1729/1728: Difference between revisions

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'''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 = 13 + 123 = 93 + 103).

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 ==

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 ==

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-'''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>).
-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 ==
-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 ==