OF THE SENSE OF HEARING.
As the sense of hearing, as well as that of seeing, gives us perceptions of remote objects, so it is subject to similar errors, and may deceive us, when we cannot rectify by the touch, the ideas which it excites. It communicates no distinct intelligence of the distance from whence a sounding body is heard: a great noise far off, and a small one near, produce the same sensation, and, unless we receive aid from some other sense, we can never distinctly tell whether the sound be a great or a small one. It is not till we have, by experience, become acquainted with any particular sound that we can judge of the distance from whence we hear it; but if, for example, we hear the sound of a bell, we are at no great loss to determine its distance, any more than we are of that of a cannon from the report, judging in both cases from similar sounds, which we have been previously acquainted with.
Every body that strikes against another produces a sound which is simple in bodies non-elastic, but is often repeated in such as are elastic. If we strike a bell, a single blow produces a sound, which is repeated while the sonorous body continues to vibrate. These undulations succeed each other so fast, that the ear supposes them one continued sound; whereas, in reality, they form many. A circumstance of this kind happened to myself, for lying on the bed half asleep, I distinctly counted five strokes of the hammer upon the bell of the clock, and rising immediately found it was but the hour of one, and was convinced by examining the machinery that it had struck no more. A person, therefore, who should for the first time, hear the toll of a bell, would very probably be able to distinguish these breaks of sound; and, in fact, we can readily ourselves perceive remission in sounds.
Sounding bodies are of two kinds; those unelastic ones, which being struck, return but a single sound; and those more elastic returning a succession of sounds, which uniting together form a tone. This tone may be considered as a number of sounds produced one after the other by the same body, as we find in a bell, which continues to sound for some time after it is struck. A continuing tone may be also produced from a non-elastic body, by repeating the blow quick and often, as when we beat a drum, or draw a bow along the string of a fiddle.
Considering the subject in this light, we shall find the number of blows or quickness of repetition will have no effect in altering the tone, but only make it more even or more distinct, whereas if we increase the force of the blow by striking the body with double the weight, this will produce a tone twice as loud as the former. From hence we may infer, that all bodies give a louder and graver tone, not in proportion to the number of times they are struck, but to the force that strikes them. And if this be so, those philosophers who make the tone of a sonorous body, a bell, or the string of an harpsichord, for instance, to depend upon the number only of its vibrations, and not the force, have mistaken what is only an effect for a cause. A bell, or an elastic string, can only be considered as a drum beaten; and the frequency of the blows can make no alteration whatsoever in the tone. The largest bells, and the longest and thickest strings, have the most forcible vibrations; and, therefore, their tones will be more loud and more grave in proportion to the size and weight of the body with which they are struck.
If we strike a body incapable of vibration with a double force, or a double mass of matter, it will produce a sound doubly grave. Music has been said, by the ancients, to have been first invented from the blows of different hammers on an anvil. Suppose then we strike an anvil with a hammer of one pound weight, and then with a hammer of two pounds, it is plain that the latter will produce a sound twice as grave as the former. But if we strike with a two pound hammer, and then with a three pound, the last will produce a sound only one third more grave than the former. If we strike with a three, and then with a four, it will likewise follow that the latter will be a quarter part more grave than the former. Now, in the comparing between all those sounds, it is obvious that the difference between one and two is more easily perceived than between two and three, three and four, or any numbers succeeding in the same proportion. The succession of sounds will be, therefore, pleasing in proportion to the ease with which they may be distinguished. That sound which is double the former, or in other words, the octave to the preceding tone, will be the most pleasing harmony. The next to that, which is as two to three, will be most agreeable. And thus universally, those sounds whose differences may be most easily compared are the most agreeable.
It is most certain that the cause of pleasure in all our senses originates from the justness of proportion, and that disproportion never creates a pleasing sensation. The lad whom Mr. Chesselden restored to sights was at first most delighted with those objects which were regular and smooth on the surface; from this it is plain that the ideas we entertain of beauty from the eye originates from regularity and proportion; it is the same with the sense of feeling, smooth, round, and uniform bodies are more pleasing than those which are rough and irregular; why should not therefore the same preference be given by the ear to the proportion of sounds?
Sound has, in common with light, the property of being extensively diffused; and also admits of reflection. The laws of this reflection, it is true, are less understood: all we know is, that sound is reflected by hard bodies, and that their being hollow, sometimes increases the reverberation. A wall or a mountain sometimes reflects sounds so distinct that we are almost induced to suppose it proceeds from them rather than from an opposite quarter. Vaults and hollow rocks also produce distinct echoes.