A one-third octave is a

logarithmic unit A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences among the magnitudes of the numbers involved. Unlike a linear scale where each u ...

of frequency ratio equal to either one third of an

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

(1200/3 = 400 cents:

major third In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...

) or one tenth of a

decade A decade (from , , ) is a period of 10 years. Decades may describe any 10-year period, such as those of a person's life, or refer to specific groupings of calendar years. Usage Any period of ten years is a "decade". For example, the statement ...

(3986.31/10 = 398.631 cents: M3 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade.

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^

. A one-third octave (base 2) is precisely 400 cents.

Base 10

IEC The International Electrotechnical Commission (IEC; ) is an international standards organization that prepares and publishes international standards for all electrical, electronic and related technologies. IEC standards cover a vast range of ...

61260-1:2014 and

ANSI The American National Standards Institute (ANSI ) is a private nonprofit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organiz ...

S1.6-2016 define a "one-third octave" as one tenth of a decade, corresponding to a frequency ratio of

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^

, and if we log10 both members of equation we have,

log=log->
 log(f2/f1)=log(2)*1/3

, which is approximately 0,1. One decidecade is equal to 100 savarts (approximately 398.631 cents).

Definitions

Base 2

Base 10

See also

References

Further reading