85/84

Interval information

Ratio	85/84
Factorization	2-2 × 3-1 × 5 × 7-1 × 17
Monzo	[-2 -1 1 -1 0 0 1⟩
Size in cents	20.48822¢
Name	monk comma
Color name	17ory1, soruyo 1sn, Soruyo comma
FJS name	[math]\displaystyle{ \text{P1}^{5,17}_{7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	12.8017
Weil height (log2 max(n, d))	12.8188
Wilson height (sopfr(nd))	36
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.82239 bits
Comma size	small
S-expression	S15 × S16 × S17
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85/84, the monk comma, is a 17-limit superparticular interval. It is the difference between 6/5 and 17/14, as well as 7/5 and 17/12.

Etymology

The word monk for this comma was introduced by Xenllium in 2023. It was translated from Japanese word 僧侶 (そうりょ, sōryo), a play of its color name, soruyo (as resembling pronunciation).

See also

• Small comma
• List of superparticular intervals