Critical bands are used to quantify the ability of the human ear to distinguish between individual frequency tones. The human ear can hear from 20 to 20,000 Hertz, but the ability to distinguish individual tones varies as a function of frequency.
At low frequencies, the human ear can distinguish changes in frequency more easily than at high frequencies. For example, the ear can distinguish a 20 Hertz difference between 500 and 520 Hertz tones more readily than a 5000 and 5020 Hertz tones.
As a result, the ear tends to have hearing ‘bands’. These bands increase in bandwidth from low to high frequency as shown in Figure 1.
Figure 1: Bandwidth of critical band increases with frequency
The bands are defined in a similar manner to bandpass filters, with a center frequency, and a bandwidth. The bandwidth has a lower and upper frequency defined by the point where there is a 3 dB rolloff.
There are twenty four critical bands in the human hearing range. Each band is referred to as a ‘bark’. Together the 24 bands are called the ‘bark scale’ as shown in Table 1.
Table 1: Critical Bands and the Bark Scale ***
The bandwidths of the critical bands are approximately constant (around 100 Hz) for frequencies below 500 Hz. Above 500 Hertz, the bandwidths increase approximately by a constant percentage value.
Critical bands are used in the calculation of several different psycho-acoustic sound metrics, including loudness, fluctuation strength, roughness, prominence ratio, and tone-to-noise-ratio. Critical bands are similiar in nature to octave bands.
*** Table based on E. Zwicker and H. Fastl, Psychoacoustics, Facts and Models, Berlin: Springer Verlag, 3rd edition, 1999
Why do critical bands exist?
Critical bands are a phenomena created by the cochlea, the hearing organ within the inner ear. The cochlea has a logarithmic spiral shape as shown in Figure 2.
Figure 2: Cochlea human hearing organ location
This shape governs the ability to distinguish frequencies in the ear. Different parts of the cochlea respond to different frequencies as shown in Figure 3.
Figure 3: Frequency map of the cochlea human hearing organ
If the cochlea was unrolled, and the frequency response mapped upon it, there is less space dedicated to the high frequency hearing ranges versus the low frequency hearing range.
This allocation of space gives the ear the ability to distinguish changes in low frequencies better than the high frequencies. Different parts of the basilar membrane, which is part of the cochlea, are excited by different frequencies ranges. These ranges correspond to the critical bands.
Critical Bands usage in Fluctuation Strength and Roughness
If two tones are in the same critical band as shown in Figure 4, they are not easily distinguishable as separate, distinct tones. Instead, the human ear perceives the separate tones to be modulating or beating.
Figure 4: Human hearing can distinguish separate tones when they are in different critical bands (4c). When tones are in the same critical band (4a and 4b) the ear perceives a modulation or beating.
The metrics roughness and fluctuation strength describe how two or more tones create a modulation or beat frequency based on these critical bands.
Fluctuation Strength - When the tones are about 4 Hertz apart, the ear hears a single tone with a low frequency modulation or beating.
Roughness - When the tones are about 70 Hertz apart, the ear hears a rapid modulation or beating.
Two Tones – With a separation of 350 Hertz, the two tones are in different critical bands, and the ear can distinguish them from each other.
Beating phenomenon occurs because the ear cannot resolve inputs whose frequency difference is smaller than the bandwidth of the critical band.
History of Critical Bands
The concept of critical bands in human hearing was first proposed by Dr. Harvey Fletcher of AT&T Bell Labs in 1933.
The formal bark scale was proposed in 1961 by Professor Eberhard Zwicker of the Technical University Munich. Zwicker named the bark scale after German physicist Heinrich Barkhausen.