181/128: Difference between revisions

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== 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. It can be used for adjustment of octave compression of even numbered [[edo]]s — 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''] (2026).

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. It can be used for adjustment of octave compression of even numbered [[edo]]s — 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.

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 == Approximation ==
-/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''] (2026).
+/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).
 /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.