315/256

Interval information

Ratio	315/256
Factorization	2-8 × 32 × 5 × 7
Monzo	[-8 2 1 1⟩
Size in cents	359.0496¢
Names	lazy third, octave-reduced 315th harmonic
Color name	Lzy3, lazoyo 3rd
FJS name	[math]\displaystyle{ \text{M3}^{5,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	16.2992
Weil height (log2 max(n, d))	16.5984
Wilson height (sopfr(nd))	34
Open this interval in xen-calc

The lazy third, 315/256 is an incredibly good approximation to the 16/13 tridecimal neutral third, differing by only a 4096/4095 schismina. However, rather than being utonal like 16/13, it is otonal, being the 315th harmonic.

The name could be derived from the fact that it is a surprisingly simple and accurate approximation of the 13th subharmonic, and so acts as a lazy way to approximate 13 in a 7-limit scale. It isn't. It's derived from the color notation (Lzy3). The accuracy and relative simplicity is merely a useful coincidence.