Definitions

fundamental-bass

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.

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 may 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, as reported by J. C. R. Licklider in 1954. 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.)

Examples

Timpani (kettle drums) are tuned by listening for the missing fundamental. Hit in the usual way (half to three-quarters the distance from the center to the rim), the fundamental note of a timpani is very weak in relation to its second through fifth harmonics. A timpani tuned to 100 Hz will produce sound most strongly at 200, 300, 400 and 500 Hz.

A violin's lowest air and body resonances generally fall between 250 Hz and 300 Hz. The fundamental frequency of the open G3 string is below 200 Hz in modern tunings as well as most historical tunings, so the lowest notes of a violin have an attenuated fundamental, although listeners seldom notice this.

The missing fundamental phenomenon is used electronically by some pro audio manufacturers to allow sound systems to seem to produce notes that are lower in pitch than they are capable of reproducing. In a hardware effects unit or a software plugin, a crossover filter is set at a low frequency above which the sound system is capable of safely reproducing tones. Musical signal content above the high-pass part of the crossover filter is sent to the main output which is amplified by the sound system. Low frequency content below the low-pass part of the crossover filter is sent to a circuit where harmonics are synthesized above the low notes. The newly created harmonics are mixed back into the main output to create a perception of the filtered-out low notes. Using a device with this synthetic process can reduce complaints from low frequency noise carrying through walls and it can be employed to reduce low frequency content in loud music that might otherwise vibrate and damage breakable valuables.

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.

References

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