Hearing Lecture notes (4): Pitch Perception
For some more material relevant to this topic see McGill auditory pages;

Pitch is the 'attribute of auditory sensation in terms of which sounds may be ordered on a musical scale'.


Pitch of pure tones is influenced mainly by their frequency, but also by intensity: high frequency pure tones go flat when played loud. The pitch of pure tones is probably coded by a combination of place and timing mechanisms:

* Place mechanisms can explain diplacusis (same tone giving different pitches in the two ears) more easily than can timing mechanisms.

* But timing theories based on phase-locked neural discharge appear to be needed in order to explain our ability to distinguish the frequencies of very short duration tones (whose place representation would be very blurred).

* Timing theories could be the whole story for musical pitch since it deteriorates at high frequencies where phase locking is weak. (The highest note on the piano is around 4 kHz; higher notes lose their sense of musical pitch). For very high frequency tones (5-20kHz) you can tell crudely which is the higher in frequency, but not what musical note is being played.

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Structure. Almost all sounds that give a sensation of pitch are periodic. Their spectrum consists of harmonics that are integer multiples of the fundamental. The pitch of a complex periodic tone is close to the pitch of a sine wave at the fundamental. Helmholtz claimed that the pitch is heard at the fundamental since the fundamental frequency gives the lowest frequency peak on the basilar membrane.

Listen to this sound (which has the fundamental frequencyof 200 Hz present)
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2.1.Missing fundamental

Seebeck (and later Schouten) showed that complex periodic sounds with NO energy at the fundamental may still give a clear pitch sensation at the fundamental (cf telephone speech - the telephone acts as a high-pass filter, removing energy below about 300 Hz).

Now listen tothis sound which has NO fundamental
Listen to the previous sound WITH the fundamental

The two sounds have the same pitch (though a different timbre).
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2.2. Helmholtz's place theory

Helmholtz suggested that the ear reintroduces energy at the fundamental by a process of distortion that produces energy at frequencies corresponding to the difference between two components physical present (i.e. at the harmonic spacing). Any pair of adjacent harmonics would generate energy at the fundamental.

Helmholtz's explanation is wrong because: Back to Main Index

2.3. Schouten's timing theory

Schouten proposed that the brain times the intervals between beats of the unresolved (see next diagram) harmonics of a complex sound, in order to find the pitch.

Schouten's theory is wrong because:
The following diagram shows the excitation pattern that would be produced on the basilar membrane separately by individual harmonics of a 200 Hz fundamental. Notice that the excitation patterns of the higher numbered harmonics are closer together than those of the low-numbered harmonics. This is because the filters have a bandwidth which is roughly a tenth of their center frequency (and so is constant on a log scale), whereas harmonics are equally spaced in frequency on a linear scale. More harmonics then get into a high-frequency filter than into a low-frequency one. The low-numbered harmonics are resolved by the basilar membrane (giving roughly sinusoidal output in their filters); but the high-numbered harmonics are not resolved. They add together in their filters to give a complex vibration which shows beats at the fundamental frequency.

Output of 1600 Hz filter

Output of 200 Hz filter

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2.4. Pattern recognition theories

Goldstein's theory states that pitch is determined by a pattern recognition process on the resolved harmonics from both ears. The brain finds the best-fitting harmonic series to the resolved frequencies, and takes its fundamental as the pitch.

Goldstein's theory accounts well for most of the data, but there is also a weak pitch sensation from periodic sounds which do not contain any resolvable harmonics or from aperiodic sounds that have a regular envelope (such as amplitude modulated noise). A theory such as Schouten's may be needed in addition to Goldstein's in order to account for such effects.

Evidence for there being two separate mechanisms for resolved and unresolved harmonics is:

* pitch discrimination and musical pitch labelling (eg A#) is much worse for sounds consisting of only unresolved harmonics;

* comparison of pitches between two sounds one having resolved and the other unresolved harmonics is worse than comparison of pitches between two sounds both with unresolved harmonics.


You should know:
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