# Bark scale

Bark scale

The Bark scale is a psychoacoustical scale proposed by Eberhard Zwicker in 1961. It is named after Heinrich Barkhausen who proposed the first subjective measurements of loudness [Zwicker, E. (1961), " [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN000033000002000248000001&idtype=cvips&gifs=yes Subdivision of the audible frequency range into critical bands] ," "The Journal of the Acoustical Society of America", 33, Feb., 1961.] .

The scale ranges from 1 to 24 and corresponds to the first 24 critical bands of hearing. The subsequent band edges are (in Hz) 20, 100, 200, 300, 400, 510, 630, 770, 920, 1080, 1270, 1480, 1720, 2000, 2320, 2700, 3150, 3700, 4400, 5300, 6400, 7700, 9500, 12000, 15500.

It is related to, but somewhat less popular than the mel scale.

To convert a frequency "f" (Hz) into Bark use::$ext\left\{Bark\right\} = 13 arctan\left(0.00076f\right) + 3.5 arctan\left(\left(f/7500\right)^2\right) ,$

or (traunmuller 1990) :$ext\left\{Critical band rate \left(bark\right)\right\} = \left[\left(26.81 f\right) / \left(1960 + f \right)\right] - 0.53 ,$

if result < 2 add 0.15*(2-result)
if result > 20.1 add 0.22*(result-20.1):$ext\left\{Critical bandwidth \left(Hz\right)\right\} = 52548 / \left(z^2 - 52.56 z + 690.39\right) ,$ with z in bark.

* Luminosity function, which describes the average sensitivity of the human eye to "light" of different wavelengths.

References

* [http://citeseer.ist.psu.edu/smith99bark.html Smith and Abel - Bark and ERB Bilinear Transforms (1999)]
* [http://www.ling.su.se/staff/hartmut/bark.htm Auditory scales of frequency representation]

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