# Bark

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The Bark is the standard unit corresponding to one of the 24 critical bands representing the width of human hearing system. Human hearing critical bands are narrow at low frequencies, but become wider at higher frequencies.

(in Hz) ${\displaystyle 0,100,200,300,400,510,630,770,920,1080,1270,1480,1720,2000,2320,2700,3150,3700,4400,5300,6400,7700,9500,12000,15500}$

converting a f to it's bark equivalent:

${\displaystyle Bark=13\cdot \arctan {\left({\frac {0.0076f}{1000}}\right)}+3.5\cdot \arctan {\left({\frac {f}{7500}}\right)^{2}}}$

Example: Widths of the critical bands gets wider towards the higher frequencies. MP3 32 equal width subbands (shown on top), based upon PQF filterbank cover the 22.05kHz bandwidth. The width of 1 MP3 subband is about ${\displaystyle 689Hz(32*689=22.05kHz)}$. Ogg Vorbis uses Bark Scale mapping in it's filterbank decomposition. Both Bark and ERB bilinear transforms are equivalent in representing the critical bands of human auditory system.

## References

• Smith, O. Julius. Abel, Johnathen. "Bark and ERB Bilinear Transforms". Dec 1999
<http://citeseer.ist.psu.edu/smith99bark.html> (17 Feb 2007)
• Smith, O. Julius. "The Bark Frequency Scale (condensed)". 3 Jan. 2006.
<http://ccrma.stanford.edu/~jos/bbt/Bark_Frequency_Scale.html> (17 Feb 2007)