The strange thing is that if we are presented with a musical tone containing only harmonics and no fundamental, we nevertheless still hear the fundamental. It is as if our brain senses what 'should' be there and fills in the missing root frequency or 'residue'. Residue perception not only explains why we can 'hear' the bass on a crummy little radio, but may also underpin speech intelligibility. It may be that our ability to interpret the spoken word relies on the residues that don't always feature strongly in voice. For example, hearing aids that add or boost the fundamental frequency seem to be more effective than ones that simply amplify the entire input signal.
Some acoustic scientists believe that residue perception also lies at the heart of music theory.
Residue perception might explain why we hear a C major chord as the 'same', no matter which inversion is sounded. But it remains a mystery how residue perception arises. If this were so, then shifting the frequencies of all the partials by the same amount should leave the perceived residue unchanged. The critical ingredient, however, is that the oscillator should be nonlinear, which means that the vigour of its response is not directly proportional to the strength of the driving. Nonlinear oscillatory systems like this can display a wide range of behaviour, ranging from a nearly resonant response to erratic, chaotic wobbles.