One-third octave

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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 {{audio|Decidecade on C.mid|Play}}).[https://books.google.com/books?id=1x_RvffW-hcC&dq=one+third+octave+base+2+10&pg=PA1325 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=

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)".(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 savarts (approximately 398.631 cents).

One-third octave

Definitions

=Base 2=

=Base 10=

See also

References

Further reading