We notice in this table that the numbers within an octave always maintain the same ratio, and that the corresponding numbers in the following octave are always the double of those in the preceding one.

Our pianos generally commence with the C, of 33 vibrations, or with a still lower, A,, = 27.5 vibrations, and extend to a""" = 3520 vibrations.

It is of the greatest interest to discover the smallest number of vibrations which is capable of producing the

sensation of a tone. An experiment of this kind has already been made by Savart, by means of the following apparatus. A large wheel is turned by a handle and causes a smaller wheel (fig. 82) to revolve by friction on the periphery. A bar, a b, is fixed on the axis of the smaller wheel, and passes through the slit, cd, in the board, ƒ g. The consequent pulses produce a tone

of considerable strength, and Savart affirms that he has even perceived a tone of constant strength with 7-8 pulses. But the musical character of these deep tones up to about 30 vibrations in a second is so extremely imperfect that they are of no use in music. Helmholtz is of the opinion that the deep tones, which Savart heard in his experiments, must have been harmonics of the fundamental tone of 7-8 vibrations. From his experiment with closed organ pipes, which have only very weak harmonics, and with large tuning-forks, the musical character only begins with about 28-30 vibrations. Deeper tones only create a buzzing and groaning sound in the ear.

The combination of the separate vibrations into one tone, is a process which goes on in the nervous apparatus of the ear. We may compare this process to the constant contraction of a muscle, which it is possible to produce by a number of excitements following each other with great rapidity. If, for instance, 8 to 10 electric shocks are directed upon a muscle in a second, the muscle will not relax to its full extent after each shock, and if the rapidity of the shocks is slightly increased, the muscle will remain contracted, as long as the excitement lasts. Now, in the organ of hearing, the auditory nerve is not continuously irritated by the apparatus for performing sympathetic vibrations, but the excitement takes place at short intervals. Our sense of hearing, however, the seat of which must be sought in the brain, combines these rapid irritations of the nerve in the same manner as the muscle, and by this combination the sensation of tone is produced.

An interesting question, also, is to determine what is

the highest perceptible tone. To settle this question Savart has arranged an experiment also by means of a wheel. The toothed wheel B (fig. 83) is made to revolve with great velocity by means of a strap, D, over a large wheel A, so that the teeth strike a card, which is pushed forward upon the plate E. The toothed wheel which Savart used had 720 teeth, and could produce 24,000 raps in a second. The tone thus produced was very weak and acute, but still distinctly audible. Des

pretz, moreover, has produced with small tuning-forks at tone of 38,016 vibrations; but tones as acute as this are said to be unpleasant and even painful to the ear. We see from these experiments that no fixed limit can be assigned to the perceptibility of acute sounds according to their pitch. This, however, is certain, that above the seventh octave, above the fifth marked c, the tones lose their pleasant musical character, and that the determination of their pitch becomes more uncertain. We may, 1 Müller-Pouillet, 'Physik.'

R

therefore, conclude with some certainty that the organ of the ear designed for musical perception is only adapted for seven octaves, and it is this adaptation which we meet with in the organs of Corti in the cochlea.

From what has already been said it appears that the sensation of tone depends upon the repetition of a motion at regular intervals with a certain velocity. A single shock can never produce a tone, so that if only one tooth were fixed on Savart's wheel it would be quite impossible to produce a tone, by the wheel striking the card during its revolution; it has, however, been observed that two teeth placed close together are sufficient to produce a tone, and, indeed, the same tone which would be produced by the full number, only with this difference-that it is interrupted by intervals. The reason is clear, for in this case also the interval has remained the same though only created by two shocks. It is, also, an interesting fact that even two irritations of the auditory nerve, if they follow each other in rapid succession, are sufficient to produce a sensation of tone, and that the pitch of the tones entirely depends upon the rapidity with which they follow each other.

In order to understand how it is possible for the auditory nerve to perceive so great a number of different tones, we must once more glance at the organs of Corti, and the distribution of the nerve-fibres there. The nerve, which pierces the axis of the cochlea, spreads out into the finest fibres, each fibre coming in contact with a sympathetic vibratory apparatus, by which it can be irritated. When a certain tone is sounded, the whole of the auditory nerve is by no means irritated, but only

a certain number of fibres which proceed to the organ which is set in vibration.

Our perception, therefore, of tones of different pitch is produced entirely by an irritation of different fibres of the auditory nerve. Through the auditory nerve the brain receives from different fibres an intimation of tones of different pitch, which intimation enables it to distinguish the sympathetic vibratory organs which have answered to the tone. The act of recognition is, indeed, quite unconscious, as are many of the faculties which we have acquired by practice; just as in the movements of our limbs we select the nerves and muscles whose action will perform the purpose which we have in view, without being conscious of the existence of these organs.

The communication of different sensations of tone through the medium of different fibres of the auditory nerve, is a process perfectly analogous to others in the region of the sensory organs. It is due to a property called the specific energy of the sensory nerves, a property which we have already closely examined in connection with the optic nerve. Not only does this nerve answer to every description of irritation, whether caused mechanically, by electricity, or by light, with the sensation of sight; but, as we are forced to assume, it consists of at least three kinds of fibres, each one of which is designed for the reception of one of the three primary colours, red, green, or violet. In the auditory nerve this principle of division of labour is still further developed. In this case each nerve-fibre is connected with one tone of a perfectly distinct pitch and can never render any other tone audible.