Periodic sounds can also be described in terms of their repetition rate and the complexity of the pressure variation. The repetition rate is related to the subjective pitch: the higher the rate the higher the pitch. Complexity is related to the subjective timbre or tone quality: differences in timbre distinguish between the same note played on, say, the violin and the organ. The simplest pressure wave has the form of a sinusoid: pressure plotted against time varies as the sine of time (see the lower part of Fig. 3). A sine wave may also be called a pure tone or simple tone, since it has a very 'pure' or 'clean' quality, like that of a tuning fork or the Greenwich time signal. For a pure tone the repetition rate, the number of complete cycles per second, is the frequency. The unit of one cycle per second is called the hertz (abbreviated Hz). The Greenwich time signal has a frequency of 1,000 Hz. The highest frequency we can hear varies from 16,000 to 20,000 Hz in young adults, but tends to decrease with increasing age. The lowest frequency which is heard as sound is about 20 Hz. Below that the pressure changes are felt as a vibration rather than heard as sound. We are most sensitive to frequencies around 1,800 Hz.
Sine waves, or pure tones, are particularly important in the study of hearing. Joseph Fourier showed that any periodic complex sound can be considered as composed of a sum of sine waves with different frequencies and levels. Conversely, any periodic sound can be synthesized by adding together sine waves with appropriate frequencies and levels. This is very useful if we are investigating how some part of the auditory system works, as it is often sufficient to measure only the way it responds to sine waves of different frequencies. The response to any complex sound can then be predicted from the response to the sine waves. The same philosophy lies behind the specification of amplifiers or loudspeakers in terms of their frequency response. It is assumed that, if an amplifier faithfully reproduces any sine wave within the audible range, and amplifies each sine wave by the same amount, then it will also faithfully reproduce any complex sound composed of those sine waves.
A further reason why sine waves are important in the study of hearing is that the ear behaves as though it carries out a Fourier analysis, although it does not do this analysis perfectly, and is therefore said to have limited resolution. Thus when we are presented with two sine waves which are sufficiently separated in frequency, we are able to hear two separate tones, each with its own pitch. This contrasts with the eye, where a mixture of two different colours (frequencies of light) is perceived as a single colour. The process by which the different frequencies in a complex sound are separated in the ear is known as frequency analysis or frequency resolution.
If we subject a complex sound to Fourier analysis, and then plot the level of each sine wave component as a function of frequency, the resulting plot is known as the spectrum of the sound. The spectrum is related to the complexity of the pressure variation: the simple sine wave has a spectrum composed of a single point, or vertical line, whereas musical instrument tones generally contain many sinusoidal components, and have a spectrum composed of many lines. The subjective timbre of sounds is more easily explained in terms of the spectrum than in terms of the pressure variation as a function of time. Sounds with many high-frequency components will seem sharp or strident, while those with mainly low-frequency components will seem dull or mellow. This correspondence between spectrum and timbre provides another example of the action of the ear as a frequency analyser. In the following sections we will discuss the physiological basis of this frequency analysis, and some of its perceptual consequences. We will also discuss the perception of pitch. Finally we will describe the major types of hearing impairments, and their perceptual consequences.
1. The anatomy and physiology of the ear
2. Theories of pitch perception
3. The ear as frequency analyser
4. Hearing impairments
5. Labyrinths of the ear
1. The anatomy and physiology of the ear
Fig. 1 illustrates the basic structure of the outer, middle, and inner ear. The outer ear consists of the pinna and the ear canal. The pinna is thought to play an important role in our ability to locate complex sounds. The spectrum of such sounds is modified by the pinna in a way that depends upon the direction of the sound source relative to the head. These spectral modifications are not perceived as changes in timbre, but rather determine the perceived direction of the sound source. They are particularly important in allowing us to distinguish whether a sound comes from behind or in front, and above or below.Sounds impinging upon the eardrum are transferred by means of three small bones in the middle ear (the smallest bones in the body, called the malleus, the incus, and the stapes) to a membrane-covered opening (the oval window) in the inner ear or cochlea. The main function of the middle ear is to improve the efficiency of transfer of energy from the air to the fluids inside the cochlea. Small muscles attached to the bones contract when we are exposed to intense sounds, reducing sound transmission to the cochlea, particularly at low frequencies. This may serve to protect the cochlea, and it may also help to stop intense low frequencies, occurring in the environment or in our own voices, making higher frequencies inaudible.
The cochlea is filled with fluids, and running along its length is a membrane called the basilar membrane. This membrane is stiff and narrow close to the oval window (called the base), while at the other end (the apex) it is wider and less stiff. In response to sine wave stimulation a wave appears on the basilar membrane travelling from the base towards the apex, at first increasing in amplitude and then decreasing. The position of the maximum in the pattern of vibration along the basilar membrane varies with frequency: high frequencies produce peaks towards the base, and low frequencies towards the apex. This is illustrated in Fig. 2. Thus the basilar membrane acts as a frequency analyser, different frequencies producing activity at different places along the basilar membrane.
The patterns shown in Fig. 2 are rather broad to account for the frequency resolution which is actually observed in human subjects (see below). However, recent work has indicated that many of the early measurements may have been in error. The basilar membrane appears to be extremely vulnerable, so that even small impairments in the physiological condition of the animal being studied alter the responses and produce broader 'tuning'. It has recently been shown that the 'tuning' on the basilar membrane, i.e. its frequency resolution, can be extremely sharp if the animal and its cochlea are in good condition.
The information which is contained in the patterns of vibration on the basilar membrane has to be transmitted to the brain in some way in order for us to perceive sound. This transmission is achieved by an electrical 'code' carried in the auditory nerve. Each auditory nerve contains the axons or 'fibres' of about 30,000 individual nerves, or neurons, and information is transmitted in each of these in the form of brief electrical impulses, called spikes or action potentials. Thus transmission takes place in an all-or-none fashion; the size of the spikes does not vary, and only the presence or absence of a spike is important. (See Adrian, Edgar Douglas.)
The vibrations on the basilar membrane are transformed to spikes by rows of special cells, called hair cells, which rest on the basilar membrane. The hair cells are among the most delicate structures in the cochlea, and they can be destroyed by intense sound, lack of oxygen, metabolic disturbance, infection, or drugs. They also tend to be lost with increasing age. Once lost they do not regenerate, and loss of hair cells is a common cause of hearing impairment.
The exact way in which information is 'coded' in the auditory nerve is not clear. However, we know that any single neuron is activated only by vibration on a limited part of the basilar membrane. Each neuron is 'tuned' and responds to only a limited range of frequencies. Thus information about frequency can be coded in terms of which neurons are active or 'firing' with spikes. This form of coding is called 'place' coding. Information about sound level may be carried both in the rate of firing (i.e. the number of spikes per second) and in terms of the number of neurons that are firing. Finally, information may also be carried in the exact timing of the spikes. For stimulating frequencies below about 5 kHz (1 kHz = 1,000 Hz), the time pattern of neural spikes reflects the time structure of the stimulus. Nerve spikes tend to occur at a particular point or phase of the stimulating waveform, a process called phase locking, although a spike will not necessarily occur on every cycle. This is illustrated in Fig. 3. For a sine wave stimulus with a frequency of, say, 1 kHz, the time for one complete cycle will be 1 millisecond (ms), and the time intervals between successive nerve impulses will be integral multiples of this, namely 1, 2, 3, 4, 5, ... ms. Thus phase locking provides another way in which the frequency of a sound may be coded. Notice that a given neuron cannot 'fire' more than a few hundred times per second. It used to be thought that the frequency of the stimulus at higher frequencies could be coded by cooperation between groups of neurons firing in volleys, the so-called 'volley' theory. In fact, the time pattern of response in a single neuron is sufficient to define the frequency of the input, provided that time intervals between firings are analysed, rather than overall firing rate.
Fig. 1. The structure of the peripheral auditory system, showing the outer, middle, and inner ear.
Fig. 2. Envelopes or outlines of patterns of vibration on the basilar membrane for low-frequency sine waves of different frequencies. Solid lines indicate the results of actual experiments, whereas the dashed lines are extrapolations.
Fig. 3. The lower trace shows the waveform of a sine wave with frequency 300 Hz. The upper trace shows the response of a single auditory nerve fibre. Note that each impulse occurs at the same phase of the waveform, although an impulse does not occur on every cycle.
2. Theories of pitch perception
The pitch of a sound is defined as that attribute of sensation in terms of which sounds may be ordered on a musical scale; variations in pitch give rise to the percept of a melody. For sine wave stimuli the pitch is related to the frequency, and for other periodic sounds it is usually related to the overall repetition rate. Classically there have been two theories of how pitch is determined. The place theory suggests that pitch is related to the distribution of activity across nerve fibres. A pure tone will produce maximum activity in a small group of neurons connected to the place on the basilar membrane which is vibrating most strongly, and the 'position' of this maximum is assumed to determine pitch. The temporal theory suggests that pitch is determined from the time pattern of neural impulses, specifically from the time intervals between successive impulses (this used to be called the volley theory, but, as discussed above, volleying is no longer considered necessary).It is generally agreed that the place theory works best at high frequencies, where the timing information is lost, and the temporal theory works best at low frequencies, where resolution on the basilar membrane is poorest (see Fig. 2). However, the frequency at which the change from one to the other occurs is still a matter of debate. We can get some clues from studies of frequency discrimination, the ability to detect a small difference in frequency between two successive tones. For low and middle frequencies a change of about 0.3 per cent is detectable, but above about 5 kHz the smallest detectable change increases markedly. Furthermore, above 5 kHz our sense of musical pitch appears to be lost, so that a sequence of different frequencies does not produce a clear sense of melody. Since 5 kHz is the highest frequency at which phase locking occurs, these results suggest that our sense of musical pitch and our ability to detect small changes in frequency depend upon the use of temporal information. Place information allows the detection of relatively large frequency changes, but it does not give rise to a sense of musical pitch.
We do not have space to deal with the pitch of complex sounds, but it is thought that relatively complex pattern-recognition processes are involved which depend upon both place and temporal information. For a review see Moore (1982).
3. The ear as a frequency analyser
We initially described how the auditory system functions as a limited-resolution frequency analyser, splitting complex sounds into their sine wave components. Although we have argued that place information is not the most important determinant of pitch, it seems almost certain that the place analysis which takes place on the basilar membrane provides the initial basis for the ear's frequency analysing abilities. We will now describe briefly some perceptual consequences of this analysis.We are all familiar with the fact that sounds we wish to hear are sometimes rendered inaudible by other sounds, a process known as masking. Fig. 4 shows masking patterns produced by a masker containing only a small range of frequencies: a narrow-band noise. The threshold elevation of the sinusoidal signal (the amount by which the masker raises the threshold) is plotted as a function of signal frequency for several different masker levels. The figure illustrates two basic points. First, the greater the masker level, the more masking there is. Secondly, more masking occurs for signal frequencies close to the masker frequency than for those farther away. This makes sense if we assume that masking will be most effective when the pattern of vibration evoked by the masker on the basilar membrane overlaps that of the signal. If the place analysis on the basilar membrane is sufficient to separate completely masker and signal, then no masking will occur. (See also auditory illusions.)
As was described earlier, the subjective timbre of a sound depends primarily on the spectrum of the sound — the level of sound at each frequency. Presumably timbre is perceived in this way because the different frequencies excite different places on the basilar membrane. The distribution of activity as a function of place determines the timbre. Obviously, this distribution can be quite complex, but each different complex tone will produce its own distribution, and hence will have its own tone colour. This helps us to distinguish between different musical instruments, and to distinguish between the different vowel sounds in human speech.
4. Hearing impairments
Hearing impairments can be classified into two broad types. Conductive hearing loss occurs when the passage of sound through to the inner ear is impeded in some way, for example by wax in the ears, or by some problem with the bones in the middle ear. It can often be cured by simple medical treatment, or by surgery, and when this is not possible a simple hearing aid can effectively alleviate the problem. Sensorineural hearing losses arise in the inner ear, or at some point 'higher up' in the auditory system. Cochlea hearing losses are often produced by damage to the hair cells and they are common in the elderly. Sensorineural hearing losses are not usually helped by surgery, and simple hearing aids are of only limited use, since the percepts of the listener are 'distorted' in various ways.One common problem in cochlea hearing loss is recruitment, an abnormally rapid growth of loudness with increasing sound level. Faint sounds may be inaudible to the sufferer, but high-level sounds are as loud to him or her as to a normal listener. A hearing aid that amplifies all sounds will overamplify intense sounds, and these will be uncomfortably loud. One way round this problem is to use hearing aids that 'compress' the dynamic range of sounds, by amplifying low-level sounds more than high-level sounds. Such aids are currently being evaluated, and have met with some success.
A second common problem in cases of cochlea hearing loss is an impairment in frequency selectivity. This has a number of consequences. First, the sufferer will be more susceptible to the effects of masking. Secondly, the ability to identify the timbre of different sounds, including speech, will be impaired. These two effects mean that the sufferer will have great difficulty in understanding speech whenever there is more than one person talking at once, or when there is background noise. Hearing aids at present cannot compensate for this problem, and as a result many people with cochlea hearing losses never go to pubs or to parties.
Further research may clarify the nature of the defects in impaired ears, and suggest ways in which those problems can be alleviated. In the meantime we should remember that for most impaired people a hearing aid does not restore normal hearing; it may make sounds louder but it does not bring them into focus. See also evolution of the ear.
Fig. 4. Masking patterns for a narrow-band noise masker centred at 410 Hz. The threshold elevation of the sine-wave signal is plotted as a function of signal frequency, with masker level as parameter.
5. Labyrinths of the ear
The labyrinths of the ear are a complex organ for attaining balance, provided by a fluid in three orthogonal circular tubes (the semicircular canals), which move beads of calcium carbonate suspended on hairs, and so activate special nerves sending signals to the brain of movement of the head. In Ménière's disease these signals occur inappropriately, through damage of the hair cells, to produce dangerous unpleasant dizziness. The condition is most frequent in middle life and it generally subsides of its own accord.(Published 1987)
— Brian C. J. Moore
- Bibliography
- Békésy, G. von(1960). Experiments in Hearing. Trans. and ed. E. G. Wever.
- Moore, B. C. J. (1982). Introduction to the Psychology of Hearing (2nd edn.).
- — — (1997). Introduction to the Psychology of Hearing (4th edn.).
