105/64

Interval information

Ratio	105/64
Factorization	2-6 × 3 × 5 × 7
Monzo	[-6 1 1 1⟩
Size in cents	857.0946¢
Name	septimal neutral sixth
Color name	zy6, zoyo 6th
FJS name	[math]\displaystyle{ \text{M6}^{5,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	12.7142
Weil height (log2 max(n, d))	13.4285
Wilson height (sopfr(nd))	27
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.26123 bits
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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.

See also

• Gallery of just intervals