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HEARING (formed from the verb “to hear,” O. Eng hymn, heran, &c., a common Teutonic verb, cf. Ger. hofen, Dutch hooren, &c.; the O. Teut. form is seen in Goth. hausjan; the initial h makes any connexion with “ ear, ” Lat. audire, or Gr. άκοίειν very doubtful), in physiology, the function of the ear (q v), and the general term for the sense or special sensation, the cause of which is an excitation of the auditory nerves by the vibrations of sonorous bodies. The anatomy of the ear is described in the separate article on that organ. A description of sonorous vibrations is given in the article sound, here we shall consider the transmission of such vibrations from the external ear to the auditory nerve, and the physiological characters of auditory sensation.

1. Transmission in External Ear -The external ear consists of the pinna, or auricle, and the external auditory meatns, or canal, at the bottom of which we find the membrona tympani, or drum head. In many animals the auricle is trumpet shaped, and, being freely movable by muscles, serves to collect sonorous waves coming from various directions The auricle of the human ear presents many irregularities of surface. If these irregularities are abolished by filling them up with a soil material such as wax or oil, leaving the entrance to the canal free, experiment shows that the intensity of sounds is weakened, and that there is more difficulty in judging of their direction. When waves of sound strike the auricle, they are partly reflected outwards, while the remainder, impinging at various angles, undergo a number of reflections so as to be directed into the auditory canal. Vibrations are transmitted along the auditory canal, partly by the air it contains and partly by its walls, to the membrana tympani. The absence of the auricle, as the result of accident or injury, does not cause diminution of hearing In the auditory canal waves of sound are reflected from side to side until they reach the membrana tympani. From the obliquity in position and peculiar curvature of this membrane, most of the waves strike it nearly perpendicularly, and in the most advantageous direction.

2 Transmission in Middle Ear.—The middle ear is a small cavity, the walls of which are rigid with the exception of the portions consisting of the membrana tympani, and the membrane of the round window and of the apparatus filling the oval window. This cavity communicates with the pharynx by the Eustachian tube, which forms an air-tube between the pharynx and the tympanum for the purpose of regulating pressure on the membrana tympani. During rest the tube is open, but it is closed during the act of deglutition. As this action is frequently taking place, not only when food or drink is introduced, but when saliva is swallowed, it is evident that the pressure of the air in the tympanum will be kept in a state of equilibrium with that of the external air on the outer surface of the membrana tympani, and that thus the membrana tympani will be rendered independent of variations of atmospheric pressure such as occur when we descend in a diving bell or ascend in a balloon. By a forcible expiration, the oral and nasal cavities being closed, air may be driven into the tympanum, while a forcible inspiration (Valsalva's experiment) will draw air from that cavity. In the first case, the membrana tympani will bulge outwards, in the second case inwards, and in both, from excessive stretching of the membrane, there will be partial deafness, especially for sounds of high pitch. Permanent occlusion of the tube is one of the most common causes of deafness.

The membrana tympani is capable of being set into vibration by a sound of any pitch included in the range of perceptible sounds. It responds exactly as to number of vibrations (pitch), intensity of vibrations (intensity), and complexity of vibration (quality or timbre). Consequently we can hear a sound of any given pitch, of a certain intensity, and in its own specific timbre or quality. Generally speaking, very high tones are heard more easily than low tones of the same intensity. As the membrana tympani is not only fixed by its margin to a ring or tube of bone, but is also adherent to the handle of the malleus, which follows its movements, its vibrations meet with considerable resistance. This diminishes the intensity of its vibrations, and prevents also the continued vibration of the membrane after an external pressure has ceased, so that a sound is not heard much longer than its physical cause lasts. The tension of the membrane may be affected (1) by differences of pressure on the two surfaces of the membrana tympani, as may occur during forcible expiration or inspiration, and (2) by muscular action, due to contraction of the tensor tympani muscle. This small muscle arises from the apex of the petrous temporal and the cartilage of the Eustachian tube, enters the tympanum at its anterior wall, and is inserted into the malleus near its root. The handle of the malleus is inserted between the layers of the membrana tympani, and, as the malleus and incus move round an axis passing through the neck of the malleus from before backwards, the action of the muscle is to pull the membrana tympani inwards towards the tympanic cavity in the form of a cone, the meridians of which are not straight but curved, with convexity outwards. When the muscle contracts, the handle of the malleus is drawn still farther inwards, and thus a greater tension of the tympanic membrane is produced. 0n relaxation of the muscle, the membrane returns to its position of equilibrium by its elasticity and by the elasticity of the chain of bones. This power of varying the tension of the membrane is an accommodating mechanism for receiving and transmitting sounds of different pitch. With different degrees of tension it will respond more readily to sounds of different pitch. Thus, when the membrane is tense, it will readily respond to high sounds, while relaxation will be the condition most adapted for low tones. In addition, increased tension of the membrane, by increasing the resistance, will diminish the intensity of vibrations. This is especially the case for sounds of low pitch.

The vibrations of the membrana tympani are transmitted to the internal ear partly by the air which the middle ear or tympanum contains, and partly by the chain of bones, consisting of the malleus, incus and stapes. Of these, transmission by the chain of bones is by far the most important. In birds and in the amphibia, this chain is represented by a single rod-like ossicle, the columella, but in man the two membranes—the membrana tympani and the membrane filling the fenestra ovalis-are connected by a Compound lever consisting of three bones, namely, the malleus, or hammer, inserted into the inembrana tympani, the incus, or anvil, and the stapes, or stirrup, the base of which is attached to a membrane coveriug the oval window. It must also be noted that in the transmission of vibrations of the membrana tympani to the fluid in the labyrinth or internal ear, through the oval window, the chain of ossicles vibrates as a whole and acts efficiently, although its length may be only a fraction of the wave-length of the sound transmitted. The chain is a lever in which the handle of the malleus forms the long arm, the fulcrum is where the short process of the incus abuts against the wall of the tympanum, while the long process of the incus, carrying the stapes, forms the short arm. The mechanism is a lever of the second order. Measurements show that the ratio of the lengths of the two arn1s is as x-5:x; the ratio of the resulting force at the stapes is therefore as xzr- 5, while the amplitudes of the movements at the tip of the handle of the malleus and the stapes is as x-5:1 Hence, while there is a diminution in amplitude there is a gain in power, and thus the pressures are conveyed with great efficiency from the membrana tympani to the labyrinth, while the amplitude of the oscillation is diminished so as to be adapted to the small capacity of the labyrinth. As the drum-head is nearly twenty times greater in area than the membrane covering the oval window, with which the base of the stapes is connected, the energy of the movements of the membrana tympani is concentrated on an area twenty times smaller; hence the pressure is increased thirty fold (1-5X2o) when it acts at the base of the stapes. Experiments on the human ear have shown that the movement of gieatest amplitude was at the tip of the handle of the malleus, o-76 mm., the movement of the tip of the long arm process of the incus was o-21 mm.; while the greatest amplitude at the base of the stapes was only o7x4 mm 0ther observations have shown the movements at the stapes to have a still smaller amplitude, varying from o-oox to o-032 mm. With tones of feeble intensity the movements must be almost infinitesimal. There may also be very minute transverse movements at the base of the stapes. 3. Transmission in the Internal Ear.-The internal ear is composed of the labyrinth, formed of the vestibule or central part, the semicircular canals, and the cochlea, each of which consists of an osseous and a membranous portion The osseous labyrinth may be regarded as an osseous mould in the petrous portion of the temporal bone, lined by tessellated endothelium, and containing a small quantity of fluid called the perzlymph. In this mould, partially surrounded by, and to some extent floating in, this fluid, there is the membranous labyrinth, in certain parts of which we find the terminal apparatus in connexion with the auditory nerve, immersed in another fluid called the endolymph. The membranous labyrinth consists of a vestibular portion formed by two small sac-like dilatation's, called the saccule and the utricle, the latter of which communicates with the semicircular canals by five openings. Each canal consists of a tube, bulging out at each extremity so as to form the so-called ampulla, in which, on a projecting ridge, called the Crista aeustzca, there are cells bearing long auditory hairs, which are the peripheral end-organs of the vestibular branches of the auditory nerve. The cochlear division of the membranous labyrinth consists of the ductus coc/zlearis, a tube of triangular form fitting in between the two cavities in the cochlea, called the scala vesiibuli, because it commences in the vestibule, and the scala tympani, because it ends in the tympanum, at the round window. These two scalae communicate at the apex of the cochlea. The roof of the ductus cochlear is is formed by a thin membrane called the membrane of Reissner, while its floor consists of the basilar membrane, on which we find the remarkable organ of C orti, which constitutes the terminal organ of the cochlear division of the auditory nerve. It is sufficient to state here that this organ consists essentially of an arrangement of epithelial cells bearing hairs which are in communication with the terminal filaments of this portion of the auditory nerve, and that groups of these hairs pass through holes in a closely investing membrane, membrana reticularis, which may act as a damping apparatus, so as quickly to stop their movements. The ductus cochlear is and the two scalae are filled with fluid. Sonorous vibrations may reach the fluid in the labyrinth by three different ways-(1) by the osseous walls of the labyrinth, (2) by the air in the tympanum and the round window, and (3) by the base of the stapes inserted into the oval window.

When the head is plunged into water, or brought into direct contact with any vibrating body, vibrations must be transmitted directly. Vibrations of the air in the mouth and in the nasal passages are also communicated directly to the walls of the cranium, and thus pass to the labyrinth. In like manner, we may experience auditive sensations, such as blowing, rubbing and hissing sounds, due to muscular contraction or to the passage of blood in vessels close to the auditory organ. It is doubtful whether any vibrations are communicated to the fluid in the labyrinth by the round window. Vibrations which cause hearing are communicated by the chain of bones. When the base of the stirrup is pushed into the oval window, the pressure in the labyrinth increases, and, as the only mobile part of the wall of the labyrinth is the membrane covering the round window, this membrane is forced outwards; when the base of the stirrup moves outwards a reverse action takes place. Thus the fluid of the labyrinth receives a series of pulses isochronous with the movements of the base of the stirrup, and these pulses affect the terminal apparatus in connexion with the auditory nerve The sacs of the internal ear, known as the utricle and saccule, receive the impulses of the base of the stapes. They are organs connected with the perception of sounds as sounds, without reference to pitch or quality. For the analysis of tone a cochlea is necessary. Even in mammals all the parts of the ear may be destroyed or affected by disease, except these sacs, without causing complete deafness.

It has been suggested by Lee (Amer. Jour. of Physiol. vol. i. No. 1, p. 128) that in fishes the sac has nothing to do with hearing, but serves for the perception of movements, such as those of rotation and translation through space, movements much coarser than those that form the physical basis of sound. He considers, also, that as fishes, with few exceptions, are dumb, they are also deaf. In the fish there are peculiar organs along the lateral line which are known to be connected with the perception of movements of the body as a whole, and Beard (Zool. Anz. Leipzig, 1884, Bd. vii. S. 140) has attenipted to trace a phylogenetic connexion between the sacs of the internal ear and the organs in the lateral line. According to this view, when animals became air-breathers, a part of the ear (the papilla acustica basilaris) was gradually evolved for the perception of delicate vibrations of sound. (See EQIHLIBRIUM.)

It is by means of the cochlea that we discriminate pitch, hear beats, and are affected by quality of tone. Since the s1ze of the membranous labyrinth is so small, measuring, in man, not more than é in in length by § in. in diameter at its widest part, and since it is a chamber consisting partly of conduits of very irregular form, it is impossible to state accurately the course of vibrations transmitted to it by impulses communicated from the base of the stirrup. In the cochlea vibrations must pass from the saccule along the scala vestibule to the apex, thus affecting the membrane of Reissner, which forms its roof; then, passing through the opening at the apex (the helicotrema), they must descend by the scala tympani to the round window, and affect in their passage the membrana basilaris, on which the organ of Corti is situated. From the round window impulses must be reflected backwards, but how they affect the advancing impulses is not known. But the problem is even more complex when we take into account the fact that impulses are transmitted simultaneously to the utricle and to the semicircular canals communicating with it by five openings. The mode of action of these vibrations or impulses upon the nervous terminations is still unknown; but to appreciate critically the hypothesis which has been advanced to explain it, it is necessary, in the first place, to refer to some of the general characters of auditory sensation.

4. General Characters of Auditory Sensations.-Certain conditions are necessary for excitation of the auditory nerve sufficient to produce a sensation. In the first place, the vibrations must have a certain amplitude and energy, if too feeble, no impression will be produced.

Various physicists have attempted to measure the sensitiveness of the ear by estimating the amplitude of the molecular movements necessary to call forth the feeblest audible sound. Thus A. Topler and L. Boltzmann, on data founded on experiments with organ pipes, state that the ear is affected by vibrations of molecules of the air not more in amplitude than -ooo4 mm. at the ear, or o-1 of the Wave-length of green light, and that the energy of such a vibration on the drum-head is not more than gh; billionth kilog., or ~I%=th of that produced upon an equal surface of the retina by a single candle at the same distance (Ann. d. Phys. u. Chem., Leipzig. 1870, Bd. cxli. S. 321). Lord Rayleigh, by two other methods, arrived at the conclusion “ that the streams of energy required to influence the eye and ear are of the same order of magnitude.” He estimated the amplitude of the movement of the aerial particles, with a sound just audible, as less than the ten-millionth of a centimetre, and the energy emitted when the sound was first becoming audible, at 42-1 ergs per second. He also states that in considering the amplitude or condensation in progressive aerial waves, at a distance of 27-4 metres from a tuning-fork, the maximum condensation was -=6-o><Io'9 cm., a result showing “that the ear is able to recognize the addition or subtraction of densities far less than those to be found in our highest vacua ” (Proc. Roy. Soc., 1877, vol. xxvi. p. 248; Land. Edin. and Dub. Phil. Mag., 1894, vol. xxxviii. p. 366).

In the next place, vibrations must have a certain duration to be perceived; and lastly, to excite a sensation of a continuous musical sound, acertain number of impulses must occur in agiven interval of time. The lower limit is about 3o, and the upper about 30,000 vibrations per second. Below 3o, the individual impulses may be observed, and above 30,000 few ears can detect any sound at all. The extreme upper limit is not more than 3 5,000 vibrations per second. Auditory sensations are of two kinds-noises and musical sounds. Noises are caused by impulses which are not regular in intensity or duration, or are not periodic, or they may be caused by a series of musical sounds occurring instantaneously so as to produce discords, as when we place our hand at random on the key-board of a piano. Musical tones are produced by periodic and regular vibrations. In musical sounds three characters are prominent—intensity, pitch and quality. Intensity depends on the amplitude of the vibration, and a greater or lesser amplitude of the vibration will cause a corresponding movement of the transmitting apparatus, and a corresponding intensity of excitation of the terminal apparatus. Pitch, as a sensation, depends on the length of time in which a single vibration is executed, or, in other words, the number of vibrations in a given interval of time. The ear is capable of appreciating the relative pitch or height of a sound as compared with another, although it may not ascertain precisely the absolute pitch of a sound. What we call an acute or high tone is produced by a large number of vibrations, while a grave or low tone is caused by few. The musical tones which can be used with advantage range between 40 and 4000 vibrations per second, extending thus from 6 to 7 octaves. According to E. H. Weber, practised musicians can perceive a difference of pitch amounting to only the -614-th of a semitone, but this is far beyond average attainment. In a few individuals, and especially in early life, there may be an appreciation of absolute pitch. Quality or timbre (or Klang) is that peculiar characteristic of a musical sound by which we may identify it as proceeding from a particular instrument or from a particular human voice. It depends on the fact that many waves of sound that reach the ear are compound wave systems, built up of constituent waves, each of which is capable of exciting a sensation of a simple tone if it be singled out and reinforced by a resonator (see SOUND), and which may sometimes be heard without a resonator, after special practice and tuition. Thus it appears that the ear must have some arrangement by which it resolves every wave system, however complex, into simple pendular vibrations When we listen to a sound of any quality we recognize that it is of a certain pitch. This depends on the number of vibrations of one tone, predominant in intensity over the others, called the fundamental or ground tone, or first partial tone. The quality, or timbre, depends on the number and intensity of other tones added to it. These are termed harmonic or partial tones, and they are related to the first partial or fundamental tone in a very simple manner, being multiples of the fundamental tone: thus-Funda-

Upper Partials or Harmonics.

mental Tone.

Notes do* do? sol? dos ml” sol* s1l>“ do* re* mi* Partial tones 1 2 3 4 5 6 7 8 9 10

Number of Q

V1b1'at10n5 l 33 66 99 132 165 198 231 264 297 330 When a simple tone, or one free from partials, is heard, it gives rise to a simple, soft, somewhat insipid sensation, as may be obtained by blowing across the mouth of an open bottle or by a tuning-fork. The lower partials added to the fundamental tone give softness combined with richness, while the higher, especially if they be very high, produce a brilliant and thr1ll1ng effect, as is caused by the brass instruments of an orchestra Such being the facts, how may they be explained physiologically P Little is yet known regarding the mode of action of the vibrations of the fluid in the labyrinth upon the terminal apparatus connected with the auditory nerve. There can be no doubt that it is a mechanical action, a communication of impulses to delicate hair-like processes, by the movements of which the nervous filaments are irritated. In the human ear it has been estimated that there are about gooo small arches formed by the rods of Corti. Each arch rests on the basilar membrane, and supports rows of cells having minute hair-like processes. It would appear also that the filaments of the auditory nerve terminate in the basilar membrane, and possibly they may be connected with the hair-cells. At one time it was supposed by Helmholtz that these fibres of Corti were elastic and that they were tuned for particular sounds, so as to form a regular series corresponding to all the tones audible to the human ear. Thus 2800 fibres distributed over the tones of seven octaves would give 400 fibres for each octave, or nearly 33 for a semitone. Helmholtz put forward the hypothesis that, when a pendular vibration reaches the ear, it excites by sympathetic vibration the fibre of Corti which is tuned for its proper number of vibrations. If, then, different fibres are tuned to tones of different pitch, it is evident that we have here a mechanism which, by exciting different nerve fibres, will give rise to sensations of pitch. When the vibration is not simple but compound, in consequence of the blending of vibrations corresponding to various harmonics or partial tones, the ear has the power of resolving this compound vibration into its elements. It can only do so by different fibres responding to the constituent vibrations of the sound-one for the fundamental tone being stro11ger, and giving the sensation of a particular pitch to the sound, and the others, corresponding to the upper partial tones, being weaker, and causing undefined sensations, which are so blended together in consciousness as to terminate in a complex sensation of a tone of a certain quality or timbre. It would appear at first sight that 33 Hbres of Corti for a semitone are not sufficient to enable us to detect all the gradations of pitch in that interval, since, as has been stated above, trained musicians may distinguish a difference of 311th of a semitone. To meet this difficulty, Helmholtz stated that if a sound is produced, the pitch of which may be supposed to come between two adjacent fibres of Corti, both of these will be set into sympathetic vibration, but the one which comes nearest to the pitch ot the sound will vibrate with greater intensity than the other, and that consequently the pitch of that sound would be thus appreciated. These theoretical views of Helmholtz have derived much support from experiments of V. Hensen, who observed that certain hairs on the antennae of M ysis, a Crustacean, when seen with a low microscopic power, vibrated with certain tones produced by a keyed horn. It was seen that certain tones of the horn set some hairs into strong vibration, and other tones other hairs. Each hair responded also to several tones of the horn Thus one hair responded strongly to rl# and d'#, more weakly to g, and very weakly to G. It was probably tuned to some pitch between d” and d”# (Sludieu uber das Gehororgan der Decapoden, Leipzig, 1863)

Histological researches have led to a modification of this hypothesis. It has been found that the rods or arches of Corti are stiff structures, not adapted for vibrating, but apparently constituting a support for the hair-cells. It is also known that there are no rods of Corti in the cochlea of birds, which are capable nevertheless of appreciating pitch. Hensen and Helmholtz suggested the view that not only may the segments of the membrana basilaris be stretched more in the radial than in the longitudinal direction, but different segments may be stretched radially with different degrees of tension so as to resemble a series of tense strings of gradually increasing length. Each string would then respo11d to a vibration of a particular pitch communicated to it by the hair-cells. The exact mechanism of the hair-cells and of the membrana reticularis, which looks like a damping apparatus, is unknown.

5 Physiological Characlers of Audilory Sensation.-Under ordinary circumstances auditory sensations are referred to the outer world. When we hear a sound, we associate it with some external cause, and it appears to originate in a particular place or to come in a particular direction This feeling of exleriorily of sound seems to require transmission through the membrana tymparii. Sounds which are sent fnrough the walls of the craniuni, as when the head is immersed in, and the external auditory canals are filled with, water, appear to originate in the body itself.

An auditory sensation lasts a short time after the cessation of the exciting cause, so that a number of separate vibrations, each capable of exciting a distinct sensation if heard alone, may succeed each other so rapidly that they are fused into a single sensation. If we listen to the puffs of a syren, or to vibrating tongues of low pitch, the single sensation is usually produced by about go or 35 vibrations per second; but when we listen to beats of considerable i11tensity, produced by two adjacent tones of sufficiently high pitch, the ear may follow as many as 132 intermissions per second.

The sensibility of the ear for sounds of different pitch is not the same. It is more sensitive for acute than for grave sounds, and it is probable that the maximum degree of acuteness is for sounds produced by about gooo vibrations per second, that is near fa% Sensibility as to pitch varies much with the individual. Thus some musicians may detect a difference of folmyth of the total number of vibrations, while other persons may have difiieulty in appreciating a semitone. 6. Analyllcal Power of lhe Ear -When we listen to a compound tone, we have the power of picking out these partials from the general mass of sound It ls known that the frequencies of the partials as compared with that of the fundamental tone are simple multiples of the frequency of the fundamental, and also that physically the waves of the partials so blend with each other as to produce waves of very complicated forms. Yet the ear, or the ear aniiqghe brain together, can resolve this complicated wave-form into its constituents, and this is done more easily lf we listen to the sound with resonators, the pitch of which corresponds, or nearly corresponds, to the frequencies of the artials. Much discussion has taken place as to how the ear accomplishes this analysis. All are agreed that there is a complicated apparatus in the cochlea which may serve this purpose; but while some are of opinion that this structure is sufficient, others hold that the analysis takes place in the brain. When a complicated wave falls on the drum-head, it must move out and in in a wa corresponding to the variations of pressure, and these variations willi in a single vibration, depend on the greater or less degree of complexity of the wave Thus a single tone will cause a movement like that of a pendulum, a simple pendular vibration, while a complex tone, although occurring in the same duration of time, will cause the drum-head to move out and in rn a much more complicated manner. The complex movement will be conveyed to the base of the stapes, thence to the vestibule, and thence to the cochlea, in which we find the ductus cochlear is containing the organ of Corti. It is to be noted also that the arts in the cochlea are so small as to constitute only a fraction ofp the wave-length of most tones audible to the human ear. Now it is evident that the cochlea must act either as a whole, all the nerve fibres being affected by any variations of pressure, or the nerve fibres may have a selective action, each fibre being excited by a wave of a definite period, or there may exist small vibratile bodies between the nerve filaments and the pressures sent into the organ. The last hypothesis gives the most rational explanation of the phenomena, and on it is founded a theory generally accepted and associated with the names of Thomas ?(9lung and Hermann Helmholtz. It may be shortly stated as o ows.»-

“ (1) In the cochlea there are vibrators, tuned to frequencies within the limits of hearing, say from 30 to 40,000 or 50,000 vibs. per second. (2) Each vibrator is capab e of exciting its appropriate nerve filament or filaments, so that a nervous impulse, corresponding to the frequency of the vibrator, is transmitted to the brainnot corresponding necessarily, as regards the number of nervous impulses, but in such a way that when the impulses along a particular nerve filament reach the brain, a state of consciousness is aroused which does correspond with the number of the physical stimuli and with the period of the auditory vibrator. (3) The mass of each vibrator is such that it will be easily set in motion, and after the stimulus has ceased it will readrly come to rest (4) Damping arrangements exist in the ear, so as quickly to extinguish movements of the vibrators. (5) If a simple tone falls on the ear, there is a pendular movement of the base of the stapes, which will affect all the parts, causing them to move; but ancy part whose natural period is nearly the same as that of the soun will respond on the principle of sympathetic resonance, a particular nerve filament or nerve filaments will be affected, and a sensation of a tone of definite pitch will be experienced, thus accounting for discrimination in pitch. (6) Intensity or loudness will depend on the amplitude of movement of the vibrating body, and consequently on the intensity of nerve stimulation. (7) If a compound wave of pressure be communicated by the base of the stapes, it will be resolved into its constituents by the vibrators corresponding to tones existing in it, each picking out its appropriate portion of the wave, and thus irritating corresponding nerve filaments, so that nervous impulses are transmitted to the brain, where they are fused in such a way as to give rise to a sensation of a particular quality or character, but still so imperfectly fused that each constituent, by a strong effort of attention, may be specially recognized " (article “ Ear, ” by M'Kendrick, Schafer's T ext-Book, loc crt).

The structure of the ductus cochlear is meets the demands of this theory, it is highly differentiated, and it can be shown that in it there are a sufficient number of elements to account for the delicate appreciation of pitch possessed by the human ear, and on the basis that the highly trained ear of a violinist can detect a difference of ggth of a semitone (M'Kendrick, Trans. Roy. Soc. Ed, 1896, vol. xxxviu. p. 780; also Schafer's T ext-Book, loc. crt.). Measurements of the cochlea have also shown such differentiation as to make it difficult to imagine that it can act as a whole. A much less com lex or an might have served this purpose (M'Kendrick, op on). II'he fohowing table, given by Retzius (Das Gehororgan der Wrrbelthfiere, Bd u S. 356), shows differentiations in the cochlea of man, the cat and the rabbit, all of wh1ch no doubt hear tones, although in all probability they have very different powers of discrimination.-Man. Cat. Rabbit.

Ear-teetli . . 2,490 2,430 1,5 50

Holes in habenula for nerves . 3,985 2,780 1,650 lnner rods of Cort1's organ 5,390 4,700 2,800

Outer rods of Corti's organ '3, 48 3,300 1,900

Inner hair-cells one row) 3,487 2,600 I,6O0

Outer hair-cells several rovl s) 1 1,750 9,900 6,100 Fibres in basilar membrane 23,750 15,700 10,500

7. Dzssonance -The theory can also be used to explain dissonance When two tones sufficiently near in pitch are simultaneously sounded, beats are produced If the beats are few in number they can be counted, because they give rise to separate and distinct sensations; but if they are numerous they blend so as to give roughness or dissonance to the interval. The roughness or dissonance is most disagreeable with about 33 beats falling on the ear per second. When two compound tones are sounded, say a minor third on a harmonium in the lower part of the keyboard, then we have beats not only between the primaries, but also between the upper partials of each of the primaries. The beating distance may, for tones of medium pitch, be fixed at about a mfnor third, but this interval will expand or intervals on low tones and contract for intervals on high ones This explains why the same interval in the lower part of the scale may give slow beats that are not disagreeable, while in the higher part it may cause harsh and un leasant dissonance. Th p e paitia s

up to the seventh are beyond beating distance, but above this they come close together. Consequently instruments (such as tongues, or reeds) that abound in upper partials cause an intolerable dissonance if one of the primaries is slightly out of tune. Some intervals are pleasant and satisfying when produced on instruments having few partials in their tones. These are concords. Others are less so, and they may give rise to an uncomfortable sensation. These are discords. In t is way unison, {, minor third g, major third 5, fourth '§ , fifth 3, minor sixth é, major sixth if and octave in are all eoncords; while a second 3, minor seventh 19° and major seventh 135, are discords. Helmholtz compares the sensation of dissonance to that of a flickering light on the eye. “Something similar I have found to be produced by simultaneously stimulating the skin, or margin of the lips, by bristles attached to tuning-forks giving forth beats If the frequency of the forks is great, the sensation is that of a most disagreeable tickling. It may be that the instinctive effort at analysis of tones close in pitch causes the disagreeable sensation ” (Schafer's Text-Book, op. crt p. 1187).

8. Other T heorres.-In 1865 Rennie objected to the analysis theory, and urged that the cochlea acted as a whole (Ztschr. f. rat. Med, Dritte Reihe, Bd. xxiv. Heft 1, S 12-64). This view was revived by Voltolini (Virchow's Archw, Bd c. S. 27) some years later, and in 1886 it was urged by E. Rutherford (Rep. Brrt. Assoc. Ad. Sc, 1886), who compared the action of the cochlea to that of a telephone plate. According to this theory, all the hairs of the auditory cells vibrate to every note, and the hair-cells transform sound vibrations into nerve vibrations or impulses, similar in frequency, amplitude and character to the sound vibrations. There is no analysis in the peripheral organ. A D. Waller, in 1891 (Proc. Physiol. Soc., jan. 20, 1891) suggested that the basilar membrane as a whole vibrates to every note, thus repeating the vibrations of the membrana tympani; and since the hair-cells move with the basilar membrane, they produce what may be called pressure patterns against the tectorial membranes, and filaments of the auditory nerve are stimulated by these pressures. Waller admits a certain degree of peripheral analysis, but he relegates ultimate analysis to the brain. These theories, dispensing with peripheral analysis, leave out of account the highly complex structure of the cochlea, or, in other words, they assign to that structure a comparatively simple function which could be Eerformed by a simple membrane capable of vibrating. We find that the cochlea becomes more elaborate as we ascend the scale of animals, until in man, who possesses greater powers of analysis than any other being, the num er of hair-cells, f1bres of the basilar membrane and arches of Corti are all much increased in number (see Retzius's table, supra). The principle of sympathetic resonance appears, therefore, to offer the most likely solution of the problem Hurst's view is that with each movement of the stapes a wave is generated which travels up the scala vestibule, througlh the helicotrema into the scala tympani and down the latter to t e fenestra rotunda. The wave, however, is not merely a movement of the basilar membrane, but an actual movement of fluid or a transmission of pressure. As the one wave ascends while the other descends, a pressure of the basilar membrane occurs at the point where they meet; this causes the basilar membrane to move towards the tectorial membrane, forcing this membrane suddenly against the apices of the hair-cells, thus irritating the nerves. The oint at which the waves meet will depend on the time interval between the waves (Hurst, “A New Theory of Hearing, ” Trans. Biol. Soc. Lwerpool, 1895, vol. ix. p. 321). More recently Max Mayer has advanced a theory somewhat similar. He supposes that with each movement of the stapes corresponding to a vibration, a wave travels up the scala vestibule, pressing the basilar membrane downwards As it meets with resistance in passing upwards, its amplitude therefore diminishes, and in this way the distance up the scala through which the wave progresses will be determined by its amplitude. The wave in its progress irritates a certain number of nerve terminations, consequently feeble tones will irritate only those nerve fibres that are near the fenestra ovalis, while stronger tones will pass farther up and irritate a larger number of nerve fibres the same number of times per unit of time. Pitch, according to this view, depends on the number of stimuli per second, while loudness depends on the number of nerve fibres irritated. Mayer also applies the theory to the explanation of the powers of the cochlea as an analyser, by supposing that with a compound tone these are at maxima and minima of stimulation. As the compound wave travels up the scala, portions of the wave corresponding to maxima and minima die away in consecutive series, until only a maximum and minimum are left; and, finally, as the wave travels farther, these also disappear. With each maximum and minimum different parts of the basilar membrane are affected, and affected a different number of times per second, according to the frequencies of the partials existing in the compound tone. Thus with a fifth, 2: 3, there are three maxima and three minima; but the compound tone is resolved into three tones having vibration frequencies in the ratio of 3 2 1. According to Mayer, we actually hear when a fifth is sounded tones of the relationship of 3: 2 ~ 1, the last (1) being the differential tone He holds, also, that combinational tones are entirely subjective (Max Mayer, Ztschr. f. Psych. und Phys. d. Srnnesorgane, Leipzig, Bd xvi. and xvii.; also Verhandl. d. physrolog. Gesellsch zu Berlrn, Feb. 18, 1898, S. 49) Two fatal objections can be urged to these theories, namely, first, it is impossible to conceive of minute waves following each other in rap1d succession in the minute tubes formin the scalae-fthe length of the scala being only a very small part ofg the wave-length of the sound, and, secondly, neither theory takes into account the differentiation of structure found 1n the epithelium of the organ of Corti Each push in and out of the base of the stapes must cause a movement of the fluid, or a pressure, 1n the scalae as a whole. There are difficulties 1n the way of applying the resonance theory to the perception of noises. No1ses have p1tch, and also each noise has a special character, if so, 1f the no1se is analysed 1nto its constituents, why IS it that it seems impossible to analyse a noise, or to perceive any musical element 1n it P Helmholtz assumed that a sound is no1s when the wave IS irregular 1n rhythm, and he suggested that the cr1sta and macula acust1ca, structures that exlst not in the cochlea but IH the vestibule, have to do with the perception of noise. These structures, however, are concerned rather in the sense of the perception of equilibrium than of sound (see EQUILIBRIUM).

9. Hitherto we have considered only the audition of a single sound, but It is possible also to have simultaneous aud1t1ve sensations, as in musical harmony It ls difficult to ascertain what IS the limit beyond which distinct auditory sensations may be perceived. We have in l1sten1ng to an orchestra a multiplicity of sensations which produces a total effect, while, at the same time, we can with ease single out and notice attentively the tones of one or two special instruments Thus the pleasure of music may arise partly from listening to simultaneous, and partly from the effect of contrast or suggestion 1n passing through successive, auditory sensations.

The principles of harmony belong to the subject of music (see HARMONY), but it is necessary here briefiy to refer to these from the physiological point of view. If two musical sounds reach the ear at the same moment, an agreeable or disagreeable sensation IS experienced, which may be termed a concord or a discord, and it can be shown by experiment with the syren that this depends upon the vibrational numbers of the two tones. The octave (1 . 2), the twelfth (1:3) and double octave (I 4) are absolutely consonant sounds, the fitth (2 3) is said to be perfectly consonant; then follow, 111 the direction of d1ssona11ce, the fourth (3 . 4), major sixth (3 .5), major third (4 5), minor S1Xtl1 (5 8) and the minor tl11rd (5 6) Helmholtz has attempted to account for this by the application of his theory of beats.

Beats are observed when two sounds of ncarly the same pitcl1 are produced together, and the number of beats er second IS equal to the difference of the number of vibrations of tife two sounds Beats giye rise to a peculiarly disagreeable intermittent sensation. The maximum rougffness of beats IS attained by 33 per second, beyond 132 per second, the 1nd1v1dual impulses are blended 1nto one uniform auditory sensation. When two notes are sounded, say on a piano, not only may the first, fundamental or prune tones beat, but partial tones of each of the primaries ma beat also, and as the difference of pltch of two simultaneous sounds augments, the number of beats, both of prime tones and of harmonics, augnients also The physiological effect of beats, though these n1ay not be individually distinguishable, IS to give roughness to the ear If harmonics or partial tones of prime tones coincide, there are no beats; if they do not colncide, the beats produced Wlll give a character of roughness to the interval Thus 1n the octave and twelfth, all the partial tones of the acute sound coincide with the partial tones of the grave sound, in the fourth, major sixth and major th1rd, only two pairs of the partial tones co1nc1de, wh1le in the minor sixth, minor th1rd and nunor seventh only one (pair of the harmonics coincide It IS possible by means o beats to measure the sensitiveness of the ear by determining the smallest difference in pitch that may glve rise to a beat. In no part of the scale can a difference smaller than 0 2 vibration er second be distinguished The sens1t1veness varies with pitch. Thus at 120 vibs per second 0-4 v1b per second, at 500 about 0-3 Vlb per second, and at 1000, 0~5 v1b per second can be distinguished This 1s a remarkable illustration of the sensitiveness of the ear. When tones of low pitch are produced that do not rapidly die aw'ay, as bv sounding heavy tuning-forks, not onlv may the beats be perceived eoiresponding to the difference beteeu the frequencies of the forks, but also other sets of beats. fhus, if the two tones have frequencies of 40 and 74, a two-order beat may be heard, one hang a frequenu of '54 and the other of 6, is 74 -4()=I+e1 posune remainder of 341 Zlutl 74-4O=2 0, or 80-74, <1 neg mu remainder of fu lhe low er beat ls heard most dlstiuctlv when the number is lem than half the frequency of the lower pr1n1ar, and the upper w hen the number IS greater. The beats we ha e been considering are produced when two notes are sounded slightly differing IH frequent or at all events their frequencies are not so great as those of two notcs separated bv a rnusit al interval, such as an octaye or a fnfth. But Lord Kelvin has shown that beats may also be produced on sl1ghtl inharmonious musical intervals (Proc Roy Soo. Ed 1878, vol IX p 602) 'lhus, take two tuning forks, z¢t~=256 and ut3=512; slightlv fiatten 14/iq so as to make its frequency 510, and we hear, not a roughness corresponding to 254 beats, but a slow beat of 2 per second. The sensation also passes through a cy cle, the beats now sounding loudly and fading away in intensity, again sounding loudly, ind so on One might suppose that the beat occurred between 510 (the frequeucv of ut; flattened) and 512, the first partial of uk, namely uts, but this is not so, as the beat is most audible when ut; IS sounded feebly. In a similar way, beats may be produced on the approximate harmonies 2 3, 3 4, 4: 5, 5: 6, 6 7, 7 . 8, I: 3, : 5, and beats may even be produced on the major chord 4 5:6by sounding utg, mn, soZ3, with .9013 or rms sllghtly flattened, “ when a peculiar beat will be heard as 1f a wheel were being' turned against a surface, one small part of which was rougher t an the rest.” These beats on imperfect harmonies appear to indicate that the ear does distinguish between an increase of pressure on the drum-head and a d1minut1on, or between a push and a pull, or, 1n other words, that It IS affected by phase. This was denied by Helmholtz.

I0 Beat T0nes.—Considerable difference of opinion exists as to whether beats can blend so as to give a sensation of tone, but R. Konig, by using pure tones of high p1tch, has settled the question. These tones were Tproduced by large tuning-forks. Thus 'I»¢lg=2048 and re@=2304. hen the beat tone is ut3=256 (2304-2048). If we strike the two forks, utg sounds as a grave or lower beat tone. Again, ut0=2048 and sz6=3840. Then (2048)2-3840=256, a negative remainder, M3, as before, and when both forks are sounded ut, will be heard. Again, ut, =2048 and sal, = 3072, and 3072-2048 = 1024, or uts, which will be distinctly heard when uts and sol, are sotgnded (Konig, Quelgues expénences d'ac0ustzgue, Paris, 1882, P- 7 - .

1 1. Combmatwn Tones.-Frequently, when two tones are sounded, not only do we hear the compound sound, from which we can pick out the constituent tones, but we may hear other tones, one of which is lower in pitch than the lowest primary, and the other IS higher in pitch than the hi her primary. These, known as combination tones, are of two cifasses. dzjerentwl tones, 1n which the frequency IS the difference of the frequencies of the generating tones, and summatwnal tones, having a frequency which IS the sum of the frequencies of the tones producing them. Differential tones, first noticed by Sorge about 1740, are easily heard. Thus an interval of a fifth, 2: 3, gives a differential tone I, that 1s, an octave below 2; a fourth, 3 4, gives I, a twelfth below 3; a major th1rd, 4 . 5, gives 1, two octaves below 4; a minor third, 516, gives 1, two octaves and a niajor third below 5; a major sixth, 3.5, gives 2, that is, a fifth below 3; and a minor sixth, 5: 8, gives 3, that is, a major sixth below 5. Summational tones, first noticed by Helmholtz, are so difficult to hear that much controversy has taken place as to their very existence. Some have contended that they are produced by beats. It appears to be proved physically that they may exist in the air outside of the ear. Further differential tones may be generated in the middle ear. Helmholtz also demonstrated their independent existence, and he states that “ whenever the vibrations of the a1r or of other elastic bod1es, which a1e set IH motion at the same time by two generating simple tones, are so powerful that they can no longer be considered infinitely small, mathematical theory shows that vibrations of the air must arise which have the same vibrational numbers as the combination tones ” (Helmholtz, Sensations 0 Tone, p. 235). The importance of these combinational tones IH the theory of hearing is obvious. If the ear can only analyse compound waves 1nto simple pendular vibrations of a certain order (simple multiples of the prime tone), how can it detect combinational tones, which do not belong to that order P Again, if such tones are purely subjective and only exist in the n11nd of the listener, the fact would be fatal to the resonance theory. There can be no doubt, however, that the ear, in dealing with them, vibrates in some part of its mechanism with each generator, Whllé it also IS affected by the combinational tone 1tself, according to its frequen< y.

I2 Hearing with two cars does not appear niaterially to influence auditive sensation, but probably the two organs are enabled, not only to correct each other's errors, but also to aid us in determining the locallty in which a sound originates. It IS asserted by G T. Fechner that one ear may perceive the same tone at a slightly higher pitch than the other, but this may probably be due to some slight pathological condition in one ear If two tones, produced by two tuning-forks, of equal pitch, are produced one near each ear, there is a uniform single sensation, if one of the tunlng-forks be made to rey olve round its axis in such a way that its tone increases and diminishes IH intensity, neither foik IS heard continuously, but both sound alternately, the fixed one l)6ll"lg only audible when the ievolvlng one is not It is difficult to decide whether excitations of corresponding elemf nts in the two ears can be distinguished from each other. It IS piobablc that the resulting sensatlons may bc distinguished, proyided one of the generating tones differs from the other in intensity or qualitv, although it may be the same in pitch Our judgment as to the directlon of sounds IS formed mainly from the different degrees of mtensltv with wh1<l1 they are heard by two ears Lord Rayleigh states that diffraction of the sound-waves will occur as they pass round the head to the ear farthest from the source of sound; thus partial tones will reach the two ears with different xntensitles, and thus quality of tone may be affected (Tmus Mzlszc. Sac, London, 1876) Silvanus P. Thompson advo-Cates a similar view, and he shows that the direction of a complex tone <an be more accurately determined than the dire<t1on of a simple tone, esptually if it be of low pitch (Phu. Wfag, 1882)  (J. G. M.)