315/256
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| Ratio | 315/256 |
| Factorization | 2-8 × 32 × 5 × 7 |
| Monzo | [-8 2 1 1⟩ |
| Size in cents | 359.04962¢ |
| Names | lazy third, octave-reduced 315th harmonic |
| Color name | Lzy3, lazoyo 3rd |
| FJS name | [math]\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]\sqrt{nd}[/math]) |
~4.26011 bits |
| 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 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.