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CHAPTER VI.

The Sensation of Music - The Monochord-The Octave and its DivisionsPerception of Grave and Acute Tones-The Irritation of the Auditory Nerve.

A tone is produced as soon as an elastic body performs, with certain rapidity, regular periodical vibrations which are conveyed to the ear by a conductor of sound. We distinguish certain peculiarities in this sensation; in the first place, its strength or intensity; secondly, the pitch of the tone; and thirdly, its colour or quality (timbre).

The intensity of a tone depends entirely upon the extent or amplitude of the sound-wave. If we compare a sound-wave with the waves upon the surface of water, we shall find that, in the latter, the extent is an index of the height, since they increase in power and mechanical action in proportion to their height. And with the amplitude of the vibration of a stretched string, we shall find that the intensity of a tone increases, although the number of vibrations in a second remains the same; and, therefore, the further we remove a string from the position it occupies when at rest, the greater will be the intensity of the tone, although its pitch remains unaltered.

The vibrations of elastic bodies, therefore, obey the same rules as the vibrations of a pendulum. A pendu

lum of a certain length will always make the same number of oscillations in a second, independently of their extent, within certain limits. The velocity of the motion increases with the extent of the oscillations; and the action of a vibrating string is exactly similar.

The vibrations of sound in the air are longitudinal; they consist of alternate expansions and condensations, and the greater the condensation the louder will be the sound produced. The particles of the air execute a motion to and fro, and the greater the extent of this motion the more will they alternately approach and recede from each other; in other words, the greater will be the condensation and expansion which they will produce. The sound-wave itself always retains the same length in the air as was imparted to it by the source of sound. During its propagation through the air the intensity of the tone decreases inversely as the square of the distance, as is the case with light. The reason of this is, that the force of the vibration from a distance I to a distance II will be spread over a surface of four times the size. In every point of the latter, therefore, the intensity will not be in the ratio of but of (1)2 = 1.

The pitch of a tone depends upon the length of its sound-waves. The longer the sound-wave, the deeper will be the tone, and the shorter the wave, the higher the tone.

To return to the vibrating string, we shall find that the length of the string represents the length of the sonorous vibrations in it. A string of a certain length will, therefore, produce vibrations of half the length of those produced by a string twice as long. Moreover, we know that the first string makes twice as many vibrations in a second

as the latter, and, at the same time, we perceive that the tones produced vary in pitch, one of them being said to be an octave above the other. We can, therefore, say that the pitch of a tone increases with the number of vibrations performed in a given time.

Let us consider, further, the sound-waves of different. tones in the air, supposing a definite number, which we will call n, of the sound-waves of a tone, to be produced in a certain space round the source of sound. If we now sound the octave of this tone, twice as many, or 2n waves will be produced in the same time. Now all soundwaves, whether small or great, are transmitted with nearly the same velocity, therefore 2 n waves will accomplish the given distance in the same length of time as n waves. In other words, the 2 n waves will now be contained within this space, each wave being only half the length of the waves of the tone of ʼn vibrations.

When, therefore, we hear two tones, one of which is an octave above the other, the upper tone conveys to the tympanic membrane twice as many sound-waves in a second as the lower one, but of only half the length; and the tympanic membrane and all the sympathetic vibratory apparatus connected with it in the ear, repeat the vibrations in the same length of time. It is very remarkable that our organ of hearing is naturally gifted with a perception of the interval of an octave. Two tones whose rate of vibration is in the ratio 1 : 2 produce upon the ear a sensation very similar to each other, which is evidently caused by their vibrations standing in such a very simple relation to each other. In spite of this, we are not in the least degree informed by our ear of the existence of the vibrations, and still less of the definite

number which are produced in a certain time, which physical research has first revealed to us. But our sense of hearing is extraordinarily delicate in its power of distinguishing between the pitch of different tones; that is to say, of distinguishing the relation between the number of the vibrations. We do not, however, recognise them as such, but simply as specific sensations of sound, for it is only through the study of physics that we have learnt to transfer the sensations of tone into relative vibrations.

The great philosopher and mathematician, Pythagoras, who lived in lower Italy 500 years B.C., and by his celebrated teaching laid the foundation of the science of mathematics, was also the discoverer of the law of vibrating strings. He constructed the monochord, which, in fig. 79, is represented in the form now used by Physicists. It is said that Pythagoras was led to the discovery of this law by watching a forge, and listening to the different pitch of the sounds produced by large and small hammers.

The monochord consists of a wooden box so constructed that strings can be stretched across it. The two bridges a and b fix the length of the string to be set in vibration. The strings are either stretched by a peg, or different degrees of tension may be given to them by weights, the string from the bridge, a, being led over a roller and the weights, P, hung on to it by a hook. By this means we are enabled to calculate the amount of tension from the weight, and to discover the influence of the tension of the string upon the pitch of the tone.

If we now strike a string of constant tension, or draw the bow across it, a tone of a continuous pitch is heard

which we will suppose to consist of n vibrations. The string, as in fig. 79, consists of sixty divisions, and if we push the bridge up to thirty, then the half-string will produce a tone which will be an octave above the other. If we take of the string, we shall have the second octave;, the third; 16, the fourth octave, and so on. Thus we see that the sensation of tone in our ear stands

The power of discriminating tones which the ear possesses is very perfect, a very slight deviation from the octave being recognised as out of tune. We can measure the half of the string with much more certainty by the ear than by the eye, for if we try to touch the half by the eye, we shall find that we generally produce a wrong tone. The violin player, who by pressure alters the length of the strings and, therefore, the pitch of the tone, never calculates the distances with his eye but by means of tactual and muscular sensation, which, with practice, forms a much more certain guide than the eye.