1729/1728
| 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).