85/64

Interval information

Ratio	85/64
Factorization	2-6 × 5 × 17
Monzo	[-6 0 1 0 0 0 1⟩
Size in cents	491.2691¢
Names	septendecimal harmonic fourth, archagall fourth
Color name	17oy4, soyo 4th
FJS name	[math]\displaystyle{ \text{P4}^{5,17} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	12.4094
Weil height (log2 max(n, d))	12.8188
Wilson height (sopfr(nd))	34
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.90123 bits
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85/64, the septendecimal harmonic fourth or archagall fourth, is a 17-limit rooted interval that comes rather close to 4/3, from which it differs by 256/255. Notably, 85/64 is one of two intervals relatively simple intervals that can be used to generate a just version of something resembling a superpyth diatonic scale, the other being 128/85.

See also

• 128/85 – its octave complement
• 96/85 – its fifth complement
• Gallery of just intervals