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, Ramanujan's comma
FJS name	[math]\displaystyle{ \text{d2}^{7,13,19} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	21.5106
Weil norm (log2 max(n, d))	21.5114
Wilson norm (sopfr(nd))	60
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1729/1728, the massma, is a 19-limit (more accurately, 2.3.7.13.19 subgroup) superparticular interval and an unnoticeable comma. The comma forms the difference between 19/18 and 96/91 semitones.

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.

1729/1728 belongs to the list of essential tempering commas in the 19-limit.

See also

• Wikipedia:1728 (number)
• Wikipedia:1729 (number)