CHAPTER XIV

HEARING

The ear, like the eye, records amplitude of vibration; loudness. It also records rapidity of vibration, musical pitch, which corresponds with colour. But it seems to have a more difficult task than the eye, since it has to analyse, or at any rate has to transmit information regarding the form of compound vibrations. The meanings of these distinctions may be illustrated by reference to a tracing on the cylinder of a phonograph. A needle attached to the posterior surface of the thin metal plate against which one speaks scratches the surface of a rotating cylinder of hardened wax. Examined with a lens, the record is seen to be an irregularly changing line. The depth of the marks is a measure of loudness. Their varying number in a given time indicates the changing pitch of the voice which produced them. Their form is a record of the quality of its tone. The work of the ear, so far as it consists in the estimation of the amplitude and rapidity of pulsations of sound, is easy to describe, but the acoustics of form are complicated.

Light is transmitted as vibrations of æther. They are transverse to the direction in which the light is travelling. Sound cannot travel through a vacuum, since it is dependent upon displacements of material particles. The particles move forwards and backwards in the direction in which sound is progressing. Sound is a sequence of pulsations, alternate condensations and rarefactions of the media which conduct it. Their particles are first pressed together, and then rebound to positions farther apart. A sequence of to-and-fro movements, each smoothly continuous throughout the whole duration of a pulsation, would produce a pure musical tone. Tuning-forks carefully bowed settle down after a few seconds into unbroken oscillations, which convey to the air the to-and-fro movements of pure tones. Such tones vary in nothing but loudness and pitch. If their pulsations are slow, we speak of the pitch as “low”; if they are rapid, we say that their pitch is high. But if the sound produced by tuning-forks (and low-toned stopped organ-pipes) be omitted from the list, no pure tones reach our ears. The notes of flutes, fiddles, trumpets, pianos, have each a certain “quality” characteristic of the instrument. Even in a violin the G string has not the same timbre as the D string. Owing to the elasticity of the substances which originate and of the substances which transmit sound, its pulsations are not simple to-and-fro movements, uninterrupted from beginning to end. Each pulsation is partially broken at intervals; and the quality of the sound depends upon the number and relative accentuation of these partial interruptions. Sound travels through air at the rate of 1,100 feet per second. This figure, divided by the number of vibrations per second of a tone, gives the wave-length in air of a tone of that particular pitch. For example, the middle C has a vibratory rate of 256. Its wave-length is, therefore, somewhat over 4 feet. The lowest tone of an organ has a wave-length of 37 feet; its highest of 3½ inches. These figures give no information, however, regarding the movement of the particles which pass on the sound. When air is transmitting a note—say the middle C—its separate molecules do not move through a distance of 4 feet. Each molecule moves but a short distance, varying with the loudness of the tone; but the “wave” of crowding runs straight forward from the piano-string to the ear, the molecules at the end of each stage of 4 feet taking on a backward movement, so that the crowding, so far as the molecules of that particular section are concerned, returns to its starting-point. Between the piano-string and the ear there is a crowding and forward movement at 0, 4, 8, 12 ... feet; a spreading and backward movement at 2, 6, 10, 14 ... feet. Most illustrations which are intended to aid the mind in forming a definite picture of the transmission of sound are liable to be misinterpreted, because they translate rectilinear movements into waves. They represent the movements of the string, and not the movements of the molecules of air between the string and the ear; but with the aid of the imagination one may picture the positions of the particles in this path. The pulse, we will suppose, has just reached the limit of 12 feet. Half-way from its 8-foot halting place the molecules are again crowded, although not so densely. One-third of the distance from the same point there again appears a tendency to crowd. This latter point marks an interval of one-third of this wave _plus_ the wave which led up to it. At the end of the ninth foot there is a crowding, though less marked—this wave _plus_ the two preceding waves, divided into fourths. Within these intervals are other points at which the molecules have closed together, the distances from a nodal point depending upon the number of waves involved, and, speaking generally, growing less marked as the number increases. Such are the very complex pulsatile movements which reach the ear.

Every musical sound produced by a piano, a violin, or other instrument, is compounded of a fundamental or prime tone, and overtones, partial tones, or harmonics. The following table shows the more important partial tones which accompany the prime tone when the middle C on a pianoforte is struck:

Number of Number of Note. Vibrations. Interval. Ratio. Overtone.

C‴ 2,048 } 7th } Super-Second 8/7 } B″♭ 1,792 } 6th } Sub-minor third 7/6 } G″ 1,536 } 5th } Minor third 6/5 } E″ 1,280 } 4th } Major third 5/4 } C″ 1,024 } 3rd } Fourth 4/3 } G′ 768 } 2nd } Fifth 3/2 } C′ 512 } 1st } Octave 2/1 C 256 } =Fundamental=

The quality of a musical note depends upon the number and relative loudness of its overtones. When several notes are sounded simultaneously, they blend into a chord or harmony, provided the intervals which separate them are equal to the intervals which separate the simpler overtones. Each of the notes yields overtones. The tones blend into a concord. Their partials are in unison. The variations in air-pressure of the compound tone are strictly periodic. If the ratios of the frequencies of its constituent notes are simple the product is a rich, full sound, such as a common chord.

At least one other character of the pulsations of sound must be taken into consideration if we wish to picture the nature of the force to which the ear responds. Tones which reach it from several instruments simultaneously are not necessarily in unison, or even in harmony. The overtones of a single note sounded on a piano or violin—the statement does not hold good for bells, nor is it strictly true of flutes or horns—must necessarily bear a simple proportional relation to their prime tone. They divide the grand pulsation into fractions “without a remainder.” But the vibrations of two tuning-forks which are slightly out of unison interfere one with the other at regular intervals. They produce “beats.” Everyone is familiar with the curious effect which is produced upon the eye when one row of railings is seen through another, or one expanse of wire-netting behind another. Sets of lines which occupy nearly the same positions in the line of sight combine to make a large pattern, which overlies the smaller pattern of the rails or netting. The same thing happens with sounds which coincide at considerable intervals, although in the case of sounds interference is as marked as reinforcement. If whilst a tuning-fork yielding 101 vibrations per second is singing another of 100 vibrations is brought into play, the vibrations of the second fork are superposed on those of the first. At a certain moment the forward movement of molecules of air induced by the first fork is reinforced by a forward push from the second. But half a second after this coincidence of phase an opposite result is produced—50½ vibrations of No. 1 have passed, but only 50 of No. 2. No. 2 is going backwards (inwards), whilst No. 1 is moving forwards (outwards). The same molecules are impelled backwards by No. 2 and forwards by No. 1. The result is a pause. The compound sound produced by the two forks reaches the ear in throbs. If the forks were vibrating at the rates of 101 and 99, there would be two pauses and two beats in every second; if at the rate of 202 and 198, four. The number of beats per second equals the difference in frequency of vibration of the tones. A pianoforte tuner does his work best if he has a musical ear, yet he may discharge his duties with competence without one. Having struck a note, he sounds its octave, holding both keys down, and listens for the beat. If the first note gave no beat with his tuning-fork, the second is in time when it likewise gives no beat with the first. We have met a tuner who did his work in this way; but it must be admitted that his tempering of the intervals of the octave with which he commenced, and consequently of the other octaves above and below it, left something to be desired. The result might have been satisfactory had he been provided with twelve tuning-forks.

The question as to whether beats, when sufficiently rapid, blend into a tone has been much discussed, without a decision. Probably they do not. The complementary question as to the cause of dissonance is also not completely closed. Two notes harmonize, as we have seen, when the ratio of their frequencies is a simple fraction. Musicians are not quite agreed as to the level of numerical complexity at which a compound tone first produces a feeling of discomfort. A good deal depends upon its position in the scale and the instruments which are combining to produce it. A minor third (⁶/₅) is on the safe side. This is the first chord in our list of intervals in which a beat can be detected. Slow beats, however, do not distress us. It is the rapid beats of conflicting overtones which give a harsh, rough character to a compound note. The level at which a line is drawn between harmony and dissonance seems to depend to a considerable extent upon musical education, using the term in its widest sense. In primitive music—Hungarian, Scotch, Welsh—intricate minor chords predominate. The minute subdivision of the octave in Indian music is quite incomprehensible to a European ear. Musical cultivation tends to eliminate complex fractions. It is, however, to be noted that the history of Western music also shows the influence of an opposite tendency. Later generations have admitted as harmonies combinations which earlier generations could not tolerate.

Pitch, quality, harmony, and dissonance are distinguished by the human ear. These are the attributes of musical or periodic sounds. In a separate class must be included noises of all kinds, termed in acoustics “aperiodic,” because the vibrations which cause them are not rhythmic. The teeth of a policeman’s rattle may click a hundred times a second, but it does not make music. Even with a rapidity of interruption greater than this (at least 500 times per second) a succession of noises fails to blend into a smooth, continuous sound. The ear recognizes the loudness, duration, and even to a very high frequency the repetition of unmusical sounds.

The ear as a sense-organ can be followed down the zoological scale to jelly-fish. In its primitive form it is a chamber lined with epithelial cells bearing hairs, containing an otolith, or ear-stone. Otoliths are rounded calcareous masses which play an important part in the ears of all animals up to fishes. Even in man they are found in the more subdivided form of otoconia. Contact of the otoliths with the sensory hairs originates impulses in the nerves with which primitive ears are abundantly provided. Advisedly we use the word “ear” in place of “auditory organ.” In all animals this organ affords information of a double nature-movement of the external medium in which the animal lives, and movements of the animal in the medium. When the animal moves, its sensory hairs are displaced with regard to the otolith; when the water in which it is swimming pulsates, its otoliths are shaken against the sensory hairs. Displacements of the animal and agitations of the water produce similar effects. The ear in this stage is an organ of touch. It might well be questioned whether an animal fitted with a piece of sensory apparatus of this kind is endowed with a sense which we may properly, after reflecting upon our own sensations, term “hearing.” It is, however, stated that certain transparent crustaceans, in which the functioning of the ear-organs may be watched through a lens, show in these organs hairs of varying length which vibrate to tones of different frequency. This observation apart, it might be doubted whether fishes hear, if we mean by the word “hearing” the recognition and discrimination of tones of high frequency—musical tones. Their ears serve equally to inform them of the changes in position of their heads and of the tremblings of the sea. The shocks transmitted through the sea are near akin to the slower vibrations of sound, if the fishermen of the Mediterranean are justified in their practice of beating a wooden clapper which rests upon the seat of the boat as they row backwards and forwards in front of a curved net. They believe that the fish are frightened by the noise; but it matters little whether we describe the fish as hearing a noise, or as feeling the percussions of the clapper conducted through the water. To the more rapid vibrations of the clapper, the fish are probably insensitive. The cochlea, which we have every reason for regarding as the organ by which sound is analysed, is not possessed by fishes. It makes its first appearance in reptiles. Birds, it is evident, are able to distinguish musical tones. Their cochleæ are very short, and are destitute of “rods of Corti.” For a moment this appears surprising, but it must be remembered that the range of tones which any bird discriminates is very short, however nicely it may value the notes within its range. In mammals the ear is clearly divided into three parts, to which the three functions which have grown out of the specialization of the sense of touch are allocated. (1) The semicircular canals are concerned with the sense of orientation. (2) The utricle and saccule reverberate to noise—the rumbling of trains, the boom of guns, the beats of dissonant musical tones. We do not know how to classify the agitations of the atmosphere which surrounds us and of the earth on which we stand, nor can we point with any certainty to the groups of stimuli which for us have taken the place of the grinding of stones on the beach and slapping of rocks by waves. (3) The organ of Corti in the cochlea discriminates and analyses musical sounds. To these three sense-organs, which are situate in the inner ear, certain structures are accessory.

The concha, which enables a horse or a cat to collect sound and to localize its source, is in ourselves merely an ornament to the side of the head.

The external meatus is a curved tube, about an inch long. Frequently a tuft of hairs guards its entrance. The wax secreted by its wall serves to attach particles of dust, and to deter insects from entering the tube. The air at the end of it is at a uniform temperature. It is closed by the membrana tympani, or drum. This membrane receives the vibrations of sound; and, in order that it may collect them with absolute impartiality, it is in every respect the opposite in shape and structure to the top of a drum. The stretched parchment which covers a drum is flat. Its tension is uniform in all its parts. Movements have the greatest amplitude at the centre. Every precaution is taken to insure its emitting, with as little confusion as may be, the particular note to which it is tuned. The drum of the ear is shaped like the mouth of a trumpet, depressed to a point, but convex from this point outwards. Its elastic fibres, which are partly radial, partly circular, are at many different tensions. Its deepest part, to which the long arm of the hammer-bone is attached, is not its centre.

The “middle ear” is an irregular cavity communicating with the pharynx by the Eustachian tube. It is filled with air at the same pressure as the atmosphere. Except during the act of swallowing, when it is at first shut tightly and then opened, the pharyngeal end of the Eustachian tube is gently closed. When one is dropped in a lift rapidly down the shaft of a mine, the difference in pressure between the external air and the air in the middle ear stretches the drum to such an extent that deafness to low tones is produced. Conversation becomes inaudible. The deafness is remedied by swallowing saliva, and thus opening the end of the Eustachian tube. The commonest cause of permanent deafness is inflammation followed by thickening of the mucous membrane of the lower end of the Eustachian tube, with its consequent closure, due to frequent sore throats. The air in the middle ear is slowly absorbed. It needs to be constantly renewed through the Eustachian tube.

On the inner wall of the middle ear are two small apertures—the oval window and the round window. Both are closed with membrane. Into the oval window is fitted the sole-plate of the stirrup-bone. Three bones—hammer, anvil, and stirrup—combine in transferring the movements of the membrana tympani to the oval window. They constitute a jointed lever, which swings about an axis passing through the ligament of the anvil (Fig. 38), the excursions of the long arm of the hammer being reduced in amplitude by one-third at the stirrup-plate. As the oval window has only one-twentieth of the area of the drum, the movements of the latter are transmitted with concentrated force. Two points in the mechanism of these bones may be specially noticed: (1) The head of the hammer is free to rotate in the cavity of the anvil, checked by a cog. Every inward movement of the drum is faithfully transmitted to the oval window; but when the drum moves outwards, the hammer does not necessarily carry the anvil with it. (2) A muscle—tensor tympani—is inserted near the elbow of the long arm of the hammer. When high notes are listened to its contraction tightens the drum, rendering it more responsive to rapid vibrations. It has a tonic action, but it does not make any special contraction for low notes.

Behind the two windows, within the solid bone, is the inner ear, which our ancestors very aptly termed a “labyrinth.” It is filled with fluid—perilymph—which is shaken by every movement of the stirrup-plate. Since water is incompressible, no waves could be raised in the perilymph were there no second aperture. Every vibration conveyed by the stirrup-plate after passing through the labyrinth ends as a vibration of the membrane which closes the round window.

Nowhere does perilymph come in contact with auditory cells. All the endings of the nerve of hearing are contained within a membranous labyrinth which lies within the bony cavities. The way in which the waves of the perilymph are dispersed over the surface of this closed sac can be inferred from the diagram (Fig. 38). They sweep round the utricle and saccule, are lost in the narrow spaces which surround the semicircular canals, run up the scala vestibuli of the cochlea. The course of the waves which traverse the cochlea is of especial interest in connection with the physiology of hearing.

The cochlea—snail-shell—is a spiral tunnel of three turns, in hard bone, about an inch in length. A shelf of bone—lamina spiralis—projects into the tunnel on its convex side. From the free margin of this spiral lamina two membranes extend to the outer wall of the tunnel—one firm, containing straight, stiff, and probably elastic fibres which radiate outwards (the basilar membrane); the other an extremely delicate film of connective tissue. The tunnel is thus divided into three compartments, known as the scala vestibuli, scala media, scala tympani. The scala media belongs to the membranous labyrinth. Waves transmitted through perilymph pass, as we have already explained, up the scala vestibuli. At the apex of the cochlea the two scalæ are in communication; but the aperture is small, and it is unlikely that waves reach the lower passage from the upper through this opening. They pass through the thin membrane which roofs the scala media, shake its endolymph, and reach the lower passage through the basilar membrane. It is noteworthy that, since the round window at the lower end of the scala tympani is, with the exception of the oval window, the only opening of the bony labyrinth, all waves transmitted through the oval window must travel part of the way or all the way up and down the cochlea.

The organ of Corti is spread out on the basilar membrane. It is an epithelial structure of extreme regularity and uniformity. Near to the edge by which the basilar membrane is attached to the spiral lamina rests a double row of rods of Corti, stiff pillars which lean one towards the other, over the tunnel of Corti, the convex head of the outer rod fitting into a concavity in the head of the inner one; in some places one outer rod fits against two inner rods, as the latter are rather the more numerous. On the inner side of the inner rod is seen, in transverse sections a single plump cell filled with cloudy protoplasm, and bearing on its free surface a tuft of very short hairs. On the outer side of the outer rod are three or four hair-cells, each with a cloudy outer segment containing the nucleus, a granular middle segment, and a stiffish stalk, which attaches it to the basilar membrane. Between the hair-cells are supporting cells, thicker below, tapering above, containing in their substance a firm fibre. Still farther to the outer side are epithelial cells, of no special interest. The purpose of the rods of Corti and the supporting cells is to give attachment and support to a reticulated membrane of exquisite delicacy, through the oblong apertures of which the hairs of the hair-cells project into the endolymph. The spiral lamina is traversed by a vast number of fibres of the auditory nerve, which, losing their medullary sheaths, pass across the tunnel of Corti as naked axons, to end amongst the hair-cells. Above the organ of Corti, attached by its edge to the spiral lamina, is a thick, gelatinous, fibrillated structure—membrana tectoria—which rests as a coverlet on the surface of the organ. It has been supposed that it serves to damp the vibrations of the hairs after they have been set in motion by the waves passing across the scala media; but it not impossibly plays a more active part in hearing than this.

The organ of Corti is, beyond doubt, the apparatus which analyses sounds; but the problem of the way in which it responds to tones of different pitch, or analyses compound tones, is not as yet even approximately solved. To escape the acoustic difficulties which have to be faced by anyone who endeavours to expound the theory of the cochlea as a piece of analytical apparatus, various suggestions as to the possibility of an action _en masse_ have been advanced. For example, the basilar membrane has been compared to a telephone-plate which takes up vibrations and transmits them through the auditory nerve to the brain. But if the organ of Corti be the transmitter, there is no ear in the brain to analyse the vibrations given out by a receiving telephone-plate; and without a receiving plate and a listening ear a telephone is purposeless. According to this hypothesis, the basilar membrane vibrates as a whole, moving the hair-cells in various “patterns”; the pressure of the hairs against the tectorial membrane causing irritation of the cells which bear them, and hence producing stimulation of various groups of nerves. Other pattern theories are somewhat similar. But it is obvious that all hypotheses of the vibration of the whole of the basilar membrane, or of large parts of it, simultaneously, leave to the mind the responsibility of reading the pattern which the impulses generated in the organ of Corti make in the brain. It is conceivable that every fraction of a semitone which a musician can discriminate, and every combination of tones which he can analyse, is transmitted to the brain by a large number of co-operating nerve-impulses; but such a theory involves a complexity of mental associations difficult to contemplate.

According to the general principles enunciated in this book, analysis of stimuli is the function of sense-organs. It cannot in all cases be compared with the analysis effected in a physical laboratory; nor is this necessary; but it must be carried so far that nerve-impulses which have no specific qualities apart from their source shall give rise to effects in consciousness which have no basis other than the topographical distribution of the said impulses in the brain. There may be sensory impulses of different orders; there may be in the brain psycho-physical substances which react to impulses of various orders in various ways; but until we have some hint of the existence of specific impulses and specific psycho-physical substances, we are not justified in postulating their existence simply in order that we may escape from physiological embarrassments.

The organ of Corti has in the highest degree the appearance of a piece of apparatus for the analysis of sound. If the basilar membrane, with the cells which rest upon it, be cut out and laid flat, the suggestion of some kind of instrument is very strong. It is a long narrow ribbon, narrowest at the bottom of the spiral, increasing to about twice the width at the apex. It is crossed by radiating fibres, presumably elastic. The cells which rest upon it carry vibrating hairs, and are supplied with nerves. The rods of Corti hold up the reticulated membrane, which keeps the hair-cells in place. It is not to be wondered at that when its structure was first discovered it was thought that the problem of the analysis of musical tones was solved. If two pianos in perfect tune are in the same room, when one is played the corresponding wires of the other twang. Anyone who sings into a piano, whilst the loud pedal raises the dampers, feels an increased fulness in his voice. This is the familiar phenomenon of resonance. Why should not the fibres of the basilar membrane resonate to the tones conveyed to the ear—the shorter ones at the base of the cochlea to high tones, the longer ones at the apex to low tones? This is the order in which we should expect the pulsations of sound which ascend the scala vestibuli to be taken up—the more rapid, near its commencement, the less rapid farther up it. But an explanation of the physics of the selection of vibrations of different frequencies by different sets of the elements which make up the organ of Corti, if such selection occurs, is still to seek. In the first place, the fibres of the basilar membrane are so exceedingly short. What could a fibre less than 0·5 millimetre in length make of the vibrations of a 36-foot organ-pipe? Even if this objection be waived, as certain eminent physicists hold that it may be, there is not a sufficient difference in length between the longest and the shortest fibres to account for the great range of tones which we are able to discriminate; nor is there any evidence that some fibres are more tightly stretched than others.

A further consideration which tempts physiologists to look upon the organ of Corti (including the basilar membrane) as a series of resonators is the somewhat remarkable agreement between the number of separate pieces of apparatus of which it appears to be composed and the number of different musical sounds which, if it were a series of resonators, it might be called upon to discriminate.

The squeak given by a bat at each turn in its flight has a pitch of about 11,000 vibrations to the second—the sixth E above the middle C (Tyndall). In a group of persons listening for the squeak there are usually some who cannot hear it. Above this the range of hearing is very variable. The suddenness of transition from perfect hearing to total want of perception makes experiments with small pipes or with a siren somewhat amusing, when a number of persons are tested at the same time. One complains that the note is intolerably loud and shrill, whilst others assert that there is perfect silence. Thirty-three thousand vibrations is usually regarded as the upper limit for the human ear, but certain physiologists place it at 40,000, or even higher. The upper limit is of little consequence, since there is very little power of discriminating rapidities above the highest note used in music—the piccolo stop of the organ, with a pitch of 4,096. It is possible that a sound with a lower frequency than 27 (the contra-bassoon) may be heard as a tone—16 according to certain writers; but again our power of discriminating very low notes is small. Over a certain range a skilled musician can tell that a note is out of tune when it is one sixty-fourth of a semitone higher or lower than it ought to be. If we assume that by allowing equal sensitiveness for a range of seven octaves, the excess of the allowance over the actual sensitiveness towards either end of this stretch would compensate for the comparatively few distinctions which the ear can make either below or above it—64 × 12 × 7 = 5,376. A much higher estimate, based upon observations which seem to show that the ear can distinguish sounds less than one sixty-fourth of a semitone apart, places the total number at 11,000.

On the assumption that one piece of apparatus is tuned to resonate for every distinguishable sound, between 5,000 and 11,000 pieces of apparatus would be required. Taking one of Corti’s arches as the centre-piece of the resonator, although the rods are certainly not vibratile structures, we find the number to be 3,848 (the number of the outer rods); if either rod with a hair-cell, or hair-cells, is the analytical element, 9,438. Counting gives 3,487 inner, 11,700 outer, hair-cells. The fibres of the basilar membrane are estimated at 24,000; the fibres of the cochlear nerve at 14,000. It will be understood that the counting of structures as minute as these yields results which cannot be more than approximately accurate. Helmholtz, assuming that each arc of Corti indicates an analytical element, accounted for the apparent deficiency in their number by assuming that a tone of which the pitch fell between two arches set both in sympathetic vibration, the arch which was nearest in pitch to the tone vibrating the more strongly. In this way he anticipated an objection which has often been brought against his theory of a long series of resonators.

In opposition to Helmholtz’s theory it is pointed out that when a violinist runs his finger up a bowed string, the pitch rises with perfect smoothness; it does not bump along from resonator to resonator. Especially in the case of very high tones given out by a siren, it is urged that at the rare intervals at which a resonator in the ear is tuned for the tone which the siren is emitting it should sound much louder than when the tone falls midway between two resonators. But the whole question of the nature of the response of the analytical elements is too obscure at present for the discussion of points so nice as this.

Many who think that Helmholtz’s theory of resonators is based upon principles of physics and of physiology which must be regarded as the starting-points of any explanation of the analysis of sounds by the ear and the mind, hold that it goes too far in searching for a separate resonator for every distinguishable tone. The cochlea, as we have already said, does not offer anything like so extensive a choice as this, if regard be had to the tension or length of its elements, and not to their numbers. Those who accept it as an axiom that the cochlea contains a series of responding instruments—but a series far more limited in range than the gamut of our sound-perceptions—seek to discover in musical tones qualities which unite them in groups. Just as in the case of colour-sensations they recognize four (or six) elementary qualities which excite four (or six) pieces of responding apparatus, so also in the case of hearing they seek for a limited number of tone-qualities and a correspondingly limited number of elementary sensations. The ideal of those who take this view is an octave of qualities and of elementary sensations sounded in the middle of the scale when _x_ nerve-endings are stimulated, as the octave above when 2_x_ nerves respond, the octave below with _x_/2. Such a conception seems to guide thought round insurmountable barriers. There is, however, a risk of making too much of the periodic intervals, because they take so important a place in music. At one side of the gap which sound bridges between the individual and his environment is an elastic body shaking at any possible rate within the range of hearing. At the other side of the gap is the ear. If, having arranged several thousands of stones along the side of the road in order of size, I were to state, picking up No. 512, “This is the fundamental of which No. 1,024 is the octave,” answer would be made to me: “It may be that the larger could be broken into halves, each as heavy as the smaller stone; but I recognize no difference between the stones in shape, colour, or hardness.” A vibrating string divides into equal segments, each of which vibrates within the vibrations of the whole string, sounding the octave. We recognize a similarity in quality between tones and their octaves because we are accustomed to hear the octave, the most prominent of overtones, in all musical sounds. Hence, from association, it has become more difficult to distinguish a note from its octave than it is to distinguish it from its fifth; but it does not follow that the effect of 1,024 vibrations upon the sensory cells more nearly resembles the effect of 512 than does that of 768. But at this point we are compelled to construct some hypothesis as to the way in which the vibrations affect the sensory cells. The protoplasm of the cells is not directly sensitive to them. We can account for the generation of impulses in the nerve connected with a particular cell, or group of cells, only on the supposition that a resonating mechanism which responds to vibrations of a certain frequency shakes the cell. Even then it seems necessary to suppose that there is an accessory mechanism which disturbs the cell-protoplasm sufficiently to render the shake effective, probably the hairs rubbing against the tectorial membrane. Anatomical study gives us no confidence in the theory of the existence of several thousands of resonators tuned to as many notes of different pitch. It remains for the physicists to say whether or not we may picture one of these minute resonators as responding to a given note in 10 separate octaves, another in 9 ... another in only 1. The physicists, on their part, may very properly ask the anatomists to point out the resonators, and even to reproduce them in models of dimensions which allow of experimental investigation.

It is generally agreed that the sensation of a chord is compounded of the sensations to which each of its constituent tones gives rise, and that our power of analysing the compound is a question of attention. A musician can direct his attention to either sensation at will. It is not equally certain that a person who has no knowledge of music can do the same. Familiarity with musical instruments gives us so exact a knowledge of the way in which compound tones are produced that it becomes a difficult matter to decide whether, when we say that we can pick out the E or the G of the common chord, it means that we can hear it as distinct from =C= and C′, or whether it means that, knowing the constitution of the chord, we think about the E or the G when we hear the compound tone, to the exclusion of its other constituents. Then, again, the several strings which we try to strike simultaneously do not actually “toe the line.” Their vibrations are not in the same phase, even though the strings be in absolute tune. Discrepancy of phase may favour the singling out of the several constituents of the chord. There we touch upon a problem which we passed over in silence when attempting to give an idea of the nature of the pulsations which reach the ear. We then (p. 405) described the partial pulsations which are superimposed upon the main pulsation as if they necessarily started simultaneously with it. We assumed that the phase difference of the partials was zero. But it is clear that differences of phase of its constituent tones may produce an almost infinite number of variations in the form of a compound “wave” of sound. Is the ear variously affected by different forms of wave? Does difference of phase result in difference of sensation? In broad terms, the answer to this question must be in the negative; although it can be shown that in certain cases a change in phase of the several constituents of a compound tone, without any alteration in their number or their loudness, makes a change in its acoustic quality. Any attempt to correlate physical changes—the movements of air in the outer ear—with the effects which they may be supposed to have upon the organ of Corti must take into account this wide range of variation of wave-form. We have called attention to the difficulties which it introduces; but have no hope of indicating the way in which they may be overcome.

Nothing connected with the physiology of the sense of hearing is more remarkable than its capacity for education. The cochlea of one human being is as extensive and as elaborate in structure as that of another, yet some men can make an infinitely more refined use of it as an analytical apparatus than can others. A native of the Torres Straits cannot distinguish as two separate notes sounds which are less than a semitone apart. Sir Michael Costa could distinguish sounds into the sixty-fourth parts of semitones. The cochlea of a cat is not less elaborate than that of a man, yet Man’s mental life is based upon the analysis of auditory sensations. His supreme advance in the animal scale has depended upon the invention of language, by means of which he communicates and receives information, thus rendering experience eternal, notwithstanding the transience of the individuals who acquire and transmit it. An animal is born, finds out, dies. A man starts with the wisdom of the race beneath his feet.

Hearing has a nebulous origin in sensations of movement or displacement. The connection between the two special senses—the sense of orientation and the sense of hearing, properly so-called—remains always intimate. David danced before the Ark of the Lord. All people, savage and civilized, associate music with movement. High in the animal scale appears the sense-organ which enables its possessor to discriminate musical tones. By its use Man has developed with great rapidity—as secular time is reckoned—an intelligence which removes him from all other animals a planet’s space. The sounding of his organ of Corti by pure tones and combinations of pure tones gives him extreme pleasure, although it in no way ministers to his intelligence. Yet there is in the enjoyment of music a quality of pleasure which makes it near akin to the satisfaction which we experience in exercising the intellect.