One-third octave



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 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade.

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 $$2^{1/3}$$. 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 $$10^{1/10}$$. This unit is referred to by ISO 18405 as a "decidecade" or "one-third octave (base 10)".

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