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.

While this interval is neutral in size, its position close to the submajor area is evident in that it acts as a bluesy version of 5/4, from which it differs by 64/63.