1729/1728: Difference between revisions
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lesser massma - clarification necessary because 1728/1727 can also be named massma just like 144/143 is named grossma |
m clarified reasoning for my proposed name "dodecentisma" |
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'''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]]. '''Lesser 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 | '''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]]. '''Lesser 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 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 referring to 1728 being a power of 12 (dodeca). </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]], 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>). | ||
Revision as of 17:37, 1 November 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. Lesser 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, 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).
Remarkably, this comma is very close to one cent.
Tempering out this comma enables the related essentially tempered chords in the 19-odd-limit.
See also
Notes
- ↑ referring to number 1728 being known as the Maß in German.
- ↑ referring to the anecdotal story of Ramanujan finding 1729 an interesting number.
- ↑ referring 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 referring to 1728 being a power of 12 (dodeca).