181/128: Difference between revisions
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{{ | {{Mathematical interest}} | ||
{{Infobox interval | {{Infobox interval | ||
| Name = octave-reduced 181st harmonic, otonal quasi-tempered tritone | | Name = octave-reduced 181st harmonic, otonal quasi-tempered tritone | ||
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== Approximation == | == Approximation == | ||
181/128 is a fraction of a cent flat of a [[semioctave]] in even equal temperaments (1<span style="font-family: 'Arial', sans-serif;">\</span>2). | 181/128 is a fraction of a cent flat of a [[semioctave]] in even equal temperaments (1<span style="font-family: 'Arial', sans-serif;">\</span>2). It is very close to 1622<span style="font-family: 'Arial', sans-serif;">\</span>3245, differing by only 3.565 × 10<sup>-5</sup> 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 if and only if the edo is an even number. | 181/128 differs from its octave complement, [[256/181]] by [[32768/32761]], measuring ~0.37¢. For edos up to [[3244edo|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 == | == See also == | ||
Latest revision as of 22:22, 10 August 2025
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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 |
otonal quasi-tempered tritone
reduced harmonic
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