Theory of Pitch:
The musical pitch of an audio signal is a perceptual feature, relevant only in the context of a human listening to that signal. The musical pitch scales that are used today were developed before people knew about frequency and spectral content, which was based on the similarity or dissimilarity of the note. Pitch is loosely related to the log of the frequency, perceived pitch increasing about an octave with every doubling in frequency. However, frequency doubling below 1000 Hz corresponds to a pitch interval slightly less than an octave, while pitch doubling above 5000 Hz corresponds to an interval slightly more than an octave. This relationship also changes with intensity. The perceived pitch of a sinusoid increases with intensity when the sinusoid is above 3000 Hz, and a sinusoid with frequency below 2000 Hz is perceived to drop in pitch as the intensity.
It is important to note that these measurements of the differences between frequency and the perception were made on isolated sinusoids. Real-world sounds have many harmonics above the fundamental frequency. The perception of pitch changes with this harmonic content as well. A richer spectrum seems to reinforce the sensation of the pitch, making the octave seem more “in-tune”. The more sine-like a waveform is, the more distinct is the notion of frequency, but the less distinct is the perception of pitch. This sensation also varies with the relationship between the partials. The more harmonically related the partials of a tone are, the more distinct the perception of pitch. Pitch perception also changes with intensity, duration and other physical features of the waveform.
There is some controversy as to how the human auditory system perceives pitch .One group of people have traditionally used pure tone pitches to measure phenomena like critical bands, masking, and pitch perception. The other group of people uses more complex tones to see how humans perceive groups of sounds and dissect the “scene” of sound around them. There are also important observations arising from the psychology, psychoacoustics and psychophysics being researched around the perception of tones and pitch, which provide insight into the problem of automatic f0 estimation.