Chapter I: Part 1

Transcriber's notes:

(1) Numbers following letters (without space) like C2 were originally
printed in subscript. Letter subscripts are preceded by an
underscore, like C_n.

(2) Characters following a carat (^) were printed in superscript.

(3) Side-notes were relocated to function as titles of their respective
paragraphs.

(4) Macrons and breves above letters and dots below letters were not
inserted.

(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek
letters.

(6) The following typographical errors have been corrected:

ARTICLE HEAT: "This line of reasoning does not appear quite
satisfactory, because it is tacitly assumed, in the reasoning by
which Carnot's principle was established, ..." 'tacitly' amended
from 'tactitly'.

ARTICLE HEBREWS, EPISTLE TO THE: "Clement himself, taking it for
granted that an epistle to Hebrews must have been written in
Hebrew, supposes that Luke translated it for the Greeks." 'been'
amended from 'beeen'.

ARTICLE HEBRIDES, THE: "The United Free Church has a strong hold on
the people, but in a few of the islands the Roman Catholics have a
great following." 'people' amended feom 'poeple'.

ARTICLE HEBRIDES, THE: "A new system of management and high rents
was imposed, in consequence of which numbers of the tacksmen, or
large tenants, emigrated to North America." 'was' amended from
'were'.

ARTICLE HEBRON: "It is an enclosure measuring 112 ft. east and west
by 198 north and south, surrounded with high rampart walls of
masonry similar in size and dressing to that of the Jerusalem Haram
walls." 'similar' amended from 'similiar'.

ARTICLE HEINE, HEINRICH: "... the beginning of a new era in German
journalism and a healthy revolt against the unwieldy prose of the
Romantic period." 'unwieldy' amended from 'unwieldly'.

ARTICLE HELIOMETER: "The reader is referred to that paper for an
exhaustive history and discussion of the instrument." 'instrument'
amended from 'intrument'.

ARTICLE HELIUM: "M. Travers, G. Senter and A. Jacquerod (Phil.
Trans. A. 1903, 200, p. 105) carefully examined the behaviour of a
constant volume gas thermometer filled with helium." 'behaviour'
amended from 'behavour'.

ARTICLE HELLENISM: "It has even been thought that some developments
of the Egyptian religion are due to Hellenistic influence, ..."
'Egyptian' amended from 'Egyptain'.

ENCYCLOPAEDIA BRITANNICA

A DICTIONARY OF ARTS, SCIENCES, LITERATURE
AND GENERAL INFORMATION

ELEVENTH EDITION

VOLUME XIII, SLICE II

HEARING to HELMOND

ARTICLES IN THIS SLICE:

HEARING HEIDEGGER, JOHANN HEINRICH
HEARN, LAFCADIO HEIDELBERG (town of Germany)
HEARNE, SAMUEL HEIDELBERG (town of Transvaal)
HEARNE, THOMAS HEIDELBERG CATECHISM, THE
HEARSE HEIDELOFF, KARL ALEXANDER VON
HEART HEIDENHEIM
HEART-BURIAL HEIFER
HEARTH HEIGEL, KARL AUGUST VON
HEARTS HEIJERMANS, HERMANN
HEAT HEILBRONN
HEATH, BENJAMIN HEILIGENSTADT
HEATH, NICHOLAS HEILSBERG
HEATH, WILLIAM HEILSBRONN
HEATH HEIM, ALBERT VON ST GALLEN
HEATHCOAT, JOHN HEIM, FRANCOIS JOSEPH
HEATHCOTE, SIR GILBERT HEIMDAL
HEATHEN HEINE, HEINRICH
HEATHFIELD, GEORGE ELIOTT HEINECCIUS, JOHANN GOTTLIEB
HEATING HEINECKEN, CHRISTIAN HEINRICH
HEAVEN HEINICKE, SAMUEL
HEBBEL, CHRISTIAN FRIEDRICH HEINSE, JOHANN JAKOB WILHELM
HEBBURN HEINSIUS, DANIEL
HEBDEN BRIDGE HEINSIUS, NIKOLAES
HEBE HEIR
HEBEL, JOHANN PETER HEIRLOOM
HEBER, REGINALD HEJAZ
HEBER, RICHARD HEJIRA
HEBERDEN, WILLIAM HEL
HEBERT, EDMOND HELDENBUCH, DAS
HEBERT, JACQUES RENE HELDER
HEBREW LANGUAGE HELEN
HEBREW LITERATURE HELENA, ST
HEBREW RELIGION HELENA (Arkansas, U.S.A.)
HEBREWS, EPISTLE TO THE HELENA (Montana, U.S.A.)
HEBRIDES, THE HELENSBURGH
HEBRON HELENUS
HECATAEUS OF ABDERA HELGAUD
HECATAEUS OF MILETUS HELGESEN, POVL
HECATE HELIACAL
HECATOMB HELIAND
HECATO OF RHODES HELICON (mountain range)
HECKER, FRIEDRICH FRANZ KARL HELICON (contrabass tuba)
HECKER, ISAAC THOMAS HELIGOLAND
HECKMONDWIKE HELIOCENTRIC
HECTOR HELIODORUS
HECUBA HELIOGABALUS (ELAGABALUS)
HEDA, WILLEM CLAASZ HELIOGRAPH
HEDDLE, MATTHEW FORSTER HELIOMETER
HEDGEHOG HELIOPOLIS
HEDGES AND FENCES HELIOSTAT
HEDON HELIOTROPE
HEDONISM HELIOZOA
HEEL HELIUM
HEEM, JAN DAVIDSZ VAN HELIX
HEEMSKERK, JOHAN VAN HELL
HEEMSKERK, MARTIN JACOBSZ HELLANICUS
HEER, OSWALD HELLEBORE
HEEREN, ARNOLD HERMANN LUDWIG HELLENISM
HEFELE, KARL JOSEF VON HELLER, STEPHEN
HEGEL, GEORG WILHELM FRIEDRICH HELLESPONT
HEGEMON OF THASOS HELLEVOETSLUIS
HEGEMONY HELLIN
HEGESIAS OF MAGNESIA HELLO, ERNEST
HEGESIPPUS (Athenian orator) HELMERS, JAN FREDERIK
HEGESIPPUS (early Christian writer) HELMERSEN, GREGOR VON
HEGESIPPUS (author of Jewish War) HELMET
HEGIUS [VON HEEK], ALEXANDER HELMHOLTZ, HERMANN LUDWIG VON
HEIBERG, JOHAN LUDVIG HELMOLD (historian)
HEIDE HELMOND (town in Holland)

HEARING (formed from the verb "to hear," O. Eng. _hyran_, _heran_, &c., a common Teutonic verb; cf. Ger. _horen_, Dutch _hooren_, &c.; the O. Teut. form is seen in Goth. _hausjan_; the initial _h_ makes any connexion with "ear," Lat. _audire_, or Gr. [Greek: akouein] 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 meatus_, or canal, at the bottom of which we find the _membrana 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 soft 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. On 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 membrana tympani, the _incus_, or anvil, and the _stapes_, or stirrup, the base of which is attached to a membrane covering 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 arms is as 1.5 : 1; the ratio of the resulting force at the stapes is therefore as 1 : 1.5; while the amplitudes of the movements at the tip of the handle of the malleus and the stapes is as 1.5 : 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 thirtyfold (1.5 X 20) when it acts at the base of the stapes. Experiments on the human ear have shown that the movement of greatest amplitude was at the tip of the handle of the malleus, 0.76 mm.; the movement of the tip of the long arm process of the incus was 0.21 mm.; while the greatest amplitude at the base of the stapes was only .0714 mm. Other observations have shown the movements at the stapes to have a still smaller amplitude, varying from 0.001 to 0.032 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 tesselated endothelium, and containing a small quantity of fluid called the _perilymph_. 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 dilatations, 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 acustica_, 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 cochlearis_, a tube of triangular form fitting in between the two cavities in the cochlea, called the _scala vestibuli_, 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 cochlearis 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 Corti_, 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 cochlearis 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 attempted 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 EQUILIBRIUM.)

It is by means of the cochlea that we discriminate pitch, hear beats, and are affected by quality of tone.

Since the size of the membranous labyrinth is so small, measuring, in man, not more than 1/2 in. in length by 1/8 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 vestibuli 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 .0004 mm. at the ear, or 0.1 of the wave-length of green light, and that the energy of such a vibration on the drum-head is not more than 1/543 billionth kilog., or 1/17th 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 = 6.0 X 10^-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; _Lond. 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, a certain _number_ of impulses must occur in a given interval of time. The lower limit is about 30, and the upper about 30,000 vibrations per second. Below 30, 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 35,000 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 keyboard 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 1/64th 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--

Fundamental Upper Partials or Harmonics.
Tone
Notes do^1 do^2 sol^2 do^3 mi^3 sol^3 si[flat]^3 do^4 re^4 mi^4
Partial tones 1 2 3 4 5 6 7 8 9 10
Number of
vibrations 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 thrilling effect, as is caused by the brass instruments of an orchestra. Such being the facts, how may they be explained physiologically?

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 3000 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 stronger, 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 fibres 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 1/64th 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 of 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 _Mysis_, 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 d[sharp] and d'[sharp], more weakly to g, and very weakly to G. It was probably tuned to some pitch between d" and d"[sharp]. (_Studien 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 respond 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 Characters of Auditory 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 _exteriority_ of sound seems to require transmission through the membrana tympani. Sounds which are sent through the walls of the cranium, 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 30 or 35 vibrations per second; but when we listen to beats of considerable intensity, 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 3000 vibrations per second, that is near fa^5[sharp]. Sensibility as to pitch varies much with the individual. Thus some musicians may detect a difference of 1/1000th of the total number of vibrations, while other persons may have difficulty in appreciating a semitone.

6. _Analytical Power of the Ear._--When we listen to a compound tone,
we have the power of picking out these partials from the general mass
of sound. It is 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 and the brain together, can
resolve this complicated wave-form into its constituents, and this is
done more easily if we listen to the sound with resonators, the pitch
of which corresponds, or nearly corresponds, to the frequencies of the
partials. 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 way corresponding to the
variations of pressure, and these variations will, 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 in 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
cochlearis containing the organ of Corti. It is to be noted also that
the parts in the cochlea are so small as to constitute only a fraction
of 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 Young and Hermann Helmholtz. It may be shortly
stated as follows:--

"(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 capable of exciting its appropriate nerve
filament or filaments, so that a nervous impulse, corresponding to the
frequency of the vibrator, is transmitted to the brain--not
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 readily 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 any part whose natural period is nearly the same as that of
the sound 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 _Text-Book_, _loc. cit._).

The structure of the ductus cochlearis 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
1/64th of a semitone (M'Kendrick, _Trans. Roy. Soc. Ed._, 1896, vol.
xxxviii. p. 780; also Schafer's _Text-Book_, loc. cit.). 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 complex
organ might have served this purpose (M'Kendrick, _op. cit._). The
following table, given by Retzius (_Das Gehororgan der Wirbelthiere_,
Bd. ii. S. 356), shows differentiations in the cochlea of man, the cat
and the rabbit, all of which no doubt hear tones, although in all
probability they have very different powers of discrimination:--

Man. Cat. Rabbit.

Ear-teeth 2,490 2,430 1,550
Holes in habenula for nerves 3,985 2,780 1,650
Inner rods of Corti's organ 5,590 4,700 2,800
Outer rods of Corti's organ 3,848 3,300 1,900
Inner hair-cells (one row) 3,487 2,600 1,600
Outer hair-cells (several rows) 11,750 9,900 6,100
Fibres in basilar membrane 23,750 15,700 10,500

7. _Dissonance._--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 minor third, but this interval will expand for
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 unpleasant dissonance. The partials 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 this way unison, 1/1,
minor third 6/5, major third 5/4, fourth 4/3, fifth 3/2, minor sixth
8/5, major sixth 5/3 and octave 2/1, are all concords; while a second
9/8, minor seventh 16/9 and major seventh 15/8, 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. cit._ p. 1187).

8. _Other Theories._--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 _Archiv_, Bd. c. S. 27) some years later, and in
1886 it was urged by E. Rutherford (_Rep. Brit. 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 performed 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 number of hair-cells, fibres 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 vestibuli, through the helicotrema into the scala tympani and
down the latter to the 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 point at which the
waves meet will depend on the time interval between the waves (Hurst,
"A New Theory of Hearing," _Trans. Biol. Soc. Liverpool_, 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 vestibuli,
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. Sinnesorgane_, Leipzig, Bd. xvi. and xvii.;
also _Verhandl. d. physiolog. Gesellsch. zu Berlin_, 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 rapid succession in the minute tubes forming the scalae--the
length of the scala being only a very small part of the wave-length of
the sound; and, secondly, neither theory takes into account the
differentiation of structure found in 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, in the scalae as a whole.

There are difficulties in the way of applying the resonance theory to
the perception of noises. Noises have pitch, and also each noise has a
special character; if so, if the noise is analysed into its
constituents, why is it that it seems impossible to analyse a noise,
or to perceive any musical element in it? Helmholtz assumed that a
sound is noisy when the wave is irregular in rhythm, and he suggested
that the crista and macula acustica, structures that exist not in the
cochlea but in 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 auditive sensations, as
in musical harmony. It is difficult to ascertain what is the limit
beyond which distinct auditory sensations may be perceived. We have in
listening 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 in
passing through successive, auditory sensations.

The principles of harmony belong to the subject of music (see
HARMONY), but it is necessary here briefly 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 (1 : 4) are absolutely consonant sounds; the
fifth (2 : 3) is said to be perfectly consonant; then follow, in the
direction of dissonance, the fourth (3 : 4), major sixth (3 : 5),
major third (4 : 5), minor sixth (5 : 8) and the minor third (5 : 6).
Helmholtz has attempted to account for this by the application of his
theory of _beats_.

Beats are observed when two sounds of nearly the same pitch are
produced together, and the number of beats per second is equal to the
difference of the number of vibrations of the two sounds. Beats give
rise to a peculiarly disagreeable intermittent sensation. The maximum
roughness of beats is attained by 33 per second; beyond 132 per
second, the individual impulses are blended into one uniform auditory
sensation. When two notes are sounded, say on a piano, not only may
the first, fundamental or prime tones beat, but partial tones of each
of the primaries may beat also, and as the difference of pitch of two
simultaneous sounds augments, the number of beats, both of prime tones
and of harmonics, augments also. The physiological effect of beats,
though these may 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 coincide, the beats
produced will give a character of roughness to the interval. Thus in
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 third, only two pairs of the partial tones
coincide, while in the minor sixth, minor third and minor seventh only
one pair of the harmonics coincide.

It is possible by means of beats to measure the sensitiveness of the
ear by determining the smallest difference in pitch that may give rise
to a beat. In no part of the scale can a difference smaller than 0.2
vibration per second be distinguished. The sensitiveness varies with
pitch. Thus at 120 vibs. per second 0.4 vib. per second, at 500 about
0.3 vib. per second, and at 1000, 0.5 vib. per second can be
distinguished. This is a remarkable illustration of the sensitiveness
of the ear. When tones of low pitch are produced that do not rapidly
die away, as by sounding heavy tuning-forks, not only may the beats be
perceived corresponding to the difference between the frequencies of
the forks, but also other sets of beats. Thus, if the two tones have
frequencies of 40 and 74, a two-order beat may be heard, one having a
frequency of 34 and the other of 6, as 74 / 40 = 1 + a positive
remainder of 34, and 74 / 40 = 2 - 6, or 80 - 74, a negative remainder
of 6. The lower beat is heard most distinctly when the number is less
than half the frequency of the lower primary, and the upper when the
number is greater. The beats we have been considering are produced
when two notes are sounded slightly differing in frequency, or at all
events their frequencies are not so great as those of two notes
separated by a musical interval, such as an octave or a fifth. But
Lord Kelvin has shown that beats may also be produced on slightly
inharmonious musical intervals (_Proc. Roy. Soc. Ed._ 1878, vol. ix.
p. 602). Thus, take two tuning-forks, ut2 = 256 and ut3 = 512;
slightly flatten ut3 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 cycle, the beats now
sounding loudly and fading away in intensity, again sounding loudly,
and so on. One might suppose that the beat occurred between 510 (the
frequency of ut3 flattened) and 512, the first partial of ut2, namely
ut3, but this is not so, as the beat is most audible when ut2 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, 1 : 3,
3 : 5, and beats may even be produced on the major chord 4 : 5 : 6 by
sounding ut3, mi3, sol3, with sol3 or mi3 slightly flattened, "when a
peculiar beat will be heard as if a wheel were being turned against a
surface, one small part of which was rougher than 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
diminution, or between a push and a pull, or, in other words, that it
is affected by phase. This was denied by Helmholtz.

10. _Beat Tones._--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 pitch, has settled the question.
These tones were produced by large tuning-forks. Thus ut6 = 2048 and
re6 = 2304. Then the beat tone is ut3 = 256 (2304-2048). If we strike
the two forks, ut3 sounds as a grave or lower beat tone. Again, ut6 =
2048 and si6 = 3840. Then (2048)2 - 3840 = 256, a negative remainder,
ut3, as before, and when both forks are sounded ut3 will be heard.
Again, ut6 = 2048 and sol6 = 3072, and 3072 - 2048 = 1024, or ut6,
which will be distinctly heard when ut6 and sol6 are sounded (Konig,
_Quelques experiences d'acoustique_, Paris, 1882, p. 87).