181/128: Difference between revisions

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Created page with "{{Infobox interval | Name = octave-reduced 181st harmonic, otonal quasi-tempered tritone | Color name = 181o4 }} '''181/128''' is the octave-reduced 181st harmonic. It can be described as an otonal quasi-tempered tritone, measuring 599.815 cents. == See also == * 256/181 – its octave complement Category:Tritone"
 
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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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'''181/128''' is the octave-reduced 181st harmonic. It can be described as an otonal quasi-tempered tritone, measuring 599.815 [[cent]]s.
'''181/128''' is the octave-reduced 181st harmonic. It can be described as an otonal quasi-tempered tritone, measuring 599.815 [[cent]]s.
== 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). 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. It can be used for adjustment of octave compression of even numbered [[edo]]s &mdash; for instance, 6ed181/128 as [[12edo]] with a slightly compressed octave, as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/J3c67AMwylw ''6ed(181/128) improv''] (excerpt with Lumatone view) and [https://www.youtube.com/watch?v=0-db7dnoiyU ''short song''] (full version) (both from 2026).
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 ==