup

	It factors into the following superparticular pairs:		It factors into the following superparticular pairs:

FloraC: -typo

2024-04-17T09:32:32Z

-typo

← Older revision		Revision as of 09:32, 17 April 2024
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 19-limit leads to the rank-7 '''ramanujanismic temperament''', or in the 2.3.7.13.19 subgroup, the rank-4 '''ramanujanic temperament'''. In either case it enables the [[ramanujanismic chords]], the [[essentially tempered chord]]s in the 19- or 21-odd-limit. The basic equivalence related to all these chords can be expressed as (7/6)(13/12)(19/12)~2/1, similar to (7/5)(11/10)(13/10)~2/1 as is enabled by the [[1001/1000\|sinbadma (1001/1000)]]. Futhermore, [[8/7]] is short of a stack consisting of 19/18 and 13/12, [[16/13]] short of a stack consisting of 19/18 and 7/6, and [[32/19]] short of a stack ~~consiting~~ of 7/6 and 13/9, all by the ramanujanisma, so that any accurate tuning of the 2.3.13.19, 2.3.7.19, or 2.3.7.13 subgroup will naturally have an accurate approximation to [[7/1\|7]], [[13/1\|13]], or [[19/1\|19]], respectively.		Tempering out this comma in the 19-limit leads to the rank-7 '''ramanujanismic temperament''', or in the 2.3.7.13.19 subgroup, the rank-4 '''ramanujanic temperament'''. In either case it enables the [[ramanujanismic chords]], the [[essentially tempered chord]]s in the 19- or 21-odd-limit. The basic equivalence related to all these chords can be expressed as (7/6)(13/12)(19/12)~2/1, similar to (7/5)(11/10)(13/10)~2/1 as is enabled by the [[1001/1000\|sinbadma (1001/1000)]]. Futhermore, [[8/7]] is short of a stack consisting of 19/18 and 13/12, [[16/13]] short of a stack consisting of 19/18 and 7/6, and [[32/19]] short of a stack consisting of 7/6 and 13/9, all by the ramanujanisma, so that any accurate tuning of the 2.3.13.19, 2.3.7.19, or 2.3.7.13 subgroup will naturally have an accurate approximation to [[7/1\|7]], [[13/1\|13]], or [[19/1\|19]], respectively.

	== Terminology ==		== Terminology ==

FloraC: Put the fact in the right context: the 7, 13, and 19 are all swappable.

2024-04-17T09:32:00Z

Put the fact in the right context: the 7, 13, and 19 are all swappable.

← Older revision		Revision as of 09:32, 17 April 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 [[subgroup]]) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]]~~. Interestingly~~, [[~~133~~/~~108~~]] = [[7/6]] * [[19/18]] ~~is a ramanujanisma flat of~~ [[16/13]]~~, so that any accurate tuning of the 2.3.7.19 subgroup will naturally have an accurate approximation of 16/13 too~~.		'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 [[subgroup]]) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]], which in turn is [[8/7]] less [[13/12]] or [[16/13]] less [[7/6]].

	Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).		Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 19-limit leads to the rank-7 '''ramanujanismic temperament''', or in the 2.3.7.13.19 subgroup, the rank-4 '''ramanujanic temperament'''. In either case it enables the [[ramanujanismic chords]], the [[essentially tempered chord]]s in the 19- or 21-odd-limit.		Tempering out this comma in the 19-limit leads to the rank-7 '''ramanujanismic temperament''', or in the 2.3.7.13.19 subgroup, the rank-4 '''ramanujanic temperament'''. In either case it enables the [[ramanujanismic chords]], the [[essentially tempered chord]]s in the 19- or 21-odd-limit. The basic equivalence related to all these chords can be expressed as (7/6)(13/12)(19/12)~2/1, similar to (7/5)(11/10)(13/10)~2/1 as is enabled by the [[1001/1000\|sinbadma (1001/1000)]]. Futhermore, [[8/7]] is short of a stack consisting of 19/18 and 13/12, [[16/13]] short of a stack consisting of 19/18 and 7/6, and [[32/19]] short of a stack consiting of 7/6 and 13/9, all by the ramanujanisma, so that any accurate tuning of the 2.3.13.19, 2.3.7.19, or 2.3.7.13 subgroup will naturally have an accurate approximation to [[7/1\|7]], [[13/1\|13]], or [[19/1\|19]], respectively.

	== Terminology ==		== Terminology ==

Godtone at 21:10, 16 April 2024

2024-04-16T21:10:58Z

← Older revision		Revision as of 21:10, 16 April 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 [[subgroup]]) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].		'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 [[subgroup]]) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]]. Interestingly, [[133/108]] = [[7/6]] * [[19/18]] is a ramanujanisma flat of [[16/13]], so that any accurate tuning of the 2.3.7.19 subgroup will naturally have an accurate approximation of 16/13 too.

	Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).		Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).

FloraC: +commatic relations

2023-05-31T13:15:59Z

+commatic relations

← Older revision		Revision as of 13:15, 31 May 2023
Line 7:		Line 7:

	Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).		Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).

			== Commatic relations ==
			This comma is the difference between the following superparticular pairs:
			* [[91/90]] and [[96/95]]
			* [[133/132]] and [[144/143]]
			* [[273/272]] and [[324/323]]
			* [[325/324]] and [[400/399]]
			* [[361/360]] and [[456/455]]
			* [[385/384]] and [[495/494]]
			* [[513/512]] and [[729/728]]
			* [[1001/1000]] and [[2376/2375]]
			* [[1216/1215]] and [[4096/4095]]
			* [[1225/1224]] and [[4200/4199]]
			* [[1521/1520]] and [[12636/12635]]
			* [[1540/1539]] and [[14080/14079]]
			* [[1701/1700]] and [[104976/104975]]
			* [[1716/1715]] and [[228096/228095]]

			It factors into the following superparticular pairs:
			* [[2926/2925]] and [[4225/4224]]
			* [[2431/2430]] and [[5985/5984]]
			* [[2401/2400]] and [[6175/6174]]
			* [[2080/2079]] and [[10241/10240]]

	== Temperaments ==		== Temperaments ==

FloraC: "Ramanujanismic chords" is to be created

2023-05-21T12:20:49Z

"Ramanujanismic chords" is to be created

← Older revision		Revision as of 12:20, 21 May 2023
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].		'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 [[subgroup]]) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].

	Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).		Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)\|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)\|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).

	Tempering out this comma ~~enables~~ the '''ramanujanismic ~~chords~~''', the [[essentially tempered chord]]s in the 19-odd-limit~~, a basic form of which comprises the steps of 7/6-13/12-19/12 closing at the octave~~.		== Temperaments ==
			Tempering out this comma in the 19-limit leads to the rank-7 '''ramanujanismic temperament''', or in the 2.3.7.13.19 subgroup, the rank-4 '''ramanujanic temperament'''. In either case it enables the [[ramanujanismic chords]], the [[essentially tempered chord]]s in the 19- or 21-odd-limit.

	== Terminology ==		== Terminology ==
	The name ''ramanujanisma'' was first proposed by [[User:Fredg999\|Frédéric Gagné]] in reference to the anecdotal story of [[Wikipedia: Ramanujan\|Ramanujan]] finding 1729 an interesting number. Alternative names include '''lesser massma''', proposed by [[User:Eliora\|Eliora]], in reference to the number 1728 being known as the ''Maß'' in German, and '''dodecentisma''', proposed by [[User:Godtone\|Godtone]], in reference to the size being close to the relative ''cent'' of ''12''edo (''dodeca'') (12 × 100 = 1200 and this comma is a low [[prime limit]] superparticular approximating 1/1200 of an octave) and in reference to 1728 being a power of 12 (''dodeca'').		The name ''ramanujanisma'' was first proposed by [[User:Fredg999\|Frédéric Gagné]] in reference to the anecdotal story of [[Wikipedia: Ramanujan\|Ramanujan]] finding 1729 an interesting number. Alternative names include ''lesser massma'', proposed by [[User:Eliora\|Eliora]], in reference to the number 1728 being known as the ''Maß'' in German, and ''dodecentisma'', proposed by [[User:Godtone\|Godtone]], in reference to the size being close to the relative ''cent'' of ''12''edo (''dodeca'') (12 × 100 = 1200 and this comma is a low [[prime limit]] superparticular approximating 1/1200 of an octave) and in reference to 1728 being a power of 12 (''dodeca'').

	== See also ==		== See also ==

TallKite at 02:51, 10 January 2023

2023-01-10T02:51:28Z

← Older revision		Revision as of 02:51, 10 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ramanujanisma		\| Name = ramanujanisma
	\| Color name = ~~Nothozo,~~ 19o3oz2, nothozo 2nd		\| Color name = 19o3oz2, nothozo 2nd,<br>Nothozo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T12:55:26Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 12:55, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 1729/1728~~
	~~\| Monzo = -6 -3 0 1 0 1 0 1~~
	~~\| Cents = 1.00158~~
	\| Name = ramanujanisma		\| Name = ramanujanisma
	\| Color name = Nothozo, 19o3oz2, nothozo 2nd		\| Color name = Nothozo, 19o3oz2, nothozo 2nd
	\| ~~FJS name = d2<sup>7,13,19</sup>~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}
	'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].		'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].
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	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]

	~~[[Category:19-limit]]~~
	~~[[Category:Unnoticeable commas]]~~
	~~[[Category:Superparticular]]~~
	[[Category:Ramanujanismic]]		[[Category:Ramanujanismic]]

Fredg999 category edits: Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

2022-03-20T22:01:52Z

Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

← Older revision		Revision as of 22:01, 20 March 2022
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	[[Category:19-limit]]		[[Category:19-limit]]
	[[Category:Unnoticeable ~~comma~~]]		[[Category:Unnoticeable commas]]
	[[Category:Superparticular]]		[[Category:Superparticular]]
	[[Category:Ramanujanismic]]		[[Category:Ramanujanismic]]