Pitch is often defined as the characteristic of a sound that makes it sound high low, or that determines its position on a musical scale. Pitch is related to the repetition rate of the waveform of a sound. For a pure tone, this corresponds to the frequency; for a complex tone it usually (but not always) corresponds to the fundamental frequency. Frequency is the most important contributor to the sensation of pitch, but not the only one by any means. Other contributors to pitch include intensity, spectrum, duration, amplitude envelope, and the presence of other sounds.
Various attempts have been made to establish a psychophysical pitch scale. If, after listening to a 4000-Hz tone followed by a tone of very low frequency, one is asked tune an oscillator to a pitch halfway between, a likely choice would be around 1000 Hz. On a scale of pitch, then, 1000 Hz is judged halfway between 0 and 4000 Hz. The unit for subjective pitch is the mel; the scale is arranged so that doubling the number of mels doubles the subjective pitch. A scale from 0 to 2400 mels covers the audible range 20 to 16,000 Hz.
A numerical scale of pitch (in mels) is not nearly so useful as a numerical scale of loudness (in sones), however. Pitch is more often related to a musical scale, where the octave is the "natural" pitch interval that is subdivided into the desired number steps.
Two major theories of pitch perception have been developed; they are usually referred to as the place (or frequency) theory and the periodicity (or time) theory. According to the place theory, the cochlea converts a vibration in time to a vibration pattern in space (along the basilar membrane), and this in turn excites a spatial pattern neural activity. The place theory explains some aspects of auditory perception but fa; to explain others.
According to the periodicity theory of pitch, the ear performs a temporal analysis of the sound wave. Presumably, the time distribution of impulses carried along the auditory nerve has encoded into it the temporal structure of the sound wave.