Missing fundamental

A sound is said to have a missing fundamental, suppressed fundamental, or phantom fundamental when its overtones suggest a fundamental frequency but the sound lacks a component at the fundamental frequency itself. However, the brain perceives the pitch of a tone not only by its fundamental frequency, but also by the ratio of the higher harmonics. Thus, we may perceive the same pitch (perhaps with a different timbre) even if the fundamental frequency is missing from a tone.

Example
For example, when a note (that is not a pure tone) has a pitch of 100 Hz, it will consist of frequency components that are close to integer multiples of that value (e.g. 100, 200, 300, 400, 500.... Hz). However, smaller loudspeakers will not produce low frequencies, and so in our example, the 100 Hz component may be missing. Nevertheless, a pitch corresponding to the fundamental may still be heard.

Explanation
It was once thought that this effect was because the missing fundamental was replaced by distortions, introduced by the physics of the ear. However, experiments subsequently showed that when a noise was added, which would have masked these distortions had they been present, listeners still heard a pitch corresponding to the missing fundamental. It is now widely accepted that the brain processes the information present in the overtones to calculate the fundamental frequency. The precise way in which it does so is still a matter of debate, but the processing seems to be based on an autocorrelation involving the timing of neural impulses in the auditory nerve.

This very concept of 'missing fundamental' being reproduced based on the overtones in the tone is nowadays used to create the illusion of bass. By processing certain overtones selectively, a rich bass effect can be created using the small speakers which cannot produce lower frequency components below 100 Hz. While speakers produce tones above 100 Hz, the processed bass overtones compel the brain to replace the missing fundamental bass signals, creating the illusion of bass.

The following recording contains several notes, followed by the same notes with a suppressed fundamental. To some listeners, the last note (a G at roughly 49 Hz) sounds nearly identical each time.

(It should be mentioned that the final bass note in each version is only likely to sound identical when played on small (eg computer) speakers that cannot produce any real bass. However, when played through large full-range speakers (or full-range headphones), the difference between the final notes becomes as apparent as it was for the higher notes.)

Differences in perception
Research conducted at Heidelberg University, as described in the January 2006 issue of the German audiophile magazine AUDIO, indicates that the general population can be divided into those who perceive missing fundamentals, and those who primarily hear overtones. The magazine article states that the difference between the perceived pitches can be up to 4 octaves.