97/84
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Ratio
97/84
Subgroup monzo
2.3.7.97 [-2 -1 -1 1⟩
Size in cents
249.1145¢
Names
nonacesimoseptimal semifourth,
homothetic semifourth
Color name
97or2
FJS name
[math]\text{M2}^{97}_{7}[/math]
Special properties
reduced
Tenney height (log2 nd)
12.9922
Weil height (log2 max(n, d))
13.1998
Wilson height (sopfr(nd))
111
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.23227 bits
Open this interval in xen-calc
| Interval information |
homothetic semifourth
(Shannon, [math]\sqrt{nd}[/math])
97/84 is the arithmetic mean of 7/6 and 8/7, which closely approximates their geometric mean, that is, the square root of 4/3, categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma S97 = 9409/9408. Therefore, 97/84 is approximated well in any ET with a good approximation of 4/3 by an even number of steps, such as by 5\24 or 11\53. It is closely related to 97/56, a semitritave.