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]}

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Definitions

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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.

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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)".^{[4]}

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