181/128

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Ratio	181/128
Subgroup monzo	2.181 [-7 1⟩
Size in cents	599.8151¢
Names	octave-reduced 181st harmonic, otonal quasi-tempered tritone
Color name	181o4
FJS name	[math]\displaystyle{ \text{A4}^{181} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	14.4998
Weil height (log2 max(n, d))	14.9997
Wilson height (sopfr(nd))	195
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181/128 is the octave-reduced 181st harmonic. It can be described as an otonal quasi-tempered tritone, measuring 599.815 cents.

Approximation

181/128 is a fraction of a cent flat of a semioctave in even equal temperaments (1\2). It is very close to 1622\3245, differing by only 3.565 × 10^-5 cents.

181/128 differs from its octave complement, 256/181 by 32768/32761, measuring ~0.37¢. For edos up to 3244, both 181/128 and 256/181 are equated in the patent val mapping if and only if the edo is an even number.

See also

• 256/181 – its octave complement