SOUND AND MUSICAL INSTRUMENTS.
Nature of sound--The ear--Musical instruments--The vibration of
strings--The sounding-board and the frame of a piano--The
strings--The striking mechanism--The quality of a note.
Sound differs from light, heat, and electricity in that it can be
propagated through matter only. Sound-waves are matter-waves, not
ether-waves. This can be proved by placing an electric bell under the
bell-glass of an air-pump and exhausting all the air. Ether still
remains inside the glass, but if the bell be set in motion no sound is
audible. Admit air, and the clang of the gong is heard quite plainly.
Sound resembles light and heat, however, thus far, that it can be
concentrated by means of suitable lenses and curved surfaces. An _echo_
is a proof of its _reflection_ from a surface.
Before dealing with the various appliances used for producing
sound-waves of a definite character, let us examine that wonderful
natural apparatus
THE EAR,
through which we receive those sensations which we call sound.
[Illustration: FIG. 133.--Diagrammatic sketch of the parts of the ear.]
Fig. 133 is a purely diagrammatic section of the ear, showing the
various parts distorted and out of proportion. Beginning at the left, we
have the _outer ear_, the lobe, to gather in the sound-waves on to the
membrane of the tympanum, or drum, to which is attached the first of a
series of _ossicles_, or small bones. The last of these presses against
an opening in the _inner ear_, a cavity surrounded by the bones of the
head. Inside the inner ear is a watery fluid, P, called _perilymph_
("surrounding water"), immersed in which is a membranic envelope, M,
containing _endolymph_ ("inside water"), also full of fluid. Into this
fluid project E E E, the terminations of the _auditory nerve_, leading
to the brain.
When sound-waves strike the tympanum, they cause it to move inwards and
outwards in a series of rapid movements. The ossicles operated by the
tympanum press on the little opening O, covered by a membrane, and every
time they push it in they slightly squeeze the perilymph, which in turn
compresses the endolymph, which affects the nerve-ends, and telegraphs a
sensation of sound to the brain.
In Fig. 134 we have a more developed sketch, giving in fuller detail,
though still not in their actual proportions, the components of the ear.
The ossicles M, I, and S are respectively the _malleus_ (hammer),
_incus_ (anvil), and _stapes_ (stirrup). Each is attached by ligaments
to the walls of the middle ear. The tympanum moves the malleus, the
malleus the incus, and the incus the stapes, the last pressing into the
opening O of Fig. 133, which is scientifically known as the _fenestra
ovalis_, or oval window. As liquids are practically incompressible,
nature has made allowance for the squeezing in of the oval window
membrane, by providing a second opening, the round window, also covered
with a membrane. When the stapes pushes the oval membrane in, the round
membrane bulges out, its elasticity sufficing to put a certain pressure
on the perilymph (indicated by the dotted portion of the inner ear).
[Illustration: FIG. 134.--Diagrammatic section of the ear, showing the
various parts.]
The inner ear consists of two main parts, the _cochlea_--so called from
its resemblance in shape to a snail's shell--and the _semicircular
canals_. Each portion has its perilymph and endolymph, and contains a
number of the nerve-ends, which are, however, most numerous in the
cochlea. We do not know for certain what the functions of the canals and
the cochlea are; but it is probable that the former enables us to
distinguish between the _intensity_ or loudness of sounds and the
direction from which they come, while the latter enables us to determine
the _pitch_ of a note. In the cochlea are about 2,800 tiny nerve-ends,
called the _rods of Corti_. The normal ear has such a range as to give
about 33 rods to the semitone. The great scientist Helmholtz has
advanced the theory that these little rods are like tiny tuning-forks,
each responding to a note of a certain pitch; so that when a string of a
piano is sounded and the air vibrations are transmitted to the inner
ear, they affect only one of these rods and the part of the brain which
it serves, and we have the impression of one particular note. It has
been proved by experiment that a very sensitive ear can distinguish
between sounds varying in pitch by only 1/64th of a semitone, or but
half the range of any one Corti fibre. This difficulty Helmholtz gets
over by suggesting that in such an ear two adjacent fibres are affected,
but one more than the other.
A person who has a "good ear" for music is presumably one whose Corti
rods are very perfect. Unlucky people like the gentleman who could only
recognize one tune, and that because people took off their hats when it
commenced, are physically deficient. Their Corti rods cannot be properly
developed.
What applies to one single note applies also to the elements of a
musical chord. A dozen notes may sound simultaneously, but the ear is
able to assimilate each and blend it with its fellows; yet it requires a
very sensitive and well-trained ear to pick out any one part of a
harmony and concentrate the brain's attention on that part.
The ear has a much larger range than the eye. "While the former ranges
over eleven octaves, but little more than a single octave is possible to
the latter. The quickest vibrations which strike the eye, as light, have
only about twice the rapidity of the slowest; whereas the quickest
vibrations which strike the ear, as a musical sound, have more than two
thousand times the rapidity of the slowest."[26] To come to actual
figures, the ordinary ear is sensitive to vibrations ranging from 16 to
38,000 per second. The bottom and top notes of a piano make respectively
about 40 and 4,000 vibrations a second. Of course, some ears, like some
eyes, cannot comprehend the whole scale. The squeak of bats and the
chirrup of crickets are inaudible to some people; and dogs are able to
hear sounds far too shrill to affect the human auditory apparatus.
Not the least interesting part of this wonderful organ is the tympanic
membrane, which is provided with muscles for altering its tension
automatically. If we are "straining our ears" to catch a shrill sound,
we tighten the membrane; while if we are "getting ready" for a deep,
loud report like that of a gun, we allow the drum to slacken.
The _Eustachian tube_ (Fig. 134) communicates with the mouth. Its
function is probably to keep the air-pressure equal on both sides of the
drum. When one catches cold the tube is apt to become blocked by mucus,
causing unequal pressure and consequent partial deafness.
Before leaving this subject, it will be well to remind our more youthful
readers that the ear is delicately as well as wonderfully made, and must
be treated with respect. Sudden shouting into the ear, or a playful
blow, may have most serious effects, by bursting the tympanum or
injuring the arrangement of the tiny bones putting it in communication
with the inner ear.
MUSICAL INSTRUMENTS.
These are contrivances for producing sonorous shocks following each
other rapidly at regular intervals. Musical sounds are distinguished
from mere noises by their regularity. If we shake a number of nails in a
tin box, we get only a series of superimposed and chaotic sensations. On
the other hand, if we strike a tuning-fork, the air is agitated a
certain number of times a second, with a pleasant result which we call a
note.
We will begin our excursion into the region of musical instruments with
an examination of that very familiar piece of furniture,
THE PIANOFORTE,
which means literally the "soft-strong." By many children the piano is
regarded as a great nuisance, the swallower-up of time which could be
much more agreeably occupied, and is accordingly shown much less respect
than is given to a phonograph or a musical-box. Yet the modern piano is
a very clever piece of work, admirably adapted for the production of
sweet melody--if properly handled. The two forms of piano now generally
used are the _upright_, with vertical sound-board and wires, and the
_grand_, with horizontal sound-board.[27]
THE VIBRATION OF STRINGS.
As the pianoforte is a stringed instrument, some attention should be
given to the subject of the vibration of strings. A string in a state of
tension emits a note when plucked and allowed to vibrate freely. The
_pitch_ of the note depends on several conditions:--(1) The diameter of
the string; (2) the tension of the string; (3) the length of the string;
(4) the substance of the string. Taking them in order:--(1.) The number
of vibrations per second is inversely proportional to the diameter of
the string: thus, a string one-quarter of an inch in diameter would
vibrate only half as often in a given time as a string one-eighth of an
inch in diameter. (2.) The length remaining the same, the number of
vibrations is directly proportional to the _square root_ of the
_tension_: thus, a string strained by a 16-lb. weight would vibrate four
times as fast as it would if strained by a 1-lb. weight. (3.) The number
of vibrations is inversely proportional to the _length_ of the string:
thus, a one-foot string would vibrate twice as fast as a two-foot
string, strained to the same tension, and of equal diameter and weight.
(4.) Other things being equal, the rate of vibration is inversely
proportional to the square root of the _density_ of the substance: so
that a steel wire would vibrate more rapidly than a platinum wire of
equal diameter, length, and tension. These facts are important to
remember as the underlying principles of stringed instruments.
Now, if you hang a wire from a cord, and hang a heavy weight from the
wire, the wire will be in a state of high tension, and yield a distinct
note if struck. But the volume of sound will be very small, much too
small for a practical instrument. The surface of the string itself is so
limited that it sets up but feeble motions in the surrounding air. Now
hang the wire from a large board and strike it again. The volume of
sound has greatly increased, because the string has transmitted its
vibrations to the large surface of the board.
To get the full sound-value of the vibrations of a string, we evidently
ought to so mount the string that it may influence a large sounding
surface. In a violin this is effected by straining the strings over a
"bridge" resting on a hollow box made of perfectly elastic wood. Draw
the bow across a string. The loud sound heard proceeds not from the
string only, but also from the whole surface of the box.
THE SOUNDING-BOARD AND FRAME OF A PIANO.
A piano has its strings strained across a _frame_ of wood or steel, from
a row of hooks in the top of the frame to a row of tapering square-ended
pins in the bottom, the wires passing over sharp edges near both ends.
The tuner is able, on turning a pin, to tension its strings till it
gives any desired note. Readers may be interested to learn that the
average tension of a string is 275 lbs., so that the total strain on the
frame of a grand piano is anything between 20 and 30 _tons_.
To the back of the frame is attached the _sounding-board_, made of
spruce fir (the familiar Christmas tree). This is obtained from Central
and Eastern Europe, where it is carefully selected and prepared, as it
is essential that the timber should be sawn in such a way that the grain
of the wood runs in the proper direction.
THE STRINGS.
These are made of extremely strong steel wire of the best quality. If
you examine the wires of your piano, you will see that they vary in
thickness, the thinnest being at the treble end of the frame. It is
found impracticable to use wires of the same gauge and the same tension
throughout. The makers therefore use highly-tensioned thick wires for
the bass, and finer, shorter wires for the treble, taking advantage of
the three factors--weight, tension, and length--which we have noticed
above. The wires for the deepest notes are wrapped round with fine
copper wire to add to their weight without increasing their diameter at
the tuning-pins. There are about 600 yards (roughly one-third of a mile)
of wire in a grand piano.
THE STRIKING MECHANISM.
We now pass to the apparatus for putting the strings in a state of
vibration. The grand piano mechanism shown in Fig. 135 may be taken as
typical of the latest improvements. The essentials of an effective
mechanism are:--(1) That the blow delivered shall be sharp and certain;
(2) that the string shall be immediately "damped," or have its vibration
checked if required, so as not to interfere with the succeeding notes of
other strings; (3) that the hammer shall be able to repeat the blows in
quick succession. The _hammer_ has a head of mahogany covered with
felt, the thickness of which tapers gradually and regularly from an inch
and a quarter at the bass end to three-sixteenths of an inch at the
extreme treble notes. The entire eighty-five hammers for the piano are
covered all together in one piece, and then they are cut apart from
each other. The consistency of the covering is very important. If too
hard, it yields a harsh note, and must be reduced to the right degree by
pricking with a needle. In the diagram the felt is indicated by the
dotted part.
[Illustration: FIG. 135.--The striking mechanism of a "grand" piano.]
The _action carriage_ which operates the hammer is somewhat complicated.
When the key is depressed, the left end rises, and pushes up the whole
carriage, which is pivoted at one end. The hammer shank is raised by the
jack B pressing upon a knob, N, called the _notch_, attached to the
under side of the shank. When the jack has risen to a certain point, its
arm, B^1, catches against the button C and jerks it from under the
notch at the very moment when the hammer strikes, so that it may not be
blocked against the string. As it rebounds, the hammer is caught on the
_repetition lever_ R, which lifts it to allow of perfect repetition.
The _check_ catches the tail of the hammer head during its descent when
the key is raised, and prevents it coming back violently on the carriage
and rest. The tail is curved so as to wedge against the check without
jamming in any way. The moment the carriage begins to rise, the rear end
of the key lifts a lever connected with the _damper_ by a vertical
wire, and raises the damper of the string. If the key is held down, the
vibrations continue for a long time after the blow; but if released at
once, the damper stifles them as the hammer regains its seat. A bar, L,
passing along under all the _damper lifters_, is raised by depressing
the loud pedal. The _soft pedal_ slides the whole keyboard along such a
distance that the hammers strike two only out of the three strings
allotted to all except the bass notes, which have only one string
apiece, or two, according to their depth or length. In some pianos the
soft pedal presses a special damper against the strings; and a third
kind of device moves the hammers nearer the strings so that they deliver
a lighter blow. These two methods of damping are confined to upright
pianos.
A high-class piano is the result of very careful workmanship. The
mechanism of each note must be accurately regulated by its tiny screws
to a minute fraction of an inch. It must be ensured that every hammer
strikes its blow at exactly the right place on the string, since on this
depends the musical value of the note. The adjustment of the dampers
requires equal care, and the whole work calls for a sensitive ear
combined with skilled mechanical knowledge, so that the instrument may
have a light touch, strength, and certainty of action throughout the
whole keyboard.
THE QUALITY OF A NOTE.
If two strings, alike in all respects and equally tensioned, are
plucked, both will give the same note, but both will not necessarily
have the same quality of tone. The quality, or _timbre_, as musicians
call it, is influenced by the presence of _overtones_, or _harmonics_,
in combination with the _fundamental_, or deepest, tone of the string.
The fact is, that while a vibrating string vibrates as a whole, it also
vibrates in parts. There are, as it were, small waves superimposed on
the big fundamental waves. Points of least motion, called _nodes_, form
on the string, dividing it into two, three, four, five, etc., parts,
which may be further divided by subsidiary nodes. The string, considered
as halved by one node, gives the first overtone, or octave of the
fundamental. It may also vibrate as three parts, and give the second
overtone, or twelfth of the fundamental;[28] and as four parts, and give
the third overtone, the double octave.
Now, if a string be struck at a point corresponding to a node, the
overtones which require that point for a node will be killed, on account
of the excessive motion imparted to the string at that spot. Thus to hit
it at the middle kills the octave, the double octave, etc.; while to hit
it at a point one-third of the length from one end stifles the twelfth
and all its sub-multiples.
A fundamental note robbed of all its harmonics is hard to obtain, which
is not a matter for regret, as it is a most uninteresting sound. To get
a rich tone we must keep as many useful harmonics as possible, and
therefore a piano hammer is so placed as to strike the string at a point
which does not interfere with the best harmonics, but kills those which
are objectionable. Pianoforte makers have discovered by experiment that
the most pleasing tone is excited when the point against which the
hammer strikes is one-seventh to one-ninth of the length of the wire
from one end.
The nature of the material which does the actual striking is also of
importance. The harder the substance, and the sharper the blow, the more
prominent do the harmonics become; so that the worker has to regulate
carefully both the duration of the blow and the hardness of the hammer
covering.
[26] Tyndall, "On Sound," p. 75.
[27] A Broadwood "grand" is made up of 10,700 separate pieces, and in
its manufacture forty separate trades are concerned.
[28] Twelve notes higher up the scale.