Chapter XIV.

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.