The Ear
The Ear (not to scale)
Alastair Disley - Assignment 2 - Human Pitch Perception
Pitch - The Ear - Critical Bands - Theories of Pitch Perception - A Brief Aside - Further Reading
To consider human pitch perception, we need a definition of pitch. The American National Standards Institute (1960) defines pitch as "that attribute of auditory sensation in terms of which sounds may be ordered on a scale extending from low to high". Another simpler definition is "our perception of the frequency of sound". Pitch is, therefore, one of the essential percepts of sound. A more complex definition of pitch can be found here.
If we, as humans, are to perceive pitch, we need some organ to detect and quantify it. That organ is the wonderfully complex ear.
The Ear (not to scale)
The Ear
The Idealised Shape of the Basilar Membrane
Critical Bands and Just Noticeable Differences
Any pure tone input to the basilar membrane gives not just a single hair cell firing, but a large number, with an ideal response pattern shown in the diagram to the left (frequency on the horizontal axis, amplitude on the vertical). If two pure tones of similar frequency are played, the response curves overlap. When two such tones are suitably close that they have a large overlap, they are said to fall within the same critical band. Thus the basilar membrane can be categorised into critical bands, and there are about 24 of these. Those at the extremes of the hearing range cover larger ranges than those at the centre, and the average coverage is about a third of an octave, which is equivalent to a musical interval of a major third.
This means that when we hear a musical interval of a third or less, the responses of the basilar membrane to each overlaps. See if you can hear the effect this creates in by playing successively smaller intervals on a piano, starting at an octave and finishing at a semitone. This works best in the lower octaves, as the critical bands are further apart there.
The semitone can still have both of its notes identified, so we can clearly perceive pitch differences of less than one critical band. The just noticeable difference is very much smaller, and again varies with frequency, but has been measured to be about a twelfth of a semitone on average. If we take two sine waves of the same frequency, and adjust the frequency of one slowly until they can be heard as two separate frequencies, the sound goes through a number of distinct changes. First, a slow beating effect is heard. Then, a rough sensation is heard as the sounds separate, until the sound is smooth once more. Listen to this audio example.
Ohm, of "V=IR" fame, also set his mind to the perception of pitch. He postulated that pitch perception was based on the tracking of lowest harmonic in a particular sound. (Ohm's acoustical law). Therefore, a pitch corresponding to a certain frequency could only be heard if there was acoustical power at that frequency. However, many instruments, such as the oboe, produce little or no acoustical energy at the fundamental frequency of the notes they produce. So how do we determine pitch when the fundamental is missing?
One theory is that we determine the pitch from the difference between two adjacent harmonics, or mathematically, we find highest number that will divide into all present frequencies. Here is an interesting example of this effect. The same tune is played in each example, but with different harmonics present. Listen to the examples, and see if the tune is clearly distinguishable in each one.
Two main theories of pitch perception have developed over the years from the results of experiments. These are the place theory and the temporal theory.
Place theory is based upon the idea that different frequencies excite different places on the basilar membrane. This is true, but this theory alone fails to explain fine frequency discrimination, or why we hear complex tones as a single pitched note. The theory also suggests that as we look at higher harmonics, where the difference between two adjacent harmonics (which is the fundamental frequency) is smaller than the critical band (which increases in size with higher cental frequency), the individual harmonics won't be resolved individually. The point at which this changes is around the seventh harmonic. The importance of this harmonic can be heard by listening to the following two examples.
Temporal theory is based on the idea that the ear analyses sound by time, and that a ny sound with a perceived pitch is periodic in nature. The temporal theory likens the basilar membrane to a bank of band-pass filters, with centre frequencies and bandwidths varying with the critical bandwith. Once again, not every effect can be explained by this theory, as one of its fundamentals is phase locking, which doesn't work over 5kHz. Yet we can perceive pitches with a fundamental above 5kHz to some degree.
Modern theories, such as that of Moore (1982) tend to combine both theories, as neither can account for all perceptual phenomena. Moore's model is like the place model in its initial frequency analysis of the sound, followed by a temporal analysis of the neural firings. However, there are still some proponents of one rule of pitch perception over another, such as this paper.
There are some other interesting effects of pitch perception, one of which is masking. A lower sound can mask, or render inaudible, a higher sound. The pitch effects of masking are inextricable from the other effects of loudness and even temporal masking, but this effect is worthy of note.
For more information on this topic, readers may like to read the following books:
Many acoustics websites are linked from this page, and you may wish to visit the author's own website. All images and sounds are original and copyright of Alastair Disley.