97/56
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Ratio
97/56
Subgroup monzo
2.7.97 [-3 -1 1⟩
Size in cents
951.0695¢
Names
nonacesimoseptimal semitwelfth,
homothetic semitwelfth
Color name
97or6
FJS name
[math]\text{M6}^{97}_{7}[/math]
Special properties
reduced
Tenney height (log2 nd)
12.4073
Weil height (log2 max(n, d))
13.1998
Wilson height (sopfr(nd))
110
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.22832 bits
Open this interval in xen-calc
| Interval information |
homothetic semitwelfth
(Shannon, [math]\sqrt{nd}[/math])
97/56 is the arithmetic mean of 7/4 and 12/7, which closely approximates their geometric mean, that is, the square root of 3/1, categorizing it as a semitwelfth. 3/1 differs from two instances of 97/56 by the 0.18-cent comma S97 = 9409/9408. Therefore, 97/56 is approximated well in any ET with a good approximation of 3/1 by an even number of steps (or in even-numbered EDTs), such as by 19\24 or 42\53. It is closely related to 97/84, a semifourth.