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 Play ).[1] An alternative (unambiguous) term for one tenth of a decade is a decidecade.[2][3]

Augmented chord in the chromatic circle Play 

One octave is a factor of 2, so decades per octave, while a third would be .

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 . 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 . 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 ,and if we log10 both members of equation we have, ,which is approximetely 0,1.

One decidecade is equal to 100 savarts (398.63 cents).

See also

References
  1. Malcolm J. Crocker, Handbook of Acoustics (1997)
  2. 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.
  3. ISO 18405 Underwater Acoustics - Terminology (International Organization for Standardization, Geneva, 2017)
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