105/64
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| Ratio | 105/64 |
| Factorization | 2-6 × 3 × 5 × 7 |
| Monzo | [-6 1 1 1⟩ |
| Size in cents | 857.09462¢ |
| Name | septimal neutral sixth |
| Color name | zy6, zoyo 6th |
| FJS name | [math]\text{M6}^{5,7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 12.7142 |
| Weil height (log2 max(n, d)) | 13.4285 |
| Wilson height (sopfr (nd)) | 27 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.56287 bits |
| open this interval in xen-calc | |
105/64 is a 7-limit neutral sixth and is 857.095¢ wide. It might be called a septimal neutral sixth.
When used as a generator, it approximates 7edo as the 6th note of the scale; the difference between 5\7 and 105/64 is 0.048¢. In addition, it only differs from the large tridecimal neutral sixth (64/39) by a schismina (4096/4095). When we also consider that 105/64 can be thought of as the octave reduced greatest common factor of 3, 5, and 7, 105/64 and its octave equivalents might be used to tune 7edo on a stringed instrument via harmonics, though so far this idea has not been tested.