1729/1728

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Interval information
Ratio 1729/1728
Monzo [-6 -3 0 1 0 1 0 1
Size in cents 1.00158
Name(s) ramanujanisma
Color name Nothozo, 19o3oz2, nothozo 2nd
FJS name d27,13,19
open this interval in xen-calc

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).

See also