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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.26011 bits
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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 is derived from the color notation (Lzy3). Coincidentally, it is also 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, although this is not the source of the name.

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.