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A one-third octave is a
logarithmic unit A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...
of
frequency ratio In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (), 1.5, and may be approximated by an equal tempered perfect fifth () which is 27 ...
equal to either one third of an
octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
(1200/3 = 400
cent Cent may refer to: Currency * Cent (currency), a one-hundredth subdivision of several units of currency * Penny (Canadian coin), a Canadian coin removed from circulation in 2013 * 1 cent (Dutch coin), a Dutch coin minted between 1941 and 1944 * ...
s:
major third In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and P ...
) or one tenth of a
decade A decade () is a period of ten years. Decades may describe any ten-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 that "du ...
(3986.31/10 = 398.631 cents: M3 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade. One octave is a factor of 2, so \log_ (2) = 0.301 decades per octave, while a third would be 0.\overline.


Definitions


Base 2

ISO ISO is the most common abbreviation for the International Organization for Standardization. ISO or Iso may also refer to: Business and finance * Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007 * 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; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
61260-1:2014 and
ANSI The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organi ...
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 (398.63 cents).


See also

*
Decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
*
Octave band An octave band is a frequency band that spans one octave (). In this context an octave can be a factor of 2 or a factor of 100.3. 2/1 = 1200 cents ≈ 10. Fractional octave bands such as or of an octave are widely used in engineering acoustics. ...
*
Pseudo-octave A pseudo-octave, pseudooctave,"Interview with Max Mathews", p.21. Author(s): C. Roads and Max Mathews. Source: ''Computer Music Journal'', Vol. 4, No. 4, (Winter, 1980), pp. 15–22. Published by: The MIT Press. or paradoxical octave"The Parad ...
*
Tritonic scale A tritonic scale is a musical scale or mode with three notes per octave. This is in contrast to a heptatonic (seven-note) scale such as the major scale and minor scale, or a dodecatonic (chromatic 12-note) scale, both common in modern Western ...


References


Further reading

* {{cite journal , title=A terminology standard for underwater acoustics and the benefits of international standardization. , author-last1=Ainslie , author-first1=Michael A. , author-last2=Halvorsen , author-first2=Michele B. , author-last3=Robinson , author-first3=Stephen P. , orig-date=2021-11-09 , date=January 2022 , issn=0364-9059 , eissn=1558-1691 , journal=
IEEE Journal of Oceanic Engineering The IEEE Journal of Oceanic Engineering is a journal published by the Institute of Electrical and Electronics Engineers. The journal's editor in chief is Associate Professor Mandar Chitre, of the National University of Singapore. According to the ...
, publisher=
IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...
, volume=47 , issue=1 , pages=179–200 , doi=10.1109/JOE.2021.3085947 , s2cid=243948953 , url=https://ieeexplore.ieee.org/document/9607022 , access-date=2022-12-20}

(22 pages) Intervals (music) Logarithmic scales of measurement