1729/1728: Difference between revisions
m clarified reasoning for my proposed name "dodecentisma" |
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| Monzo = -6 -3 0 1 0 1 0 1 | | Monzo = -6 -3 0 1 0 1 0 1 | ||
| Cents = 1.00158 | | Cents = 1.00158 | ||
| Name = | | Name = ramanujanisma | ||
| Color name = | | Color name = nothozo comma | ||
| FJS name = | | FJS name = | ||
| Sound = | | Sound = | ||
}} | }} | ||
'''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] | '''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. | |||
== 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''). | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
[[Category:19-limit]] | [[Category:19-limit]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Ramanujanismic]] | |||
Revision as of 14:15, 5 January 2022
| Interval information |
reduced
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. 1728, being 12 to the 3rd power, is also known as mass. 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 chords in the 19-odd-limit, a basic form of which comprises the steps of 7/6-13/12-19/12 closing at the octave.
Terminology
The name ramanujanisma was first proposed by Frédéric Gagné in reference to the anecdotal story of Ramanujan finding 1729 an interesting number. Alternative names include lesser massma, proposed by Eliora, in reference to the number 1728 being known as the Maß in German, and dodecentisma, proposed by Godtone, in reference to the size being close to the relative cent of 12edo (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).