Bark

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

converting a f to it's bark equivalent:

$Bark=13*\arctan {(0.76f\div 1000)}+3.5*\arctan {((f\div 7500)^{2})}$

Figure: Human hearing critical bands versus Layer 3 32 equal width subbands

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 $689Hz(32*689=22.05kHz)$. Both Bark and ERB bilinear transforms are equivalent in representing the critical bands of human auditory system.

Additional reading:

• Bark and ERB Bilinear Transforms, Julius O. Smith and Johnathen Abel (1999)
• The Bark Frequency Scale (condensed), Julius O. Smith (2005)