Bark scale

Chart of the critical bands of the Bark scale

Since the direct measurements of the critical bands are subject to error, the values in this table have been generously rounded.[1]

In his letter "Subdivision of the Audible Frequency Range into Critical Bands", Zwicker states:

"These bands have been directly measured in experiments on the threshold for complex sounds, on masking, on the perception of phase, and most often on the loudness of complex sounds. In all these phenomena, the critical band seems to play an important role. It must be pointed out that the measurements taken so far indicate that the critical bands have a certain width, but that their position on the frequency scale is not fixed; rather, the position can be changed continuously, perhaps by the ear itself."

Thus the important attribute of the Bark scale is the width of the critical band at any given frequency, not the exact values of the edges or centers of any band.

To convert a frequency f (Hz) into Bark use:

${\displaystyle {\text{Bark}}=13\arctan(0.00076f)+3.5\arctan((f/7500)^{2})\,}$

or (Traunmüller, 1990)[4]

${\displaystyle {\text{Bark}}=[(26.81f)/(1960+f)]-0.53\,}$

or (Wang, Sekey & Gersho, 1992)[5]

${\displaystyle {\text{Bark}}=6\sinh ^{-1}(f/600)}$

• Luminosity function, which describes the average sensitivity of the human eye to light of different wavelengths.
• Fletcher–Munson curves
• Equivalent rectangular bandwidth, the ERB scale
• Critical bands

• Smith and Abel – Bark and ERB Bilinear Transforms (1999)
• Auditory scales of frequency representation