1729/1728 - Revision history

DisasterBlaster: elaborated on Ramanujan's tale and added the story as a footnote. I assume the efn will not form a heading.

2026-08-01T18:47:53Z

elaborated on Ramanujan's tale and added the story as a footnote. I assume the efn will not form a heading.

← Older revision		Revision as of 18:47, 1 August 2026
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	== 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\|Srinivasa Ramanujan]] finding 1729 an interesting number<ref>Before Srinivasa Ramanujan had died of amoebic dysentery in 1920, the year prior in 1919 fellow mathematician and Ramanujan's own mentor [[wikipedia:G._H._Hardy\|G. H. Hardy]] had visited him while he lay ill in Putney, London, UK. The number of the taxicab he had ridden was 1729 and Hardy would then hope its perceived dullness was not a bad omen, to that of which Ramanujan stated this fact.</ref>. This comes from its property of being the second of ''n'' 'taxicab' numbers whose cubic sum not only is restricted to two components but also to ''n'' equivalencies (the first is two and the third is 87539319). Alternative names include ''lesser massma'', proposed by [[User:Eliora\|Eliora]], in reference to the number 1728 being known as the ''Maß'' in German (although this is actually an urban legend as 1728 shares in common the expression great gross with English, and is thus called ''großes Gros''), 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 ==

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>).
Line 32:		Line 32:

	== 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
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]]. 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]]