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A one-third octave is a of equal to either one third of an (1200/3 = 400 cents: ) or one tenth of a decade (3986.31/10 = 398.631 cents: M3 ). Malcolm J. Crocker, Handbook of Acoustics (1997) An alternative (unambiguous) term for one tenth of a decade is a decidecade.von Benda-Beckmann, A. M., Aarts, G., Sertlek, H. Ö., Lucke, K., Verboom, W. C., Kastelein, R. A., ... & Ainslie, M. A. (2015). Assessing the impact of underwater clearance of unexploded ordnance on harbour porpoises (Phocoena phocoena) in the Southern North Sea. Aquatic Mammals, 41(4), 503.ISO 18405 Underwater Acoustics - Terminology (International Organization for Standardization, Geneva, 2017)

Definitions
Base 2
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 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)".(This makes sense as, if we want one third of an octave, the ratio will be f2/f1=2^{1/3}, and if we log10 both members of equation we have, log{(f2/f1)}=log{(2^{1/3})}-> 
log(f2/f1)=log(2)*1/3, which is approximately 0,1.

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

See also

Further reading
  • Https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9607022" target="_blank" rel="nofollow">[2] (22 pages)

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