Augmented chord in the chromatic circle Play (help·info)

A one-third octave is a logarithmic unit of frequency ratio equal to either one third of an octave (1200/3 = 400 cents: major third) or one tenth of a decade (3986.31/10 = 398.631 cents: M3 Play (help·info)).^[1] An alternative (unambiguous) term for one tenth of a decade is a decidecade.^[2][3]

Definitions

Base 2

ISO 18405:2017 defines a "one-third octave" (or "one-third octave (base 2)") as one third of an octave, corresponding to a frequency ratio of ${\displaystyle 2^{1/3))$. A one-third octave (base 2) is precisely 400 cents.

Base 10

IEC 61260-1:2014 and ANSI S1.6-2016 define a "one-third octave" as one tenth of a decade, corresponding to a frequency ratio of ${\displaystyle 10^{1/10))$. This unit is referred to by ISO 18405 as a "decidecade" or "one-third octave (base 10)".^[4]

One decidecade is equal to 100 savarts (approximately 398.631 cents).