Critical Bands

The principle of critical bands is one of the most fundamental aspect of our audition. It is related to the mechanical response of the basilar membrane inside the cochlea in the inner ear. It governs many of the hearing phenomena. In very general terms, critical bands are the perceptual expression of the frequency scale. More specifically, the bandwidth of a critical band marks the limit above or below which many hearing phenomena suddenly change. The three most famous examples that demonstrate this are the following:

• Loudness: If a narrow band of noise is spread over the frequency scale, while maintaining its energy constant, the sound loudness remains the same as long as the band of noise is smaller than the critical band. But when the noise bandwidth becomes larger than the critical bandwidth, then the sound loudness starts increasing (even though the energy is still the same);

• Masking: In the case of simultaneous masking, the masking threshold of a target sound (for example pure tone at a given frequency) only depends on the masker’s energy contained within the critical band centered on the target sound frequency. This means that if the masker’s energy increases within the critical band, then the masking threshold will also increase. But if the masker’s energy increases or decreases in other frequency bands, the masking threshold remains the same.

• Roughness: When two pure tones with sufficiently different frequencies are presented simultaneously, a polyphonic sound is perceived (the two frequencies are perceived). But when the frequency difference becomes smaller than the critical bandwidth, a single frequency (corresponding to the arithmetic mean of the two) is heard, and this sound is perceived as "rough" because of the amplitude modulation created by the interference between the two frequencies.

The critical bandwidth is not constant and depends on its center frequency (generally increases with it). Critical bands are usually modeled by either Bark bands introduced by Zwicker, or ERB bands defined by Moore and colleagues (even though critical bands and Bark bands are often confused). The large majority of psychoacoustic indicators (Loudness, Sharpness, Roughness, Tonality metrics, etc.) are based on this concept, through a filter bank decomposition of the sound where each filter corresponds to a given critical band.