The critical band is the ear's frequency resolution width; partials within it interfere and cause roughness

The basilar membrane in the cochlea acts as a bank of bandpass filters. Each filter has a frequency range called the critical band — approximately 100 Hz wide at low frequencies, growing to ~20% of center frequency above 500 Hz. Two partials falling within the same critical band interact: they cause beating that is perceived as roughness (sensory dissonance). Partials farther apart than the critical bandwidth cause little or no roughness and are heard as distinct tones. The critical band is the key psychoacoustic unit: it determines when partials clash and when they fuse. Dissonance is maximal when two partials are separated by about 1/4 of the critical bandwidth, and decreases to near zero when they are separated by a full critical bandwidth or more.

Examples

Two sine waves 5 Hz apart (both ~1000 Hz) fall within the critical band and cause fast beating. Two sine waves 300 Hz apart at ~1000 Hz are outside the critical band and sound like two distinct tones without roughness. In a piano chord, partials of different notes that fall within each other’s critical bands contribute to sensory dissonance.

Assessment

At a center frequency of 1000 Hz, the critical bandwidth is approximately 160 Hz. Two partials are at 1000 Hz and 1040 Hz (40 Hz apart). Are they inside or outside the critical band? Predict whether they will cause roughness. Now move the second partial to 1200 Hz — what changes?