Analytical expressions for the tonotopic sensory scale

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Abstract
Accuracy and simplicity of analytical expressions for the relations between frequency and critical bandwidth as well as critical‐band rate (in Bark) are assessed for the purpose of applications in speech perception research and in speech technology. The equivalent rectangular bandwidth (ERB) is seen as a measure of frequency resolution, while the classical critical‐band rate is considered a measure of tonotopic position. For the conversion of frequency to critical‐band rate, and vice versa, the inversible formula z=[26.81/(1+1960/f )]−0.53 is proposed. Within the frequency range of the perceptually essential vowelformants (0.2–6.7 kHz), it agrees to within ±0.05 Bark with the Bark scale, originally published in the form of a table.

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