Pitch, Models of

Pitch is the subjective attribute of sound that changes when one hears different musical notes played on the same instrument at a fixed loudness and duration. Musical notes with different subjective pitches vary in the frequency per second of repeating cycles of compression and rarefaction of air molecules—equivalent to the fundamental frequency (f0) of naturally occurring complex waveforms. For such periodic sounds, increases in frequency are associated with increases in pitch. However, sounds that are not strictly periodic can also give rise to pitch sensations (e.g., chimes, footsteps, and hand claps). As an example, the sibilants in the words see and she are not strictly periodic, but they seem to differ in pitch.

Models of pitch perception are based on finding the f0 or the approximate f0 when it is not present or the harmonics are mistuned, and the models take into account how the basilar membrane in the cochlea of the inner ear transforms the incoming acoustic signal. This membrane is triangular, and it changes in thickness such that it is narrow and thin at one end and wide and thick at the other.

As it vibrates in response to incoming sounds, low- or high-frequency sounds tend to produce a maximum movement toward the wide/thick or narrow/thin end, respectively. Hair cell receptors positioned along the basilar membrane trigger neural firings along the VIIIth nerve to the brain in response to membrane movements to input frequency components; this is the basis of the place theory of hearing.

Any model of pitch has to be based on the neural firings emerging from the inner ear in response to the input sound, and to describe pitch perception, models have been developed that are based on frequency analysis (spectral or pattern recognition approaches) and/or on time analysis (temporal approach).

A sound that has a clear pitch, or note, associated with it has a repeating (or approximately repeating, if the harmonics are mistuned) waveform. The upper part of the figure shows a synthesized pulse waveform with 19 harmonics that rise linearly in f0 from 100 to 400 Hz. In terms of the frequency components that are present in a repeating waveform, or are periodic, they must be exact integer (2*f0, 3*f0, 4*f0, 5*f0 …) multiples of the f0, and they are known as “harmonics.”

The place mechanism signals to the brain the frequencies of individual components in the input sound, and models of pitch have to start with this principle. An early model of pitch perception was proposed by Ohm in 1843 (Ohm's acoustical [Page 868]law), which suggests that “a pitch corresponding to a certain frequency can only be heard if the acoustical wave contains power at that frequency.” If f0 is absent, Ohm's law suggests that the pitch would jump up an octave to the next lowest component, 2*f0, but this is not what happens in practice, as noted by Seebeck's “missing fundamental” experiments with a siren. The minimum frequency spacing between adjacent harmonics (which is f0) provides a basis for finding f0 and the place model of pitch.

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