HEARING
The ear, like the eye, records amplitude of vibration; loudness. It
also records rapidity of vibration, musical pitch, which corresponds
with colour. But it seems to have a more difficult task than the eye,
since it has to analyse, or at any rate has to transmit information
regarding the form of compound vibrations. The meanings of these
distinctions may be illustrated by reference to a tracing on the
cylinder of a phonograph. A needle attached to the posterior surface of
the thin metal plate against which one speaks scratches the surface of
a rotating cylinder of hardened wax. Examined with a lens, the record
is seen to be an irregularly changing line. The depth of the marks is a
measure of loudness. Their varying number in a given time indicates the
changing pitch of the voice which produced them. Their form is a record
of the quality of its tone. The work of the ear, so far as it consists
in the estimation of the amplitude and rapidity of pulsations of sound,
is easy to describe, but the acoustics of form are complicated.
Light is transmitted as vibrations of æther. They are transverse to
the direction in which the light is travelling. Sound cannot travel
through a vacuum, since it is dependent upon displacements of material
particles. The particles move forwards and backwards in the direction
in which sound is progressing. Sound is a sequence of pulsations,
alternate condensations and rarefactions of the media which conduct
it. Their particles are first pressed together, and then rebound to
positions farther apart. A sequence of to-and-fro movements, each
smoothly continuous throughout the whole duration of a pulsation,
would produce a pure musical tone. Tuning-forks carefully bowed settle
down after a few seconds into unbroken oscillations, which convey to
the air the to-and-fro movements of pure tones. Such tones vary in
nothing but loudness and pitch. If their pulsations are slow, we speak
of the pitch as “low”; if they are rapid, we say that their pitch is
high. But if the sound produced by tuning-forks (and low-toned stopped
organ-pipes) be omitted from the list, no pure tones reach our ears.
The notes of flutes, fiddles, trumpets, pianos, have each a certain
“quality” characteristic of the instrument. Even in a violin the G
string has not the same timbre as the D string. Owing to the elasticity
of the substances which originate and of the substances which
transmit sound, its pulsations are not simple to-and-fro movements,
uninterrupted from beginning to end. Each pulsation is partially
broken at intervals; and the quality of the sound depends upon the
number and relative accentuation of these partial interruptions. Sound
travels through air at the rate of 1,100 feet per second. This figure,
divided by the number of vibrations per second of a tone, gives the
wave-length in air of a tone of that particular pitch. For example, the
middle C has a vibratory rate of 256. Its wave-length is, therefore,
somewhat over 4 feet. The lowest tone of an organ has a wave-length of
37 feet; its highest of 3½ inches. These figures give no information,
however, regarding the movement of the particles which pass on the
sound. When air is transmitting a note—say the middle C—its separate
molecules do not move through a distance of 4 feet. Each molecule
moves but a short distance, varying with the loudness of the tone; but
the “wave” of crowding runs straight forward from the piano-string to
the ear, the molecules at the end of each stage of 4 feet taking on a
backward movement, so that the crowding, so far as the molecules of
that particular section are concerned, returns to its starting-point.
Between the piano-string and the ear there is a crowding and forward
movement at 0, 4, 8, 12 ... feet; a spreading and backward movement at
2, 6, 10, 14 ... feet. Most illustrations which are intended to aid
the mind in forming a definite picture of the transmission of sound
are liable to be misinterpreted, because they translate rectilinear
movements into waves. They represent the movements of the string, and
not the movements of the molecules of air between the string and the
ear; but with the aid of the imagination one may picture the positions
of the particles in this path. The pulse, we will suppose, has just
reached the limit of 12 feet. Half-way from its 8-foot halting place
the molecules are again crowded, although not so densely. One-third of
the distance from the same point there again appears a tendency to
crowd. This latter point marks an interval of one-third of this wave
_plus_ the wave which led up to it. At the end of the ninth foot there
is a crowding, though less marked—this wave _plus_ the two preceding
waves, divided into fourths. Within these intervals are other points
at which the molecules have closed together, the distances from a
nodal point depending upon the number of waves involved, and, speaking
generally, growing less marked as the number increases. Such are the
very complex pulsatile movements which reach the ear.
Every musical sound produced by a piano, a violin, or other instrument,
is compounded of a fundamental or prime tone, and overtones, partial
tones, or harmonics. The following table shows the more important
partial tones which accompany the prime tone when the middle C on a
pianoforte is struck:
Number of Number of
Note. Vibrations. Interval. Ratio. Overtone.
C‴ 2,048 } 7th
} Super-Second 8/7
}
B″♭ 1,792 } 6th
} Sub-minor third 7/6
}
G″ 1,536 } 5th
} Minor third 6/5
}
E″ 1,280 } 4th
} Major third 5/4
}
C″ 1,024 } 3rd
} Fourth 4/3
}
G′ 768 } 2nd
} Fifth 3/2
}
C′ 512 } 1st
} Octave 2/1
C 256 } =Fundamental=
The quality of a musical note depends upon the number and relative
loudness of its overtones. When several notes are sounded
simultaneously, they blend into a chord or harmony, provided the
intervals which separate them are equal to the intervals which separate
the simpler overtones. Each of the notes yields overtones. The tones
blend into a concord. Their partials are in unison. The variations in
air-pressure of the compound tone are strictly periodic. If the ratios
of the frequencies of its constituent notes are simple the product is a
rich, full sound, such as a common chord.
At least one other character of the pulsations of sound must be taken
into consideration if we wish to picture the nature of the force to
which the ear responds. Tones which reach it from several instruments
simultaneously are not necessarily in unison, or even in harmony. The
overtones of a single note sounded on a piano or violin—the statement
does not hold good for bells, nor is it strictly true of flutes or
horns—must necessarily bear a simple proportional relation to their
prime tone. They divide the grand pulsation into fractions “without a
remainder.” But the vibrations of two tuning-forks which are slightly
out of unison interfere one with the other at regular intervals. They
produce “beats.” Everyone is familiar with the curious effect which
is produced upon the eye when one row of railings is seen through
another, or one expanse of wire-netting behind another. Sets of lines
which occupy nearly the same positions in the line of sight combine
to make a large pattern, which overlies the smaller pattern of the
rails or netting. The same thing happens with sounds which coincide at
considerable intervals, although in the case of sounds interference
is as marked as reinforcement. If whilst a tuning-fork yielding 101
vibrations per second is singing another of 100 vibrations is brought
into play, the vibrations of the second fork are superposed on those
of the first. At a certain moment the forward movement of molecules of
air induced by the first fork is reinforced by a forward push from the
second. But half a second after this coincidence of phase an opposite
result is produced—50½ vibrations of No. 1 have passed, but only 50
of No. 2. No. 2 is going backwards (inwards), whilst No. 1 is moving
forwards (outwards). The same molecules are impelled backwards by No.
2 and forwards by No. 1. The result is a pause. The compound sound
produced by the two forks reaches the ear in throbs. If the forks
were vibrating at the rates of 101 and 99, there would be two pauses
and two beats in every second; if at the rate of 202 and 198, four.
The number of beats per second equals the difference in frequency of
vibration of the tones. A pianoforte tuner does his work best if he has
a musical ear, yet he may discharge his duties with competence without
one. Having struck a note, he sounds its octave, holding both keys
down, and listens for the beat. If the first note gave no beat with
his tuning-fork, the second is in time when it likewise gives no beat
with the first. We have met a tuner who did his work in this way; but
it must be admitted that his tempering of the intervals of the octave
with which he commenced, and consequently of the other octaves above
and below it, left something to be desired. The result might have been
satisfactory had he been provided with twelve tuning-forks.
The question as to whether beats, when sufficiently rapid, blend into a
tone has been much discussed, without a decision. Probably they do not.
The complementary question as to the cause of dissonance is also not
completely closed. Two notes harmonize, as we have seen, when the ratio
of their frequencies is a simple fraction. Musicians are not quite
agreed as to the level of numerical complexity at which a compound
tone first produces a feeling of discomfort. A good deal depends upon
its position in the scale and the instruments which are combining
to produce it. A minor third (⁶/₅) is on the safe side. This is the
first chord in our list of intervals in which a beat can be detected.
Slow beats, however, do not distress us. It is the rapid beats of
conflicting overtones which give a harsh, rough character to a compound
note. The level at which a line is drawn between harmony and dissonance
seems to depend to a considerable extent upon musical education, using
the term in its widest sense. In primitive music—Hungarian, Scotch,
Welsh—intricate minor chords predominate. The minute subdivision of
the octave in Indian music is quite incomprehensible to a European
ear. Musical cultivation tends to eliminate complex fractions. It is,
however, to be noted that the history of Western music also shows the
influence of an opposite tendency. Later generations have admitted as
harmonies combinations which earlier generations could not tolerate.
Pitch, quality, harmony, and dissonance are distinguished by the
human ear. These are the attributes of musical or periodic sounds.
In a separate class must be included noises of all kinds, termed in
acoustics “aperiodic,” because the vibrations which cause them are
not rhythmic. The teeth of a policeman’s rattle may click a hundred
times a second, but it does not make music. Even with a rapidity of
interruption greater than this (at least 500 times per second) a
succession of noises fails to blend into a smooth, continuous sound.
The ear recognizes the loudness, duration, and even to a very high
frequency the repetition of unmusical sounds.
The ear as a sense-organ can be followed down the zoological scale to
jelly-fish. In its primitive form it is a chamber lined with epithelial
cells bearing hairs, containing an otolith, or ear-stone. Otoliths are
rounded calcareous masses which play an important part in the ears
of all animals up to fishes. Even in man they are found in the more
subdivided form of otoconia. Contact of the otoliths with the sensory
hairs originates impulses in the nerves with which primitive ears
are abundantly provided. Advisedly we use the word “ear” in place of
“auditory organ.” In all animals this organ affords information of
a double nature-movement of the external medium in which the animal
lives, and movements of the animal in the medium. When the animal
moves, its sensory hairs are displaced with regard to the otolith; when
the water in which it is swimming pulsates, its otoliths are shaken
against the sensory hairs. Displacements of the animal and agitations
of the water produce similar effects. The ear in this stage is an
organ of touch. It might well be questioned whether an animal fitted
with a piece of sensory apparatus of this kind is endowed with a sense
which we may properly, after reflecting upon our own sensations, term
“hearing.” It is, however, stated that certain transparent crustaceans,
in which the functioning of the ear-organs may be watched through a
lens, show in these organs hairs of varying length which vibrate to
tones of different frequency. This observation apart, it might be
doubted whether fishes hear, if we mean by the word “hearing” the
recognition and discrimination of tones of high frequency—musical
tones. Their ears serve equally to inform them of the changes in
position of their heads and of the tremblings of the sea. The shocks
transmitted through the sea are near akin to the slower vibrations of
sound, if the fishermen of the Mediterranean are justified in their
practice of beating a wooden clapper which rests upon the seat of the
boat as they row backwards and forwards in front of a curved net. They
believe that the fish are frightened by the noise; but it matters
little whether we describe the fish as hearing a noise, or as feeling
the percussions of the clapper conducted through the water. To the more
rapid vibrations of the clapper, the fish are probably insensitive.
The cochlea, which we have every reason for regarding as the organ by
which sound is analysed, is not possessed by fishes. It makes its first
appearance in reptiles. Birds, it is evident, are able to distinguish
musical tones. Their cochleæ are very short, and are destitute of
“rods of Corti.” For a moment this appears surprising, but it must be
remembered that the range of tones which any bird discriminates is
very short, however nicely it may value the notes within its range. In
mammals the ear is clearly divided into three parts, to which the three
functions which have grown out of the specialization of the sense of
touch are allocated. (1) The semicircular canals are concerned with
the sense of orientation. (2) The utricle and saccule reverberate to
noise—the rumbling of trains, the boom of guns, the beats of dissonant
musical tones. We do not know how to classify the agitations of the
atmosphere which surrounds us and of the earth on which we stand, nor
can we point with any certainty to the groups of stimuli which for
us have taken the place of the grinding of stones on the beach and
slapping of rocks by waves. (3) The organ of Corti in the cochlea
discriminates and analyses musical sounds. To these three sense-organs,
which are situate in the inner ear, certain structures are accessory.
The concha, which enables a horse or a cat to collect sound and to
localize its source, is in ourselves merely an ornament to the side of
the head.
[Illustration: FIG. 38.—THE EXTERNAL, MIDDLE, AND INTERNAL EAR OF THE
LEFT SIDE.
From right to left, the figure shows the concha and
lobule of the ear in profile; the external meatus
(abbreviated); the drum, divided vertically, its
posterior half visible; the hammer-bone, with
the tip of its long arm attached to the drum, an
arrow indicating the point of attachment and line
of action of the tensor tympani muscle; the anvil
attached by a ligament to the bony wall of the
middle ear; the stirrup, with its foot-plate almost
filling the oval window; the labyrinth, with the
three semicircular canals above, and the scala
vestibuli below. The curled black line shows the
situation of the scala media, or ductus cochleæ
(which contains the organ of Corti). Pulsations
of sound which move the membrana tympani are
transmitted by the three bones to the oval window.
They shake the perilymph, producing waves which
travel along the scala vestibuli to the apex of the
cochlea, whence they return by the scala tympani
to the round window (if they do not take a shorter
course through the ductus cochleæ). The Eustachian
tube opens out of the lower part of the middle ear.]
The external meatus is a curved tube, about an inch long. Frequently
a tuft of hairs guards its entrance. The wax secreted by its wall
serves to attach particles of dust, and to deter insects from entering
the tube. The air at the end of it is at a uniform temperature. It
is closed by the membrana tympani, or drum. This membrane receives
the vibrations of sound; and, in order that it may collect them with
absolute impartiality, it is in every respect the opposite in shape and
structure to the top of a drum. The stretched parchment which covers
a drum is flat. Its tension is uniform in all its parts. Movements
have the greatest amplitude at the centre. Every precaution is taken to
insure its emitting, with as little confusion as may be, the particular
note to which it is tuned. The drum of the ear is shaped like the
mouth of a trumpet, depressed to a point, but convex from this point
outwards. Its elastic fibres, which are partly radial, partly circular,
are at many different tensions. Its deepest part, to which the long arm
of the hammer-bone is attached, is not its centre.
The “middle ear” is an irregular cavity communicating with the
pharynx by the Eustachian tube. It is filled with air at the same
pressure as the atmosphere. Except during the act of swallowing, when
it is at first shut tightly and then opened, the pharyngeal end of
the Eustachian tube is gently closed. When one is dropped in a lift
rapidly down the shaft of a mine, the difference in pressure between
the external air and the air in the middle ear stretches the drum to
such an extent that deafness to low tones is produced. Conversation
becomes inaudible. The deafness is remedied by swallowing saliva,
and thus opening the end of the Eustachian tube. The commonest cause
of permanent deafness is inflammation followed by thickening of the
mucous membrane of the lower end of the Eustachian tube, with its
consequent closure, due to frequent sore throats. The air in the middle
ear is slowly absorbed. It needs to be constantly renewed through the
Eustachian tube.
On the inner wall of the middle ear are two small apertures—the
oval window and the round window. Both are closed with membrane.
Into the oval window is fitted the sole-plate of the stirrup-bone.
Three bones—hammer, anvil, and stirrup—combine in transferring the
movements of the membrana tympani to the oval window. They constitute a
jointed lever, which swings about an axis passing through the ligament
of the anvil (Fig. 38), the excursions of the long arm of the hammer
being reduced in amplitude by one-third at the stirrup-plate. As
the oval window has only one-twentieth of the area of the drum, the
movements of the latter are transmitted with concentrated force. Two
points in the mechanism of these bones may be specially noticed: (1)
The head of the hammer is free to rotate in the cavity of the anvil,
checked by a cog. Every inward movement of the drum is faithfully
transmitted to the oval window; but when the drum moves outwards,
the hammer does not necessarily carry the anvil with it. (2) A
muscle—tensor tympani—is inserted near the elbow of the long arm of
the hammer. When high notes are listened to its contraction tightens
the drum, rendering it more responsive to rapid vibrations. It has a
tonic action, but it does not make any special contraction for low
notes.
Behind the two windows, within the solid bone, is the inner ear,
which our ancestors very aptly termed a “labyrinth.” It is filled
with fluid—perilymph—which is shaken by every movement of the
stirrup-plate. Since water is incompressible, no waves could be raised
in the perilymph were there no second aperture. Every vibration
conveyed by the stirrup-plate after passing through the labyrinth ends
as a vibration of the membrane which closes the round window.
Nowhere does perilymph come in contact with auditory cells. All the
endings of the nerve of hearing are contained within a membranous
labyrinth which lies within the bony cavities. The way in which the
waves of the perilymph are dispersed over the surface of this closed
sac can be inferred from the diagram (Fig. 38). They sweep round the
utricle and saccule, are lost in the narrow spaces which surround the
semicircular canals, run up the scala vestibuli of the cochlea. The
course of the waves which traverse the cochlea is of especial interest
in connection with the physiology of hearing.
The cochlea—snail-shell—is a spiral tunnel of three turns,
in hard bone, about an inch in length. A shelf of bone—lamina
spiralis—projects into the tunnel on its convex side. From the free
margin of this spiral lamina two membranes extend to the outer wall
of the tunnel—one firm, containing straight, stiff, and probably
elastic fibres which radiate outwards (the basilar membrane); the
other an extremely delicate film of connective tissue. The tunnel is
thus divided into three compartments, known as the scala vestibuli,
scala media, scala tympani. The scala media belongs to the membranous
labyrinth. Waves transmitted through perilymph pass, as we have already
explained, up the scala vestibuli. At the apex of the cochlea the
two scalæ are in communication; but the aperture is small, and it is
unlikely that waves reach the lower passage from the upper through
this opening. They pass through the thin membrane which roofs the
scala media, shake its endolymph, and reach the lower passage through
the basilar membrane. It is noteworthy that, since the round window at
the lower end of the scala tympani is, with the exception of the oval
window, the only opening of the bony labyrinth, all waves transmitted
through the oval window must travel part of the way or all the way up
and down the cochlea.
[Illustration: FIG. 39.—A SECTION THROUGH THE AXIS OF THE COLUMN OF
THE COCHLEA.
The spiral sheet of nerve-fibres which supplies the
organ of Corti is cut in eight places. If the
bundle to the lowest coil of the shell (on the left
side of the diagram) is followed, it will be seen
to bear ganglion-cells where it enters the bony
spiral lamina. This lamina divides the tube into
two canals—scala vestibuli above, scala tympani
below. From the edge of the lamina the membrane of
Corti stretches to the outer wall. Above the organ
of Corti is the membrana tectoria, and above this
a very thin membrane which cuts off the ductus
cochleæ from the scala vestibuli.]
The organ of Corti is spread out on the basilar membrane. It is an
epithelial structure of extreme regularity and uniformity. Near to
the edge by which the basilar membrane is attached to the spiral
lamina rests a double row of rods of Corti, stiff pillars which lean
one towards the other, over the tunnel of Corti, the convex head of
the outer rod fitting into a concavity in the head of the inner one;
in some places one outer rod fits against two inner rods, as the
latter are rather the more numerous. On the inner side of the inner
rod is seen, in transverse sections a single plump cell filled with
cloudy protoplasm, and bearing on its free surface a tuft of very
short hairs. On the outer side of the outer rod are three or four
hair-cells, each with a cloudy outer segment containing the nucleus,
a granular middle segment, and a stiffish stalk, which attaches it to
the basilar membrane. Between the hair-cells are supporting cells,
thicker below, tapering above, containing in their substance a firm
fibre. Still farther to the outer side are epithelial cells, of no
special interest. The purpose of the rods of Corti and the supporting
cells is to give attachment and support to a reticulated membrane of
exquisite delicacy, through the oblong apertures of which the hairs
of the hair-cells project into the endolymph. The spiral lamina is
traversed by a vast number of fibres of the auditory nerve, which,
losing their medullary sheaths, pass across the tunnel of Corti as
naked axons, to end amongst the hair-cells. Above the organ of Corti,
attached by its edge to the spiral lamina, is a thick, gelatinous,
fibrillated structure—membrana tectoria—which rests as a coverlet on
the surface of the organ. It has been supposed that it serves to damp
the vibrations of the hairs after they have been set in motion by the
waves passing across the scala media; but it not impossibly plays a
more active part in hearing than this.
[Illustration: FIG. 40.—ORGAN OF CORTI.
The spiral lamina, on the left of the drawing,
gives attachment to the membrane of Corti, which
stretches to the opposite wall. Below the membrane
is a bloodvessel which runs its whole length
beneath the tunnel of Corti. The tunnel is formed
by pillars—the inner on the left, the outer on
the right—which meet above it. On the left of the
inner pillar is a hair-cell; to the left of this
a nerve-cell with two nuclei. To the right of the
outer pillar is a space; to the right of this four
hair-cells alternating with four supporting cells,
which hold up the reticulated membrane through
apertures in which the tufts of hairs project.
Three nerve-fibres are seen in the spiral lamina;
they cross the tunnel to ramify between the rows of
outer hair-cells. The lamina tectoria rests upon
the tufts of hairs.]
The organ of Corti is, beyond doubt, the apparatus which analyses
sounds; but the problem of the way in which it responds to tones
of different pitch, or analyses compound tones, is not as yet even
approximately solved. To escape the acoustic difficulties which have
to be faced by anyone who endeavours to expound the theory of the
cochlea as a piece of analytical apparatus, various suggestions as
to the possibility of an action _en masse_ have been advanced. For
example, the basilar membrane has been compared to a telephone-plate
which takes up vibrations and transmits them through the auditory nerve
to the brain. But if the organ of Corti be the transmitter, there is
no ear in the brain to analyse the vibrations given out by a receiving
telephone-plate; and without a receiving plate and a listening ear a
telephone is purposeless. According to this hypothesis, the basilar
membrane vibrates as a whole, moving the hair-cells in various
“patterns”; the pressure of the hairs against the tectorial membrane
causing irritation of the cells which bear them, and hence producing
stimulation of various groups of nerves. Other pattern theories
are somewhat similar. But it is obvious that all hypotheses of the
vibration of the whole of the basilar membrane, or of large parts of
it, simultaneously, leave to the mind the responsibility of reading
the pattern which the impulses generated in the organ of Corti make in
the brain. It is conceivable that every fraction of a semitone which a
musician can discriminate, and every combination of tones which he can
analyse, is transmitted to the brain by a large number of co-operating
nerve-impulses; but such a theory involves a complexity of mental
associations difficult to contemplate.
According to the general principles enunciated in this book, analysis
of stimuli is the function of sense-organs. It cannot in all cases
be compared with the analysis effected in a physical laboratory; nor
is this necessary; but it must be carried so far that nerve-impulses
which have no specific qualities apart from their source shall give
rise to effects in consciousness which have no basis other than the
topographical distribution of the said impulses in the brain. There
may be sensory impulses of different orders; there may be in the brain
psycho-physical substances which react to impulses of various orders in
various ways; but until we have some hint of the existence of specific
impulses and specific psycho-physical substances, we are not justified
in postulating their existence simply in order that we may escape from
physiological embarrassments.
The organ of Corti has in the highest degree the appearance of a piece
of apparatus for the analysis of sound. If the basilar membrane, with
the cells which rest upon it, be cut out and laid flat, the suggestion
of some kind of instrument is very strong. It is a long narrow ribbon,
narrowest at the bottom of the spiral, increasing to about twice the
width at the apex. It is crossed by radiating fibres, presumably
elastic. The cells which rest upon it carry vibrating hairs, and
are supplied with nerves. The rods of Corti hold up the reticulated
membrane, which keeps the hair-cells in place. It is not to be wondered
at that when its structure was first discovered it was thought that the
problem of the analysis of musical tones was solved. If two pianos in
perfect tune are in the same room, when one is played the corresponding
wires of the other twang. Anyone who sings into a piano, whilst the
loud pedal raises the dampers, feels an increased fulness in his voice.
This is the familiar phenomenon of resonance. Why should not the fibres
of the basilar membrane resonate to the tones conveyed to the ear—the
shorter ones at the base of the cochlea to high tones, the longer ones
at the apex to low tones? This is the order in which we should expect
the pulsations of sound which ascend the scala vestibuli to be taken
up—the more rapid, near its commencement, the less rapid farther up
it. But an explanation of the physics of the selection of vibrations
of different frequencies by different sets of the elements which make
up the organ of Corti, if such selection occurs, is still to seek. In
the first place, the fibres of the basilar membrane are so exceedingly
short. What could a fibre less than 0·5 millimetre in length make of
the vibrations of a 36-foot organ-pipe? Even if this objection be
waived, as certain eminent physicists hold that it may be, there is not
a sufficient difference in length between the longest and the shortest
fibres to account for the great range of tones which we are able to
discriminate; nor is there any evidence that some fibres are more
tightly stretched than others.
A further consideration which tempts physiologists to look upon the
organ of Corti (including the basilar membrane) as a series of
resonators is the somewhat remarkable agreement between the number of
separate pieces of apparatus of which it appears to be composed and
the number of different musical sounds which, if it were a series of
resonators, it might be called upon to discriminate.
The squeak given by a bat at each turn in its flight has a pitch of
about 11,000 vibrations to the second—the sixth E above the middle
C (Tyndall). In a group of persons listening for the squeak there
are usually some who cannot hear it. Above this the range of hearing
is very variable. The suddenness of transition from perfect hearing
to total want of perception makes experiments with small pipes or
with a siren somewhat amusing, when a number of persons are tested
at the same time. One complains that the note is intolerably loud
and shrill, whilst others assert that there is perfect silence.
Thirty-three thousand vibrations is usually regarded as the upper limit
for the human ear, but certain physiologists place it at 40,000, or
even higher. The upper limit is of little consequence, since there
is very little power of discriminating rapidities above the highest
note used in music—the piccolo stop of the organ, with a pitch of
4,096. It is possible that a sound with a lower frequency than 27
(the contra-bassoon) may be heard as a tone—16 according to certain
writers; but again our power of discriminating very low notes is small.
Over a certain range a skilled musician can tell that a note is out of
tune when it is one sixty-fourth of a semitone higher or lower than
it ought to be. If we assume that by allowing equal sensitiveness for
a range of seven octaves, the excess of the allowance over the actual
sensitiveness towards either end of this stretch would compensate for
the comparatively few distinctions which the ear can make either below
or above it—64 × 12 × 7 = 5,376. A much higher estimate, based upon
observations which seem to show that the ear can distinguish sounds
less than one sixty-fourth of a semitone apart, places the total number
at 11,000.
On the assumption that one piece of apparatus is tuned to resonate
for every distinguishable sound, between 5,000 and 11,000 pieces of
apparatus would be required. Taking one of Corti’s arches as the
centre-piece of the resonator, although the rods are certainly not
vibratile structures, we find the number to be 3,848 (the number of
the outer rods); if either rod with a hair-cell, or hair-cells, is the
analytical element, 9,438. Counting gives 3,487 inner, 11,700 outer,
hair-cells. The fibres of the basilar membrane are estimated at 24,000;
the fibres of the cochlear nerve at 14,000. It will be understood that
the counting of structures as minute as these yields results which
cannot be more than approximately accurate. Helmholtz, assuming that
each arc of Corti indicates an analytical element, accounted for the
apparent deficiency in their number by assuming that a tone of which
the pitch fell between two arches set both in sympathetic vibration,
the arch which was nearest in pitch to the tone vibrating the more
strongly. In this way he anticipated an objection which has often been
brought against his theory of a long series of resonators.
In opposition to Helmholtz’s theory it is pointed out that when a
violinist runs his finger up a bowed string, the pitch rises with
perfect smoothness; it does not bump along from resonator to resonator.
Especially in the case of very high tones given out by a siren, it is
urged that at the rare intervals at which a resonator in the ear is
tuned for the tone which the siren is emitting it should sound much
louder than when the tone falls midway between two resonators. But the
whole question of the nature of the response of the analytical elements
is too obscure at present for the discussion of points so nice as this.
Many who think that Helmholtz’s theory of resonators is based upon
principles of physics and of physiology which must be regarded as
the starting-points of any explanation of the analysis of sounds by
the ear and the mind, hold that it goes too far in searching for a
separate resonator for every distinguishable tone. The cochlea, as we
have already said, does not offer anything like so extensive a choice
as this, if regard be had to the tension or length of its elements,
and not to their numbers. Those who accept it as an axiom that the
cochlea contains a series of responding instruments—but a series far
more limited in range than the gamut of our sound-perceptions—seek
to discover in musical tones qualities which unite them in groups.
Just as in the case of colour-sensations they recognize four (or six)
elementary qualities which excite four (or six) pieces of responding
apparatus, so also in the case of hearing they seek for a limited
number of tone-qualities and a correspondingly limited number of
elementary sensations. The ideal of those who take this view is an
octave of qualities and of elementary sensations sounded in the middle
of the scale when _x_ nerve-endings are stimulated, as the octave
above when 2_x_ nerves respond, the octave below with _x_/2. Such a
conception seems to guide thought round insurmountable barriers. There
is, however, a risk of making too much of the periodic intervals,
because they take so important a place in music. At one side of the gap
which sound bridges between the individual and his environment is an
elastic body shaking at any possible rate within the range of hearing.
At the other side of the gap is the ear. If, having arranged several
thousands of stones along the side of the road in order of size, I
were to state, picking up No. 512, “This is the fundamental of which
No. 1,024 is the octave,” answer would be made to me: “It may be that
the larger could be broken into halves, each as heavy as the smaller
stone; but I recognize no difference between the stones in shape,
colour, or hardness.” A vibrating string divides into equal segments,
each of which vibrates within the vibrations of the whole string,
sounding the octave. We recognize a similarity in quality between
tones and their octaves because we are accustomed to hear the octave,
the most prominent of overtones, in all musical sounds. Hence, from
association, it has become more difficult to distinguish a note from
its octave than it is to distinguish it from its fifth; but it does
not follow that the effect of 1,024 vibrations upon the sensory cells
more nearly resembles the effect of 512 than does that of 768. But at
this point we are compelled to construct some hypothesis as to the way
in which the vibrations affect the sensory cells. The protoplasm of
the cells is not directly sensitive to them. We can account for the
generation of impulses in the nerve connected with a particular cell,
or group of cells, only on the supposition that a resonating mechanism
which responds to vibrations of a certain frequency shakes the cell.
Even then it seems necessary to suppose that there is an accessory
mechanism which disturbs the cell-protoplasm sufficiently to render
the shake effective, probably the hairs rubbing against the tectorial
membrane. Anatomical study gives us no confidence in the theory of the
existence of several thousands of resonators tuned to as many notes
of different pitch. It remains for the physicists to say whether or
not we may picture one of these minute resonators as responding to a
given note in 10 separate octaves, another in 9 ... another in only 1.
The physicists, on their part, may very properly ask the anatomists
to point out the resonators, and even to reproduce them in models of
dimensions which allow of experimental investigation.
It is generally agreed that the sensation of a chord is compounded of
the sensations to which each of its constituent tones gives rise, and
that our power of analysing the compound is a question of attention. A
musician can direct his attention to either sensation at will. It is
not equally certain that a person who has no knowledge of music can
do the same. Familiarity with musical instruments gives us so exact
a knowledge of the way in which compound tones are produced that it
becomes a difficult matter to decide whether, when we say that we can
pick out the E or the G of the common chord, it means that we can hear
it as distinct from =C= and C′, or whether it means that, knowing the
constitution of the chord, we think about the E or the G when we hear
the compound tone, to the exclusion of its other constituents. Then,
again, the several strings which we try to strike simultaneously do not
actually “toe the line.” Their vibrations are not in the same phase,
even though the strings be in absolute tune. Discrepancy of phase may
favour the singling out of the several constituents of the chord. There
we touch upon a problem which we passed over in silence when attempting
to give an idea of the nature of the pulsations which reach the ear. We
then (p. 405) described the partial pulsations which are superimposed
upon the main pulsation as if they necessarily started simultaneously
with it. We assumed that the phase difference of the partials was
zero. But it is clear that differences of phase of its constituent
tones may produce an almost infinite number of variations in the
form of a compound “wave” of sound. Is the ear variously affected by
different forms of wave? Does difference of phase result in difference
of sensation? In broad terms, the answer to this question must be in
the negative; although it can be shown that in certain cases a change
in phase of the several constituents of a compound tone, without any
alteration in their number or their loudness, makes a change in its
acoustic quality. Any attempt to correlate physical changes—the
movements of air in the outer ear—with the effects which they may be
supposed to have upon the organ of Corti must take into account this
wide range of variation of wave-form. We have called attention to the
difficulties which it introduces; but have no hope of indicating the
way in which they may be overcome.
Nothing connected with the physiology of the sense of hearing is
more remarkable than its capacity for education. The cochlea of one
human being is as extensive and as elaborate in structure as that of
another, yet some men can make an infinitely more refined use of it
as an analytical apparatus than can others. A native of the Torres
Straits cannot distinguish as two separate notes sounds which are less
than a semitone apart. Sir Michael Costa could distinguish sounds into
the sixty-fourth parts of semitones. The cochlea of a cat is not less
elaborate than that of a man, yet Man’s mental life is based upon the
analysis of auditory sensations. His supreme advance in the animal
scale has depended upon the invention of language, by means of which
he communicates and receives information, thus rendering experience
eternal, notwithstanding the transience of the individuals who acquire
and transmit it. An animal is born, finds out, dies. A man starts with
the wisdom of the race beneath his feet.
Hearing has a nebulous origin in sensations of movement or
displacement. The connection between the two special senses—the sense
of orientation and the sense of hearing, properly so-called—remains
always intimate. David danced before the Ark of the Lord. All people,
savage and civilized, associate music with movement. High in the
animal scale appears the sense-organ which enables its possessor to
discriminate musical tones. By its use Man has developed with great
rapidity—as secular time is reckoned—an intelligence which removes
him from all other animals a planet’s space. The sounding of his organ
of Corti by pure tones and combinations of pure tones gives him extreme
pleasure, although it in no way ministers to his intelligence. Yet
there is in the enjoyment of music a quality of pleasure which makes
it near akin to the satisfaction which we experience in exercising the
intellect.