161/128

Interval information

Ratio	161/128
Subgroup monzo	2.7.23 [-7 1 1⟩
Size in cents	397.1003¢
Names	arithmetic mean major third, octave-reduced 161th harmonic
Color name	23oz4
FJS name	[math]\displaystyle{ \text{M3}^{7,23} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	14.3309
Weil height (log2 max(n, d))	14.6618
Wilson height (sopfr(nd))	44
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.12125 bits
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In just intonation, 161/128, the arithmetic mean major third is the frequency ratio between the 161th and the 128th harmonic. It is the arithmetic mean between the just major third and the Pythagorean major third: (5/4 + 81/64)/2 = 161/128.

It can also be calculated from the syntonic comma: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.