1729/1728

Interval information

Ratio	1729/1728
Factorization	2-6 × 3-3 × 7 × 13 × 19
Monzo	[-6 -3 0 1 0 1 0 1⟩
Size in cents	1.001582¢
Names	massma, ramanujanisma, dodecentisma
FJS name	[math]\displaystyle{ \text{d2}^{7,13,19} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	21.5106
Weil height (log2 max(n, d))	21.5114
Wilson height (sopfr(nd))	60
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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, ramanujanisma, and dodecentisma 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.

See also

• List of superparticular intervals
• Unnoticeable comma