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 (help·info)).[1] An alternative (unambiguous) term for one tenth of a decade is a decidecade.[2][3]
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 [math]\displaystyle{ 2^{1/3} }[/math]. 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 [math]\displaystyle{ 10^{1/10} }[/math]. 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).
See also
- Decibel
- Octave band
- Pseudo-octave
- Tritonic scale
References
- ↑ Malcolm J. Crocker, Handbook of Acoustics (1997)
- ↑ 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)
- ↑ (This makes sense as, if we want one third of an octave, the ratio will be [math]\displaystyle{ f2/f1=2^{1/3} }[/math], and if we log10 both members of equation we have, [math]\displaystyle{ log{(f2/f1)}=log{(2^{1/3})}-\gt log(f2/f1)=log(2)*1/3 }[/math], which is approximately 0,1.
Further reading
- "A terminology standard for underwater acoustics and the benefits of international standardization.". IEEE Journal of Oceanic Engineering (IEEE) 47 (1): 179–200. January 2022. doi:10.1109/JOE.2021.3085947. ISSN 0364-9059. [1] (22 pages)
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