85/84
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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]\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]\sqrt{nd}[/math])
~3.82239 bits
Comma size
small
S-expression
S15 × S16 × S17
open this interval in xen-calc
| Interval information |
Soruyo comma
reduced
(Shannon, [math]\sqrt{nd}[/math])
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).