81/76

81/76, Boethius' chromatic semitone, is a 19-limit interval of about 110.3 cents in size. It differs from 2187/2048, the Pythagorean apotome, by 513/512, the undevicesimal schisma or Boethius' comma, hence the name. It also differs from 16/15 by 1216/1215, and is the difference between 19/16 (otonal minor third) and 81/64 (Pythagorean major third) and thus is 81/80 larger than 20/19.

Interval information

Ratio	81/76
Subgroup monzo	2.3.19 [-2 4 -1⟩
Size in cents	110.307¢
Name	Boethius' chromatic semitone
Color name	19u1, inu 1sn, Inu comma
FJS name	[math]\displaystyle{ \text{A1}_{19} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	12.5878
Weil norm (log2 max(n, d))	12.6797
Wilson norm (sopfr(nd))	35
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Temperaments

This interval has been proposed to be used as a comma to be tempered out, though the musical utility of it is unknown yet. The name dog comma was suggested by Xenllium in 2023, translated from Japanese word 犬 (いぬ, inu), a play of its color name, inu (as the identical pronunciation).

See also

• Large comma