Perception of sound intensity, pitch and timbre

To physically characterize a pure sound, all we need to do is specify three parameters of the associated pressure wave: its amplitude (on which its acoustic power per unit area and level in decibels depend), its frequency or period and, finally, its phase, in the chosen time frame. A periodic sound requires a slightly more complex description in the time domain, but Fourier analysis makes it easy to uniquely decompose the pressure wave into a sum of harmonic components, whose frequencies are all multiples of the fundamental frequency; the amplitude and phase of each of these allow us to characterize, completely and uniquely, the sound under consideration. Finally, it is possible to generalize the Fourier transform decomposition method to any complex sound, obtaining components that are no longer necessarily at discrete frequencies, nor multiples of a given fundamental.

This spectral-type analysis has long seemed relevant to the perception of sound via the auditory nervous system. Indeed, before the transduction stage, which enables the auditory nerve to convey nerve impulses organized according to the physical structure of the excitatory sound, the cochlea performs an analysis of the sound, sorting out the mechanical excitations according to a principle of tonotopy: the components of the sound at different frequencies bring into resonance, according to complex mechanisms, different sections of the basilar membrane along which the sensory cells are distributed. Tonotopy, which provides a kind of spectrum of the sound signal reaching the cochlea, is then respected all the way along the auditory pathways to the cortex.

In the case of a pure sound, intuition easily allows us to link the sensations associated with perception with the physical quantities that give rise to them: the sensation of sonic strength, also known as sonicity or sonoria (which means that a sound is louder or softer) seems naturally linked to the amplitude, power or level of the sound; the sensation of pitch (expressed by the adjectives "low" or "high") appears closely linked to frequency. It's more difficult to give a subjective description of a complex sound, even a periodic one, and we're quickly led to introduce notions revolving around what we call the timbre of the sound. Finally, the central nervous system has a certain ability to push the analysis of a sound as far as attempts to identify its source, based on perceived characteristics: it's a natural tendency to try to trace the timbre of a sound back to the nature of the instrument that produced it. Nevertheless, establishing general relationships between the physical and perceptual characteristics of sounds has been a laborious task for psychoacousticians since the first half of the XIX ^e ...