The ear perceives a 'missing fundamental' pitch from upper harmonics alone

When a sound contains harmonics 3f₀, 4f₀, 5f₀ but not the fundamental f₀, the auditory system perceives a pitch at f₀ — the ‘virtual pitch’ or ‘missing fundamental.’ The ear extracts pitch by finding the best-fitting harmonic template to the partials present, estimating the common fundamental even when it is absent. This is why a telephone can convey speech with frequencies only above 300 Hz, yet listeners hear the speaker’s full bass voice. Virtual pitch is a form of holistic (as opposed to analytic) listening, where the ear fuses partials into a single percept. When partials do not fit a harmonic template, pitch perception degrades and the sound may be heard as noise or as multiple tones.

Examples

Westminster Chimes played with partials at 780, 1040, and 1300 Hz (harmonics 3, 4, 5 of 260 Hz) — the ear hears a melody at 260 Hz even though that frequency is absent. Bass guitar through a small speaker with poor bass response still sounds bass-y because of virtual pitch.

Assessment

Explain why removing the fundamental frequency of a bass guitar note from a recording does not eliminate the perception of that bass pitch. Then predict whether a set of partials at 500, 750, 1000 Hz (ratios 2:3:4) will produce a clear virtual pitch, and at what fundamental.