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 ...

frequency ratio R, or r, is the eighteenth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ar'' (pronounced ), plural ''ars''. The lette ...

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

savart The savart is a unit of measurement for musical pitch intervals (). One savart is equal to one thousandth of a decade ( 10/1: 3,986.313714 cents): 3.9863 cents. Musically, in just intonation, the interval of a decade is precisely a just major ...

s (approximately 398.631 cents).

Definitions

Base 2

Base 10

See also

References

Further reading