1729/1728: Difference between revisions
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'''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]]. '''Massma'''<ref>referring to number 1728 being known as the ''Maß'' in German. </ref>, '''ramanujanisma'''<ref>referring to the anecdotal story of [[Wikipedia: Ramanujan|Ramanujan]] finding 1729 an interesting number. </ref>, and '''dodecentisma'''<ref>referring to the size being close to the cent relative to 12edo. </ref> have been proposed as the name. The comma forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]]. | '''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]]. '''Massma'''<ref>referring to number 1728 being known as the ''Maß'' in German. </ref>, '''ramanujanisma'''<ref>referring to the anecdotal story of [[Wikipedia: Ramanujan|Ramanujan]] finding 1729 an interesting number. </ref>, and '''dodecentisma'''<ref>referring to the size being close to the cent relative to 12edo. </ref> have been proposed as the name. The comma forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]]. | ||
Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729|1729]] is known for being Ramanujan's number and the first number that can be expressed as a sum of more than 1 integer cubes. | 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 a sum of more than 1 integer cubes. | ||
Remarkably, this comma is very close to one cent. | Remarkably, this comma is very close to one cent. | ||
Revision as of 14:36, 29 October 2021
| Interval information |
ramanujanisma,
dodecentisma
reduced
1729/1728 is a 19-limit (more accurately, 2.3.7.13.19 subgroup) superparticular interval and an unnoticeable comma. Massma[1], ramanujanisma[2], and dodecentisma[3] have been proposed as the name. The comma forms the difference between the octave and a stack of 7/6, 13/12 and 19/12.
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 a sum of more than 1 integer cubes.
Remarkably, this comma is very close to one cent.
Tempering out this comma enables the related essentially tempered chords in the 19-odd-limit.