97/84

Interval information

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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.23227 bits
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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.