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A biologist looks at psycho-acoustics
Journal of Sound and Vibration (1972) 21 (1), 115-126
A BIOLOGIST
LOOKS
AT PSYCHO-ACOUSTICSt
A. TUMARKIN 45 Rodney Street, Liverpool 1, England
(Received 18 October 1971) To a biologist, a puzzling aspect of psycho-acoustics is the absence of the concept of function. The widespread custom in psycho-acoustics of regarding a living structure as a machine, and consequently describing its behaviour in terms of its response to measured inputs, has serious limitations. It is argued that unless these limitations are realized little progress can be made towards a satisfactory understanding of the workings of human sensory systems. Any biologist who strays into the domain of psycho-acoustics is likely to be puzzled by the absence of a feature that dominates his own landscape. This is the concept of function. In his own domain, the term involves life itself, as in the phrase "functional adaptation". At a lower level, as in physiology, the word is used as it is in applied physics. A living structure is regarded as a machine, and its behaviour is described in terms of its response to measured inputs. Finally, there is the familiar mathematical meaning. In the domain of physics only the second and third aspects are found. The physicist lives in a dead world of meter measurements, and he is satisfied if a measured input yields a measurable response. In the domain of psychology the situation is more complex. It is many years since the existence of orders of magnitude in sensations led Fechner to his famous law, and within recent years the definite (albeit limited) value of such concepts as the I.Q. index has encouarged some psychologists to hope that the brain itself might be defined and understood in mathematical terms. Behaviourists in particular maintain that the only way to learn about any system, alive or dead, is to observe its behaviour under rigidly controlled conditions. No one would deny the success of this approach in animal experimental psychology, but it is arguable that error might creep in whenever the psychologist in his anxiety to obtain measurable results follows too slavishly the rigid procedures of the physicist. In studying a complex system the physicist endeavours to hold constant all parameters except the one under consideration, and he admits no restriction on the nature or magnitude of his input. Nor has he any criteria for evaluating his results except measurability on some meter. The behaviourist who follows that path too zealously is in danger of becoming so remote from the biologist that words lose their agreed meaning and communication begins to break down. Nowhere is the gulf between biologist and psychologist greater than in the domain of psycho-acoustics. Take for example the word "threshold". The biologist conceives this in terms of a "'gestalt": the whole animal and its environment. The threshold is the least change in that gestalt that results in the animal taking purposive action. In deference to the behaviourist, one must here exclude situations in which the animal may be aware of a change in the environment, but takes no obvious purposive action. Consider, for example, the relation between a grazing antelope and a hunting lion. The antelope, whilst grazing peacefully, begins to show signs of unease. It lifts its head to survey the terrain, sniffs suspiciously, t Presented at the Psychological Acoustics Section of the 1971 Spring Meeting of the British Acoustical So¢iety, Birmingham, England, on 5 to 7 April 1971. A number of other papers from the Meeting will be published in future issues. 8* 115
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A. TUMARKIN
pricks up its ears, and tenses its muscles. If the lion appears it bounds away; if not, it returns to its meal. No physicist could possibly analyse such a complex event, and so the concept "threshold", for him, refers to individual parameters. Consider the most familiar physical threshold of all, that of loudness. Originally this was envisaged as a precise crossing between silence and signal. Figure I shows the distribution of threshold pressures in 198 so-called normal ears as measured at the National Physical Laboratory [1]. These results were obtained with impeccable technique, and may be accepted with complete confidence. Unfortunately the assumption that they represent the performance of the biologically normal ear is not so acceptable since there is no certainty that any of these ears was biologically normal, and there is ample evidence that some of them were not. It is true that all the ears were rather cursorily clinically examined and passed as normal, but none was examined under the operating microscope, or X-rayed. Yet both these tests are mandatory if minor pathology is 50
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to be detected. Moreover, even if all ears had passed the most searching clinical scrutiny, there would still be no certainty that they were normal, since both middle and inner ear disease can occur without any overt clinical evidence (as, for example, in otosclerosis and various forms o f perceptive deafness). The physicist is, in fact, trapped in a vicious circle. If he aspires to measure the biologically normal ear he must obviously select such ears for his investigation. But the essential criterion for such ears is that they should conform to the very function he seeks to establish. It is noteworthy that in the present group, no less than 17 members could not hear 15 kHz. The inclusion of such ears in a group of ostensibly normal ears is biologically indefensible. After all, the ear is a premier sense organ of superlative sensitivity and efficiency, and it has played a major role in the evolution of the mammals. Originally they were tiny creatures no bigger than a rat or even a mouse. They were probably nocturnal, and for their survival they depended even more on their ears than on their eyes. In particular, the highest tones were essential for the localization of sounds. Man no longer needs hearing of that quality, and indeed his hearing may be degenerating. Nevertheless it is difficult to believe that Nature, the supreme craftsman, would turn out this superlative instrument in batches that showed a variance that no child would accept in a penny toy. It cannot be doubted that the National Physical Laboratory (N.P.L.) group included a considerable number of pathological ears, and this goes far to explain the lower skirt of all the distribution curves: i.e., individuals with thresholds up to 20 dB below the mean. But how can one explain the considerable number that heard as much as 20 dB better than the mean 9.I suggest that this is due, in some measure, to the fact that the true mean lies somewhere in the upper skirt, and that the majority of all the ears tested were biologically subnormal.
A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
117
This assertion is supported by considerable ancillary evidence. Every otologist knows that middle ear inflammation is widespread in childhood. Few escape it entirely. In addition, however, evidence is now emerging of equally widespread degeneration of the inner ear. Bredberg [2], by meticulously counting the hair cells, has shown that their number is diminishing almost from the day we are born. It is not surprising therefore that the N.P.L. found so many "normal" young adults unable to hear 15 kHz. Work at Salford [3] has confirmed, beyond any doubt, the widespread incidence of high tone inner ear deafness of unknown aetiology in otherwise normal adults. It cannot be doubted that this is merely the tip of the iceberg, and that by strict biological standards, the hearing of most people is subnormal. From a practical point of view, this is no serious matter since so-called civilized man has no need of biologically normal hearing. A working man may lose 60 ~ of his pitch range without ranking forlcompensation, and he may drop 25 dB below the N.P.L. mean without
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so ranking. But it is far otherwise in psycho-acoustic research. An enormous amount of such work, ostensibly dealing with the performance of the normal ear, must now come under suspicion because so many of the subjects were pathological. It is, for example, not uncommon for a worker to take as his criterion of normality the ability to hear within 20 dB of the N.P.L. mean. This means that he may be comparing individuals whose hearing differs by as much as 40 dB. The situation is, of course, complicated by unavoidable variance. This may be physical, physiological, or psychological. The first calls for no discussion. Physiological variance can arise from random neural noise, and also from variations in the response of the end organ due to its innervation. For example, a pure tone stimulates a fairly wide band of hair cells, but, because of lateral inhibition, only the information from the centrally placed cells is transmitted. But when the tone becomes extremely faint, these cells no longer receive enough energy to activate the associated nerve fibre. Inhibition ceases and information begins to come in from cells on the fringe of the stimulation area. Figure 2 shows how the outer cells on the basilar membrane (that are responsible for threshold detection) combine in groups to energize a single nerve fibre. Thus, as the signal intensity approaches threshold, the information area (as opposed to the area of actual mechanical displacement) actually widens, whilst pitch perception becomes less efficient. With further reduction in intensity, the specific neural activity begins to merge with the random neural activity. The observer is aware that something is happening, but cannot define it. Finally he enters a zone
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A. TUMARKIN
of uncertainty in which he is not sure whether he has heard anything at all. This brings us to psychological variance. Imagine a fixed line that is being compared with another line that was originally much longer but is steadily contracting until it is obviously shorter. Is there a point at which we can say that they are equal ? Such a point must exist, but we can never know it. The physicist accepts this, and presents his results in the usual way, with mean and all embracing variance. The biologist ignores it since it has no vital significance. But the psychologist makes determined efforts to explore this shadowy domain, arguing as follows. Suppose the observer admits he is uncertain when the difference is 1 ram. Then he must be more uncertain when it is ½ mm and it should be possible to equate the magnitude of his uncertainty with the probability of a wrong judgment. The ambition of the psychologist is to find a measure for these hypothetical magnitudes. Fifteen years ago, hopes were high that the mathematical apparatus of communication theory might be applicable to this problem, and many investigations were carried out to evaluate that possibility. Little or no success attended those efforts, and today few if any audiologists regard the d' index as meaningful. As Zwislocki [4] has said, the concept does not transcend the bounds of mathematical formalism. The purpose of the d' index was to act as a model that would on the one hand be amenable to mathematical analysis, and on the other hand would bear sufficient resemblance to the auditory system to support meaningful comparisons. Unfortunately the restrictions imposed by the first condition made it impossible to comply to any useful extent with the second. Inevitably the results obtained with human observers bore little resemblance to those predicted by the model. To begin with it was necessary to postulate a highly artificial distribution for the noise. No attempt was made to consider what form noise might take within the living system. Fourier series, band-limited, Gaussian noise (despite being physically unrealizable) has two great virtues. It is easily handled in terms of mean and variance, and it submits to a simple sampling theorem, viz. T
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in which the energy in a wave form is derived from its amplitude at 2 WTpoints. It seems possible that workers were attracted to this model because sampling a wave bears a superficial resemblance to what we imagine goes on in the brain when we recognize a familiar event. Although we do not have the faintest inkling of how this is achieved, nevertheless we can reasonably assume that it consists of some sort of matching of an incoming pattern with an established memory pattern, and that this entails something akin to sampling or scanning. Even the recognition of an unfamiliar meaningless event such as a threshold pure tone must involve both pattern matching and memory (albeit short term) since, in order to detect a change from noise to signal plus noise, we must be able to compare an existing pattern with an immediately preceding one. On the other hand, since the process of ascertaining the threshold consists of presenting sounds of diminishing intensity it seems at first sight reasonable to think of the brain as simply measuring power. Green [5] puts this as follows: "Basically in a two interval forced choice, the optimum detecting device simply measures the power in two wave forms and selects the larger, and it is eminently reasonable that the auditory mechanism might also perform that task." Unfortunately, this "reasonable" assumption is completely at variance with accepted biological thought. One of the most important if not fundamental functions of the central nervous system is to recognize change. This applies afortiori to threshold detection. Thus when the observer is given his first interval he at once compares it with the
A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
1 19
preceding "silence", and decides whether it contains a signal or not. He cannot avoid doing this because that is exactly what his auditory system was designed to do. Similarly when he is given the second interval he compares it with the "silence" that intervened between it and the first interval. Neither of these judgments requires or permits any comparison between first and second interval. In other words we are not dealing with two intervals but with two pairs o f intervals. The observer's judgments should be independent of each other were it not for the mischievous intervention of the experimenter who insists on one "yes" for each pair of signals, when in fact it is possible for two positives or two negatives to occur. Be that as it may, there are certainly no grounds for believing that the auditory system can arrange two subliminal signals in order of magnitude, and this error has led to some quite extraordinary experiments. For example, an observer performing an N-interval forced choice is informed whenever he is in error and is instructed to make a second choice. It has been claimed that the hit rate of the second choice is better than would be achieved by pure guesswork, and the conclusion is drawn that he must have been able to draw on stored information in his memory bank. The implication is that, as in the case of the 2 I.F.C., he must have measured the power (or something monotonic with power) in each interval and stored in his memory bank a list of those quantities in order of magnitude: i.e., he must have assigned ordinal numbers to each interval. In the light of what has been said about the two interval test, the incredibility of this N-interval test needs no emphasis, but the reader may confirm this by means of a quite simple test. Let an observer be given in succession a signal at 40, 43, 46 and finally 40 dB once more. On instruction to order them in magnitude he invariably places the final 40 dB below the initial 40 dB, and he continues to do s o even though he is allowed to know the precise intensities. Many variations on this theme can be designed, all depending on the fact that the prime function of the auditory system is to detect change. In experiments of this type, the brain is essentially concerned with the present, which it judges by comparing it with the immediate past. The more remote past has little or no influence on its judgments, and, as the above experiment shows, the first signal, although only separated from the fourth by a few moments, is virtually remote because two other signals have intervened. It is clear therefore that the brain is unable to store magnitude estimates of supraliminal signals (from a biological point of view such a function would be useless) and we may be confident that it is even less interested in subliminal messages. Having thus dismissed the theory of ordinal mensuration we may now consider an even more extravagant claim, namely that of cardinal mensuration. Green [5] says, in defence of his ordinal mensuration, "Subjective scales of loudness assume that the subject can do much more". In this he is referring to the sone and phon scales which are based on the assertion that man can attach cardinal numbers to the ratio of two loudness magnitudes in the same way as a physicist cart attach such numbers to the ratio of two intensities. (N.B. This scale is usually given in phons but I shall refer to dB because it will simplify the argument, and in any case most of the basic work was done on 1 kHz.) The biologist's reaction to this scale must be one of utter incredulity. It is impossible to imagine how such a function could have come into existence if only because the ability to enumerate in such a complex fashion has only appeared within the last few thousand years. It is admittedly not entirely impossible that such a bizarre and useless function might suddenly appear without any obvious cause in the accepted neo-Darwinian sense, but the extreme unlikelihood of such an event must warn us to scrutinize most carefully the evidence on which this function rests. I propose to argue that that evidence carries no conviction whatsoever. First, let us consider the concept of measurement itself. For that purpose we turn to the work of Professor S. S. Stevens [6], who has written so extensively on this subject. He states
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[6] that "Measurement is the assignment of numbers to objects or events according to some rule" and he gives scales resulting from four different rules (nominal, ordinal, interval and ratio.). Unfortunately his definition is useless since he does not tell us what he means by number. In the case of loudness, since the scale is ratio, we need the cardinal number, and without venturing too deeply into that metaphysical morasse, we call on Russell [7] who tells us that it is the class of all those classes that bear a one-to-one relation to each other. This suffices for our purpose since it emphasizes the essential quality of precision. This is usually taken for granted in any graph or equation relating two quantities in the physical world, but we shall find it completely lacking in sensation mensuration. This requirement naturally must not be pushed to extremes since, if we were to require from the measurements of applied physics the precision of pure mathematics, no branch of applied physics could survive. Granting therefore that the whole body of physics is only probably correct, we may 201
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physical measurements. What little value they have is completely lost in the accepted sone/dB relation. Tones: halving and doubling; median = 10.0 dB, mean = 10.9 dB. nevertheless assert that, within that framework, the plausibility of any theory ostensibly based on measurements is proportional to the consistency and accuracy of those measurements. By that criterion the sone (together with all other so-called scales of sensation magnitude) entirely fails to pass even the most liberal and tolerant scrutiny. It seems as if scientists working in the field of psycho-acoustics are prepared to overlook variations and internal contradictions in their findings so extreme that if they occurred in a purely physical experiment would lead immediately to the abandonment of the underlying hypothesis. For example, Figure 3 shows some of Stevens' early results for the power ratio corresponding to a doubling of the loudness sensation. Estimates vary from about 3 dB to about 23 dB and the range is actually minimized by the logarithmic notation. In linear terms the range is from about two to about 200. But even if one accepts the log values the range is surely sufficient to exclude the sone from the company of measurable quantities as I have defined them. We have only to consider what would happen if the same group of listeners had been given the necessary apparatus and told to measure the intensity ratio of two sounds. Not only would the answers fall within an extremely narrow range, but any one that did not would be immediately suspect, since intensity refers to a public event and can only have one magnitude whilst sones refer to private events and each listener's magnitudes, however aberrant, are as valid as those of any other. Nevertheless, these widely ranging pseudo-numbers have been ruthlessly constrained. The first step was to present the mean of large groups of listeners together with interquartile variance. Next the mean alone was presented. Then came the simplified equation, and finally only the exponent of the curve. The motive behind this ruthless condensation was presumably
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A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
the quest for some general principle applicable to the auditory process, and that in its turn was to be an element in a grand design. By the accumulation of a host of exponents relative to all other sensations it was hoped that light might be thrown on the workings of the central nervous system. In the event, nothing of the sort transpired, and by the very magnitude of their aspirations the seekers after psychometric functions overlooked what little of value there was in their original observations. The remarkable fact is that any listeners at all should be prepared to assign numbers, however capricious, to the magnitude of their sensations. It is idle of the biologist to argue that since this serves no useful function it could not have evolved. The phenomenon exists and demands some explanation. In the early days of the sone it was suggested that listeners try to project the sounds outwards and then estimate their relative distance. This theory was 60
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Figure 4. Proposed basis for sensation magnitude estimates. Any observer has a rough idea of a moderate magnitude in any sensation, and he will assign to it his moderate number. The above results confirm the widespread variance exhibited in Figures 3 and 5. soon exploded by the demonstration that similar numbers can be assigned to sensations such as an electric shock that have no such external correlate. The first clue to the enigma came from an observation by Zwislocki [8] that at first sight seems even less plausible. "When people are asked to name a number that is neither large nor small but medium they usually choose one that is greater than unity but less than ten (modes seem to fall on five and seven). From a mathematical point of view this makes no sense, but people are not logical machines, and probably from usage numbers appear to become symbols uniquely associated with subjective magnitude. In other words a psychological or natural unit evolves." Figure 4 shows our own findings in 44 cases. Sixteen people did indeed choose between two and nine inclusive, whilst 28 chose 10-75 inclusive. No one could believe that there is any such thing as a natural medium number. These figures exhibit the same sort of range as we encounter in the sone itself. Nevertheless two questions demand consideration. (i) Why do so many people choose between two to 75 rather than between, say, 2000 and 20 000 ? (ii) What bearing if any does this observation have on the psychometric function itself'? With regard to the first question Zwislocki's suggestion is apposite. It would be easy to list a host of objects or events in the daily life of the ordinary citizen to which a number less than 100 applies, whilst very few range beyond that point. It has also been suggested that
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an individual's personality may reflect itself to some extent in the size of the number he considers medium. The relevance to psycho-metric functions is obvious. Confining ourselves to loudness (although the argument applies equally to all other sensations) we know that by sharing the experience of public events, people learn to agree approximately on the meaning of "a faint sound", "a fairly loud sound", "a very loud sound" and so on. Music indeed utilizes the familiar notation from pianissimmo to fortissimo which every musician interprets in roughly the same way. What more natural than to assign to a sound of moderate loudness the magnitude of a medium number? Of course one number cannot establish a scale, but the listener already has another reference point of a more fundamental nature, namely the threshold. He has a more or less hazy idea of a very faint sound, a faint taste, a faint itch and so on, and will presumably attach to it a magnitude in the neighbourhood of unity. Now the average individual lives under conditions in which 30 dB would be considered very quiet whilst 60 dB would be considered moderately loud. Applying these figures to the Salford medium numbers we find that people are likely to assign a magnitude between two and 75 to an intensity range of the order of 30 dB. These values are not significantly different from Stevens' original findings. Certain conclusions follow from this hypothesis. To begin with, if an individual's medium number is indeed an expression of his daily life and personality we should expect that number to remain fairly constant throughout his life. We have indeed found that an individual's estimate for doubling remains unchanged after an interval of a year. On the other hand, since medium numbers vary so widely we should expect similar inter-individual variations in sensation magnitudes. This too we have found. Figure 5 shows the different exponents found at Salford [9]. They vary from 0.013 up to 0.07. The significance of this massive inter-individual variance was submerged in the earlier work by the ruthless process of averaging to which I referred above. In that respect we may refer to the work of Rowley and Studebaker [9]. Following an investigation designed to test the validity of Stevens' power law, they conclude "The Stevens' power law does seem to describe the loudness function well". They add, however, "The steepness of the function is biased by a number of factors: e.g., training, past experience, previous knowledge and experience of sound intensity". In particular they add "A group of audiology students used numbers that closely matched the decibel scale. Practice and repeated instructions intended to explain the difference between the decibel and the loudness scales did not significantly alter their judgments. Therefore they were excluded from the study". Two points emerge from this work. First, an individual's experience does indeed have a determining effect on his loudness judgments. In other words, psychometric functions are acquired characteristics and in no way represent intrinsic properties of the auditory system, and, secondly, the efforts of these scientists to force certain subjects to alter their judgments simply because they did not conform to the anticipated law, and their subsequent exclusion of those same subjects because they refused to conform after exhortation, hardly encourages us to accept their finally censored results as evidence. Let us now consider two further attempts that have been made to shore up the crumbling fabric of the psychometric function. It can be reasonably argued that the validity of the domain of applied physics is increased every time some new phenomenon proves amenable to orthodox measuring techniques. Psycho-physicists seem to have been imbued with the hope of validating their own theories in much the same way. Thus Guirao and Stevens [11] report five extra dimensions to the auditory sensation, namely density, volume, softness, smallness, and diffusiveness, and they go so far as to propose mathematical functions relating them: for example, (loudness) equals (density) times (volume) and (softness) equals (smallness) times (diffusiveness). In view of what has been said about the sone scale itself it is difficult to believe that such hieroglyphics really constitute mathematical functions. More
A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
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important however is the implication of the belief that such functions can exist in any meaningful sense. The three classical dimensions of the auditory stimulus, i.e. intensity, frequency, and duration, arc commonly identified with three dimensions of the auditory I
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transform from stimulus parameter to perceptual aspect and the identification of the physical correlate in the stimulus, can only be established if a monotone variation in the stimulus parameter can be shown to produce a monotone variation in an identifiable aspect of the perception". No one has produced any convincing evidence of any such correlation in any of these hypothetical new dimensions of the auditory sensation. Finally we come to Stevens' cross-modality validations [13]. It appears that, having secured widespread acceptance of the psychometric functions relating to a large number of sensations, each with its own individual exponent, he felt that the next step was to investigate the relations between those same exponents. With that end in view Stevens first established the power function of a hand dynamometer. He instructed subjects to assign numbers to their sensations as they applied squeezes of varying magnitude. These were correlated with the meter readings to provide the required function. He says, "Equipped with this dynamometer, and the measured exponent for handgrip we have gauged the growth of sensation in nine other continua by asking observers to emit squeezes instead of numbers. The resulting exponents agree remarkably well with exponents measured directly by magnitude estimation". These findings, widely acclaimed as a further validation of a universal power law, are in fact nothing of the sort. They can easily be shown to be an inevitable consequence of the procedure I have described above. Indeed they could be predicted without any recourse to experiment. Whatever the sensation, every individual has a rough idea of certain reference points. We have already noted the threshold and the medium. To this we may add an upper limit. In audiology this is variously described as the threshold of feeling, or of pain, etc., and similar bounds clearly exist (albeit very imprecisely) in all other sensations. The range between lower and upper bounds varies enormously in different sensations, and this undoubtedly accounts for the inter-sensory variation in exponent, quite apart from the wide inter-individual variation in any given sensation that we have already noted. In any given individual, however, just as we have recognized the stability of his personal loudness estimates, so we expect to find a stability in his personal cross-matching. Indeed we shall expect him to be more accurate in matching a very faint squeeze with a very faint taste (or any other faint sensation) than in assigning a number to it. The same holds for a moderate sensation, and also (albeit even less precisely) to an upper bound. Not only, therefore, could these cross-modalities be predicted, but we have daily evidence of exactly that same phenomenon. Every musician who "squeezes" his piano keys in order to produce a loudness sensation specified in his score does with far greater precision exactly what Stevens' subjects achieved, and there can surely be no doubt that this is an "acquired characteristic" in no wise different from learning to walk. Nothing more could be achieved by any further cataloguing of the many anomalies with which this theory abounds, and I now turn to the question of whether despite its many grave imperfections it yet might possess some virtue, whether practical or theoretical. Stevens has in fact claimed both those virtues. In 1962 he wrote [13] "The I.S.O. has recently fixed on a function representing the relation between loudness and sound pressure to be used in engineering calculations. Thus the psycho-physical law is coming to have practical applications in the market place". Alas nothing could be further from the truth. In the decade that followed that pronouncement the sone never once proved of any value in the market place. For example, one year later the Wilson report [14] appeared. This comprehensive study of the effect of noise on almost every aspect of human activity cursorily mentions the sone but makes no use of it. For example, the N.P.L. used a group of 57 observers to assess the noise emitted by various motor vehicles. Here, par excellence, was a situation in which the sone would have been invaluable if indeed it existed. Yet it was not even mentioned. Observers were simply required to report their judgments under four very broad qualitative categories: quiet, acceptable, noisy, and very noisy.
A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
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It is unnecessary to labour this point since the wealth of other competing indices such as dB(A), PN(A), N.N.I., NOY, etc., all testify to the complexity of the problem and the folly of the sone. Nor indeed has any real success attended more elaborate efforts to compute the loudness of complex sounds by means of differential weighting of psychometric functions and nomograms. Thus Corless and Winzer [15] say, "The loudness of several complex sounds computed on the basis of Stevens' model did not agree with the results of Zwicker's method. The results were not related in any consistent way and both sets of computations were at variance with the subjects' response". Finally I come to the question of possible theoretical importance. Here again we may quote from Stevens [13]: "The scientific leverage that comes from having an equation that is adequate to the first order sensory transduction is simply this. Once the first order effect is reduced to a formula, the second order departures from the basic law may conceivably lead to new and deeper understanding. One is reminded, for example, that the discovery of the planet Neptune resulted from a stubborn refusal of the planet Uranus to follow the law of the Heavens as ordained by Newton. Do perturbations in the power law foretell the discovery of new factors in the sensory process ? That question sets a new task for the future". We may pass over without further comment the comparison with the formidable calculations of Adams and Leverrier, not to mention the awe inspiring creations of the Master. It will suffice to state explicitly that in the decade that has followed Stevens' pronouncement no light whatsoever has been thrown on the workings of the central system by the sone or any other psycho-metric function, and there are no grounds for hoping that any further work along those lines will be any more fruitful. CONCLUSION I spoke at the outset of the bewilderment of the biologist on entering the domain of psychoacoustics. As he continues his exploration he must come to the conclusion that he is wandering in a land of mystery and magic. He will encounter disembodied wraiths of quondam physicists who have lost their only entitlement to reality, the cardinal number. And he will encounter bewitched psychologists, forever, and in vain, endeavouring to capture that same talisman, little realizing that for them it is but a mere will-o-the-wisp, as useless as it is unattainable. It :is indeed a barren and desolate land. REFERENCES 1. R. S. DADSONand J. H. KInG 1952 Journal of Laryngology 13, 366-378. A determination of the normal threshold of hearing. 2. G. BREDBERG1968 Acta otolaryngica Supplement No. 236. Cellular pattern and nerve supply of the human organ of Corti. 3. M. E. BRYAN and W. TEr~a'EST1971 In Occupational Hearing Loss. (D. W. Robinson, ed.) pp. 143-150. London: Academic Press. Noise damage liability--evidence as to the state of knowledge. 4. J. Zwmt~CKI1960 Journal of the Acoustical Society of America 32,1046-1060. Theory of temporal auditory summation. 5. D. M. GRErN 1960 Journal of the Acoustical Society of America 32, 124-134. The optimum detecting device. 6. S. S. STEVENS1959 In Measurement: Definition and Theories (Churchman and Ratoosh, eds.). New York: Wiley Measurement, psycho-physics and utility. 7. B. RUSSELL1948 The Principles of Mathematics. London: Allen and Unwin. Second edition. 8. J. ZWlSLOCKI1968 Journal of the Acoustical Society of America 43, 60-64. 9. C. M. DE B~ENZA, M. E. BRYANand W. TEMPEST1970 Journal of Sound and Vibration 11, 399-410. Individual loudness functions.
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10. R. R. ROWLEYand G. A. STUDEBAKER1969 Journal of the Acoustical Society of America 45, 1186-1192. Monaural loudness-intensity relationships for a 1000-Hz tone. 11. M. GUIRAOand S. S. STEVENS1964 Journal of the Acoustical Society of America 36, 1176-1181. Measurement of auditory density. 12. R. A. JENKINS1961 Journal of the Acoustical Society of America 33, 1550-1557. Perception of pitch timbre and loudness. 13. S.S. STEVENS1962 (January) American Psychologist 29-39. The surprising simplicity of sensory metrics. 14. Command 2056 1963 Noise: final report of the committee on the problem of noise. London: H.M.S.O. 15. R. CORLESSand H. WINZER 1964 Journal of the Acoustical Society of America 38, 424-428. Loudness of complex sounds.
A BIOLOGIST
LOOKS
AT PSYCHO-ACOUSTICSt
A. TUMARKIN 45 Rodney Street, Liverpool 1, England
(Received 18 October 1971) To a biologist, a puzzling aspect of psycho-acoustics is the absence of the concept of function. The widespread custom in psycho-acoustics of regarding a living structure as a machine, and consequently describing its behaviour in terms of its response to measured inputs, has serious limitations. It is argued that unless these limitations are realized little progress can be made towards a satisfactory understanding of the workings of human sensory systems. Any biologist who strays into the domain of psycho-acoustics is likely to be puzzled by the absence of a feature that dominates his own landscape. This is the concept of function. In his own domain, the term involves life itself, as in the phrase "functional adaptation". At a lower level, as in physiology, the word is used as it is in applied physics. A living structure is regarded as a machine, and its behaviour is described in terms of its response to measured inputs. Finally, there is the familiar mathematical meaning. In the domain of physics only the second and third aspects are found. The physicist lives in a dead world of meter measurements, and he is satisfied if a measured input yields a measurable response. In the domain of psychology the situation is more complex. It is many years since the existence of orders of magnitude in sensations led Fechner to his famous law, and within recent years the definite (albeit limited) value of such concepts as the I.Q. index has encouarged some psychologists to hope that the brain itself might be defined and understood in mathematical terms. Behaviourists in particular maintain that the only way to learn about any system, alive or dead, is to observe its behaviour under rigidly controlled conditions. No one would deny the success of this approach in animal experimental psychology, but it is arguable that error might creep in whenever the psychologist in his anxiety to obtain measurable results follows too slavishly the rigid procedures of the physicist. In studying a complex system the physicist endeavours to hold constant all parameters except the one under consideration, and he admits no restriction on the nature or magnitude of his input. Nor has he any criteria for evaluating his results except measurability on some meter. The behaviourist who follows that path too zealously is in danger of becoming so remote from the biologist that words lose their agreed meaning and communication begins to break down. Nowhere is the gulf between biologist and psychologist greater than in the domain of psycho-acoustics. Take for example the word "threshold". The biologist conceives this in terms of a "'gestalt": the whole animal and its environment. The threshold is the least change in that gestalt that results in the animal taking purposive action. In deference to the behaviourist, one must here exclude situations in which the animal may be aware of a change in the environment, but takes no obvious purposive action. Consider, for example, the relation between a grazing antelope and a hunting lion. The antelope, whilst grazing peacefully, begins to show signs of unease. It lifts its head to survey the terrain, sniffs suspiciously, t Presented at the Psychological Acoustics Section of the 1971 Spring Meeting of the British Acoustical So¢iety, Birmingham, England, on 5 to 7 April 1971. A number of other papers from the Meeting will be published in future issues. 8* 115
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pricks up its ears, and tenses its muscles. If the lion appears it bounds away; if not, it returns to its meal. No physicist could possibly analyse such a complex event, and so the concept "threshold", for him, refers to individual parameters. Consider the most familiar physical threshold of all, that of loudness. Originally this was envisaged as a precise crossing between silence and signal. Figure I shows the distribution of threshold pressures in 198 so-called normal ears as measured at the National Physical Laboratory [1]. These results were obtained with impeccable technique, and may be accepted with complete confidence. Unfortunately the assumption that they represent the performance of the biologically normal ear is not so acceptable since there is no certainty that any of these ears was biologically normal, and there is ample evidence that some of them were not. It is true that all the ears were rather cursorily clinically examined and passed as normal, but none was examined under the operating microscope, or X-rayed. Yet both these tests are mandatory if minor pathology is 50
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to be detected. Moreover, even if all ears had passed the most searching clinical scrutiny, there would still be no certainty that they were normal, since both middle and inner ear disease can occur without any overt clinical evidence (as, for example, in otosclerosis and various forms o f perceptive deafness). The physicist is, in fact, trapped in a vicious circle. If he aspires to measure the biologically normal ear he must obviously select such ears for his investigation. But the essential criterion for such ears is that they should conform to the very function he seeks to establish. It is noteworthy that in the present group, no less than 17 members could not hear 15 kHz. The inclusion of such ears in a group of ostensibly normal ears is biologically indefensible. After all, the ear is a premier sense organ of superlative sensitivity and efficiency, and it has played a major role in the evolution of the mammals. Originally they were tiny creatures no bigger than a rat or even a mouse. They were probably nocturnal, and for their survival they depended even more on their ears than on their eyes. In particular, the highest tones were essential for the localization of sounds. Man no longer needs hearing of that quality, and indeed his hearing may be degenerating. Nevertheless it is difficult to believe that Nature, the supreme craftsman, would turn out this superlative instrument in batches that showed a variance that no child would accept in a penny toy. It cannot be doubted that the National Physical Laboratory (N.P.L.) group included a considerable number of pathological ears, and this goes far to explain the lower skirt of all the distribution curves: i.e., individuals with thresholds up to 20 dB below the mean. But how can one explain the considerable number that heard as much as 20 dB better than the mean 9.I suggest that this is due, in some measure, to the fact that the true mean lies somewhere in the upper skirt, and that the majority of all the ears tested were biologically subnormal.
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This assertion is supported by considerable ancillary evidence. Every otologist knows that middle ear inflammation is widespread in childhood. Few escape it entirely. In addition, however, evidence is now emerging of equally widespread degeneration of the inner ear. Bredberg [2], by meticulously counting the hair cells, has shown that their number is diminishing almost from the day we are born. It is not surprising therefore that the N.P.L. found so many "normal" young adults unable to hear 15 kHz. Work at Salford [3] has confirmed, beyond any doubt, the widespread incidence of high tone inner ear deafness of unknown aetiology in otherwise normal adults. It cannot be doubted that this is merely the tip of the iceberg, and that by strict biological standards, the hearing of most people is subnormal. From a practical point of view, this is no serious matter since so-called civilized man has no need of biologically normal hearing. A working man may lose 60 ~ of his pitch range without ranking forlcompensation, and he may drop 25 dB below the N.P.L. mean without
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so ranking. But it is far otherwise in psycho-acoustic research. An enormous amount of such work, ostensibly dealing with the performance of the normal ear, must now come under suspicion because so many of the subjects were pathological. It is, for example, not uncommon for a worker to take as his criterion of normality the ability to hear within 20 dB of the N.P.L. mean. This means that he may be comparing individuals whose hearing differs by as much as 40 dB. The situation is, of course, complicated by unavoidable variance. This may be physical, physiological, or psychological. The first calls for no discussion. Physiological variance can arise from random neural noise, and also from variations in the response of the end organ due to its innervation. For example, a pure tone stimulates a fairly wide band of hair cells, but, because of lateral inhibition, only the information from the centrally placed cells is transmitted. But when the tone becomes extremely faint, these cells no longer receive enough energy to activate the associated nerve fibre. Inhibition ceases and information begins to come in from cells on the fringe of the stimulation area. Figure 2 shows how the outer cells on the basilar membrane (that are responsible for threshold detection) combine in groups to energize a single nerve fibre. Thus, as the signal intensity approaches threshold, the information area (as opposed to the area of actual mechanical displacement) actually widens, whilst pitch perception becomes less efficient. With further reduction in intensity, the specific neural activity begins to merge with the random neural activity. The observer is aware that something is happening, but cannot define it. Finally he enters a zone
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of uncertainty in which he is not sure whether he has heard anything at all. This brings us to psychological variance. Imagine a fixed line that is being compared with another line that was originally much longer but is steadily contracting until it is obviously shorter. Is there a point at which we can say that they are equal ? Such a point must exist, but we can never know it. The physicist accepts this, and presents his results in the usual way, with mean and all embracing variance. The biologist ignores it since it has no vital significance. But the psychologist makes determined efforts to explore this shadowy domain, arguing as follows. Suppose the observer admits he is uncertain when the difference is 1 ram. Then he must be more uncertain when it is ½ mm and it should be possible to equate the magnitude of his uncertainty with the probability of a wrong judgment. The ambition of the psychologist is to find a measure for these hypothetical magnitudes. Fifteen years ago, hopes were high that the mathematical apparatus of communication theory might be applicable to this problem, and many investigations were carried out to evaluate that possibility. Little or no success attended those efforts, and today few if any audiologists regard the d' index as meaningful. As Zwislocki [4] has said, the concept does not transcend the bounds of mathematical formalism. The purpose of the d' index was to act as a model that would on the one hand be amenable to mathematical analysis, and on the other hand would bear sufficient resemblance to the auditory system to support meaningful comparisons. Unfortunately the restrictions imposed by the first condition made it impossible to comply to any useful extent with the second. Inevitably the results obtained with human observers bore little resemblance to those predicted by the model. To begin with it was necessary to postulate a highly artificial distribution for the noise. No attempt was made to consider what form noise might take within the living system. Fourier series, band-limited, Gaussian noise (despite being physically unrealizable) has two great virtues. It is easily handled in terms of mean and variance, and it submits to a simple sampling theorem, viz. T
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in which the energy in a wave form is derived from its amplitude at 2 WTpoints. It seems possible that workers were attracted to this model because sampling a wave bears a superficial resemblance to what we imagine goes on in the brain when we recognize a familiar event. Although we do not have the faintest inkling of how this is achieved, nevertheless we can reasonably assume that it consists of some sort of matching of an incoming pattern with an established memory pattern, and that this entails something akin to sampling or scanning. Even the recognition of an unfamiliar meaningless event such as a threshold pure tone must involve both pattern matching and memory (albeit short term) since, in order to detect a change from noise to signal plus noise, we must be able to compare an existing pattern with an immediately preceding one. On the other hand, since the process of ascertaining the threshold consists of presenting sounds of diminishing intensity it seems at first sight reasonable to think of the brain as simply measuring power. Green [5] puts this as follows: "Basically in a two interval forced choice, the optimum detecting device simply measures the power in two wave forms and selects the larger, and it is eminently reasonable that the auditory mechanism might also perform that task." Unfortunately, this "reasonable" assumption is completely at variance with accepted biological thought. One of the most important if not fundamental functions of the central nervous system is to recognize change. This applies afortiori to threshold detection. Thus when the observer is given his first interval he at once compares it with the
A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
1 19
preceding "silence", and decides whether it contains a signal or not. He cannot avoid doing this because that is exactly what his auditory system was designed to do. Similarly when he is given the second interval he compares it with the "silence" that intervened between it and the first interval. Neither of these judgments requires or permits any comparison between first and second interval. In other words we are not dealing with two intervals but with two pairs o f intervals. The observer's judgments should be independent of each other were it not for the mischievous intervention of the experimenter who insists on one "yes" for each pair of signals, when in fact it is possible for two positives or two negatives to occur. Be that as it may, there are certainly no grounds for believing that the auditory system can arrange two subliminal signals in order of magnitude, and this error has led to some quite extraordinary experiments. For example, an observer performing an N-interval forced choice is informed whenever he is in error and is instructed to make a second choice. It has been claimed that the hit rate of the second choice is better than would be achieved by pure guesswork, and the conclusion is drawn that he must have been able to draw on stored information in his memory bank. The implication is that, as in the case of the 2 I.F.C., he must have measured the power (or something monotonic with power) in each interval and stored in his memory bank a list of those quantities in order of magnitude: i.e., he must have assigned ordinal numbers to each interval. In the light of what has been said about the two interval test, the incredibility of this N-interval test needs no emphasis, but the reader may confirm this by means of a quite simple test. Let an observer be given in succession a signal at 40, 43, 46 and finally 40 dB once more. On instruction to order them in magnitude he invariably places the final 40 dB below the initial 40 dB, and he continues to do s o even though he is allowed to know the precise intensities. Many variations on this theme can be designed, all depending on the fact that the prime function of the auditory system is to detect change. In experiments of this type, the brain is essentially concerned with the present, which it judges by comparing it with the immediate past. The more remote past has little or no influence on its judgments, and, as the above experiment shows, the first signal, although only separated from the fourth by a few moments, is virtually remote because two other signals have intervened. It is clear therefore that the brain is unable to store magnitude estimates of supraliminal signals (from a biological point of view such a function would be useless) and we may be confident that it is even less interested in subliminal messages. Having thus dismissed the theory of ordinal mensuration we may now consider an even more extravagant claim, namely that of cardinal mensuration. Green [5] says, in defence of his ordinal mensuration, "Subjective scales of loudness assume that the subject can do much more". In this he is referring to the sone and phon scales which are based on the assertion that man can attach cardinal numbers to the ratio of two loudness magnitudes in the same way as a physicist cart attach such numbers to the ratio of two intensities. (N.B. This scale is usually given in phons but I shall refer to dB because it will simplify the argument, and in any case most of the basic work was done on 1 kHz.) The biologist's reaction to this scale must be one of utter incredulity. It is impossible to imagine how such a function could have come into existence if only because the ability to enumerate in such a complex fashion has only appeared within the last few thousand years. It is admittedly not entirely impossible that such a bizarre and useless function might suddenly appear without any obvious cause in the accepted neo-Darwinian sense, but the extreme unlikelihood of such an event must warn us to scrutinize most carefully the evidence on which this function rests. I propose to argue that that evidence carries no conviction whatsoever. First, let us consider the concept of measurement itself. For that purpose we turn to the work of Professor S. S. Stevens [6], who has written so extensively on this subject. He states
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[6] that "Measurement is the assignment of numbers to objects or events according to some rule" and he gives scales resulting from four different rules (nominal, ordinal, interval and ratio.). Unfortunately his definition is useless since he does not tell us what he means by number. In the case of loudness, since the scale is ratio, we need the cardinal number, and without venturing too deeply into that metaphysical morasse, we call on Russell [7] who tells us that it is the class of all those classes that bear a one-to-one relation to each other. This suffices for our purpose since it emphasizes the essential quality of precision. This is usually taken for granted in any graph or equation relating two quantities in the physical world, but we shall find it completely lacking in sensation mensuration. This requirement naturally must not be pushed to extremes since, if we were to require from the measurements of applied physics the precision of pure mathematics, no branch of applied physics could survive. Granting therefore that the whole body of physics is only probably correct, we may 201
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physical measurements. What little value they have is completely lost in the accepted sone/dB relation. Tones: halving and doubling; median = 10.0 dB, mean = 10.9 dB. nevertheless assert that, within that framework, the plausibility of any theory ostensibly based on measurements is proportional to the consistency and accuracy of those measurements. By that criterion the sone (together with all other so-called scales of sensation magnitude) entirely fails to pass even the most liberal and tolerant scrutiny. It seems as if scientists working in the field of psycho-acoustics are prepared to overlook variations and internal contradictions in their findings so extreme that if they occurred in a purely physical experiment would lead immediately to the abandonment of the underlying hypothesis. For example, Figure 3 shows some of Stevens' early results for the power ratio corresponding to a doubling of the loudness sensation. Estimates vary from about 3 dB to about 23 dB and the range is actually minimized by the logarithmic notation. In linear terms the range is from about two to about 200. But even if one accepts the log values the range is surely sufficient to exclude the sone from the company of measurable quantities as I have defined them. We have only to consider what would happen if the same group of listeners had been given the necessary apparatus and told to measure the intensity ratio of two sounds. Not only would the answers fall within an extremely narrow range, but any one that did not would be immediately suspect, since intensity refers to a public event and can only have one magnitude whilst sones refer to private events and each listener's magnitudes, however aberrant, are as valid as those of any other. Nevertheless, these widely ranging pseudo-numbers have been ruthlessly constrained. The first step was to present the mean of large groups of listeners together with interquartile variance. Next the mean alone was presented. Then came the simplified equation, and finally only the exponent of the curve. The motive behind this ruthless condensation was presumably
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the quest for some general principle applicable to the auditory process, and that in its turn was to be an element in a grand design. By the accumulation of a host of exponents relative to all other sensations it was hoped that light might be thrown on the workings of the central nervous system. In the event, nothing of the sort transpired, and by the very magnitude of their aspirations the seekers after psychometric functions overlooked what little of value there was in their original observations. The remarkable fact is that any listeners at all should be prepared to assign numbers, however capricious, to the magnitude of their sensations. It is idle of the biologist to argue that since this serves no useful function it could not have evolved. The phenomenon exists and demands some explanation. In the early days of the sone it was suggested that listeners try to project the sounds outwards and then estimate their relative distance. This theory was 60
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an individual's personality may reflect itself to some extent in the size of the number he considers medium. The relevance to psycho-metric functions is obvious. Confining ourselves to loudness (although the argument applies equally to all other sensations) we know that by sharing the experience of public events, people learn to agree approximately on the meaning of "a faint sound", "a fairly loud sound", "a very loud sound" and so on. Music indeed utilizes the familiar notation from pianissimmo to fortissimo which every musician interprets in roughly the same way. What more natural than to assign to a sound of moderate loudness the magnitude of a medium number? Of course one number cannot establish a scale, but the listener already has another reference point of a more fundamental nature, namely the threshold. He has a more or less hazy idea of a very faint sound, a faint taste, a faint itch and so on, and will presumably attach to it a magnitude in the neighbourhood of unity. Now the average individual lives under conditions in which 30 dB would be considered very quiet whilst 60 dB would be considered moderately loud. Applying these figures to the Salford medium numbers we find that people are likely to assign a magnitude between two and 75 to an intensity range of the order of 30 dB. These values are not significantly different from Stevens' original findings. Certain conclusions follow from this hypothesis. To begin with, if an individual's medium number is indeed an expression of his daily life and personality we should expect that number to remain fairly constant throughout his life. We have indeed found that an individual's estimate for doubling remains unchanged after an interval of a year. On the other hand, since medium numbers vary so widely we should expect similar inter-individual variations in sensation magnitudes. This too we have found. Figure 5 shows the different exponents found at Salford [9]. They vary from 0.013 up to 0.07. The significance of this massive inter-individual variance was submerged in the earlier work by the ruthless process of averaging to which I referred above. In that respect we may refer to the work of Rowley and Studebaker [9]. Following an investigation designed to test the validity of Stevens' power law, they conclude "The Stevens' power law does seem to describe the loudness function well". They add, however, "The steepness of the function is biased by a number of factors: e.g., training, past experience, previous knowledge and experience of sound intensity". In particular they add "A group of audiology students used numbers that closely matched the decibel scale. Practice and repeated instructions intended to explain the difference between the decibel and the loudness scales did not significantly alter their judgments. Therefore they were excluded from the study". Two points emerge from this work. First, an individual's experience does indeed have a determining effect on his loudness judgments. In other words, psychometric functions are acquired characteristics and in no way represent intrinsic properties of the auditory system, and, secondly, the efforts of these scientists to force certain subjects to alter their judgments simply because they did not conform to the anticipated law, and their subsequent exclusion of those same subjects because they refused to conform after exhortation, hardly encourages us to accept their finally censored results as evidence. Let us now consider two further attempts that have been made to shore up the crumbling fabric of the psychometric function. It can be reasonably argued that the validity of the domain of applied physics is increased every time some new phenomenon proves amenable to orthodox measuring techniques. Psycho-physicists seem to have been imbued with the hope of validating their own theories in much the same way. Thus Guirao and Stevens [11] report five extra dimensions to the auditory sensation, namely density, volume, softness, smallness, and diffusiveness, and they go so far as to propose mathematical functions relating them: for example, (loudness) equals (density) times (volume) and (softness) equals (smallness) times (diffusiveness). In view of what has been said about the sone scale itself it is difficult to believe that such hieroglyphics really constitute mathematical functions. More
A BIOLOGIST LOOKS AT PSYCHO-ACOUSTICS
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important however is the implication of the belief that such functions can exist in any meaningful sense. The three classical dimensions of the auditory stimulus, i.e. intensity, frequency, and duration, arc commonly identified with three dimensions of the auditory I
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transform from stimulus parameter to perceptual aspect and the identification of the physical correlate in the stimulus, can only be established if a monotone variation in the stimulus parameter can be shown to produce a monotone variation in an identifiable aspect of the perception". No one has produced any convincing evidence of any such correlation in any of these hypothetical new dimensions of the auditory sensation. Finally we come to Stevens' cross-modality validations [13]. It appears that, having secured widespread acceptance of the psychometric functions relating to a large number of sensations, each with its own individual exponent, he felt that the next step was to investigate the relations between those same exponents. With that end in view Stevens first established the power function of a hand dynamometer. He instructed subjects to assign numbers to their sensations as they applied squeezes of varying magnitude. These were correlated with the meter readings to provide the required function. He says, "Equipped with this dynamometer, and the measured exponent for handgrip we have gauged the growth of sensation in nine other continua by asking observers to emit squeezes instead of numbers. The resulting exponents agree remarkably well with exponents measured directly by magnitude estimation". These findings, widely acclaimed as a further validation of a universal power law, are in fact nothing of the sort. They can easily be shown to be an inevitable consequence of the procedure I have described above. Indeed they could be predicted without any recourse to experiment. Whatever the sensation, every individual has a rough idea of certain reference points. We have already noted the threshold and the medium. To this we may add an upper limit. In audiology this is variously described as the threshold of feeling, or of pain, etc., and similar bounds clearly exist (albeit very imprecisely) in all other sensations. The range between lower and upper bounds varies enormously in different sensations, and this undoubtedly accounts for the inter-sensory variation in exponent, quite apart from the wide inter-individual variation in any given sensation that we have already noted. In any given individual, however, just as we have recognized the stability of his personal loudness estimates, so we expect to find a stability in his personal cross-matching. Indeed we shall expect him to be more accurate in matching a very faint squeeze with a very faint taste (or any other faint sensation) than in assigning a number to it. The same holds for a moderate sensation, and also (albeit even less precisely) to an upper bound. Not only, therefore, could these cross-modalities be predicted, but we have daily evidence of exactly that same phenomenon. Every musician who "squeezes" his piano keys in order to produce a loudness sensation specified in his score does with far greater precision exactly what Stevens' subjects achieved, and there can surely be no doubt that this is an "acquired characteristic" in no wise different from learning to walk. Nothing more could be achieved by any further cataloguing of the many anomalies with which this theory abounds, and I now turn to the question of whether despite its many grave imperfections it yet might possess some virtue, whether practical or theoretical. Stevens has in fact claimed both those virtues. In 1962 he wrote [13] "The I.S.O. has recently fixed on a function representing the relation between loudness and sound pressure to be used in engineering calculations. Thus the psycho-physical law is coming to have practical applications in the market place". Alas nothing could be further from the truth. In the decade that followed that pronouncement the sone never once proved of any value in the market place. For example, one year later the Wilson report [14] appeared. This comprehensive study of the effect of noise on almost every aspect of human activity cursorily mentions the sone but makes no use of it. For example, the N.P.L. used a group of 57 observers to assess the noise emitted by various motor vehicles. Here, par excellence, was a situation in which the sone would have been invaluable if indeed it existed. Yet it was not even mentioned. Observers were simply required to report their judgments under four very broad qualitative categories: quiet, acceptable, noisy, and very noisy.
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It is unnecessary to labour this point since the wealth of other competing indices such as dB(A), PN(A), N.N.I., NOY, etc., all testify to the complexity of the problem and the folly of the sone. Nor indeed has any real success attended more elaborate efforts to compute the loudness of complex sounds by means of differential weighting of psychometric functions and nomograms. Thus Corless and Winzer [15] say, "The loudness of several complex sounds computed on the basis of Stevens' model did not agree with the results of Zwicker's method. The results were not related in any consistent way and both sets of computations were at variance with the subjects' response". Finally I come to the question of possible theoretical importance. Here again we may quote from Stevens [13]: "The scientific leverage that comes from having an equation that is adequate to the first order sensory transduction is simply this. Once the first order effect is reduced to a formula, the second order departures from the basic law may conceivably lead to new and deeper understanding. One is reminded, for example, that the discovery of the planet Neptune resulted from a stubborn refusal of the planet Uranus to follow the law of the Heavens as ordained by Newton. Do perturbations in the power law foretell the discovery of new factors in the sensory process ? That question sets a new task for the future". We may pass over without further comment the comparison with the formidable calculations of Adams and Leverrier, not to mention the awe inspiring creations of the Master. It will suffice to state explicitly that in the decade that has followed Stevens' pronouncement no light whatsoever has been thrown on the workings of the central system by the sone or any other psycho-metric function, and there are no grounds for hoping that any further work along those lines will be any more fruitful. CONCLUSION I spoke at the outset of the bewilderment of the biologist on entering the domain of psychoacoustics. As he continues his exploration he must come to the conclusion that he is wandering in a land of mystery and magic. He will encounter disembodied wraiths of quondam physicists who have lost their only entitlement to reality, the cardinal number. And he will encounter bewitched psychologists, forever, and in vain, endeavouring to capture that same talisman, little realizing that for them it is but a mere will-o-the-wisp, as useless as it is unattainable. It :is indeed a barren and desolate land. REFERENCES 1. R. S. DADSONand J. H. KInG 1952 Journal of Laryngology 13, 366-378. A determination of the normal threshold of hearing. 2. G. BREDBERG1968 Acta otolaryngica Supplement No. 236. Cellular pattern and nerve supply of the human organ of Corti. 3. M. E. BRYAN and W. TEr~a'EST1971 In Occupational Hearing Loss. (D. W. Robinson, ed.) pp. 143-150. London: Academic Press. Noise damage liability--evidence as to the state of knowledge. 4. J. Zwmt~CKI1960 Journal of the Acoustical Society of America 32,1046-1060. Theory of temporal auditory summation. 5. D. M. GRErN 1960 Journal of the Acoustical Society of America 32, 124-134. The optimum detecting device. 6. S. S. STEVENS1959 In Measurement: Definition and Theories (Churchman and Ratoosh, eds.). New York: Wiley Measurement, psycho-physics and utility. 7. B. RUSSELL1948 The Principles of Mathematics. London: Allen and Unwin. Second edition. 8. J. ZWlSLOCKI1968 Journal of the Acoustical Society of America 43, 60-64. 9. C. M. DE B~ENZA, M. E. BRYANand W. TEMPEST1970 Journal of Sound and Vibration 11, 399-410. Individual loudness functions.
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10. R. R. ROWLEYand G. A. STUDEBAKER1969 Journal of the Acoustical Society of America 45, 1186-1192. Monaural loudness-intensity relationships for a 1000-Hz tone. 11. M. GUIRAOand S. S. STEVENS1964 Journal of the Acoustical Society of America 36, 1176-1181. Measurement of auditory density. 12. R. A. JENKINS1961 Journal of the Acoustical Society of America 33, 1550-1557. Perception of pitch timbre and loudness. 13. S.S. STEVENS1962 (January) American Psychologist 29-39. The surprising simplicity of sensory metrics. 14. Command 2056 1963 Noise: final report of the committee on the problem of noise. London: H.M.S.O. 15. R. CORLESSand H. WINZER 1964 Journal of the Acoustical Society of America 38, 424-428. Loudness of complex sounds.