1729/1728: Difference between revisions
fixed explanation of "Ramanujan's number" |
lesser massma - clarification necessary because 1728/1727 can also be named massma just like 144/143 is named grossma |
||
| Line 4: | Line 4: | ||
| 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 = massma, <br>ramanujanisma, <br>dodecentisma | | Name = lesser massma, <br>ramanujanisma, <br>dodecentisma | ||
| Color name = | | Color name = | ||
| 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''' 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 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]], 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 11:09, 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.