§ 10. General Theory of Sound-Sensation.—Anatomical research seems to show that the immediate stimulus to the terminations of the auditory nerve is constituted by the vibrations of the basilar membrane. The main clue to the way in which this membrane acts is found in physical and psychological data. On the physical side, we have the broad fact that impulses which would separately give rise to distinct waves of sound, blend their effects before they reach the ear into a single resultant effect. They produce a single wave, the form of which is mathematically accounted for by their combination. This is true whether the several impulses come from separate material objects or from the same object. Thus the vibrations which produce ordinary sounds are complex in their mode of origin. The forms which they consequently assume can be mathematically resolved into a combination of the forms of certain constituent simple waves. These simple waves are called pendular, because their form is like that described by the sweep of a pendulum. Though one, not many waves, is produced by the impulses which simultaneously set the air in vibration, yet each of these impulses acts separately on the organ of hearing. This is known to be so because the several sensations corresponding to each are distinguishable in consciousness. We can analyse a single note into its partial tones, and we can distinguish a number of notes sounded simultaneously from different sources. This is the startingpoint for the theory of sound-sensations. The organ of hearing must be so constructed as to respond separately to the several impulses which produce the complex wave.

The most simple and obvious, if not the only, way of accounting for this analytic power of the ear is that propounded by Helmholtz, and now commonly, though not universally, accepted. It proceeds on the analogy of certain physical phenomena. If a tuningfork, which produces a simple tone without overtones, be laid on the top of a piano, and if the corresponding note is sounded by touching one of the keys, the tuningfork vibrates in sympathy with it. If the lower octave of the note be sounded, the tuningfork again vibrates in sympathy; for its own note, being an octave of the note sounded on the piano, is contained in this as one of its overtones. It can be similarly made to vibrate in sympathy with any of the notes which contain its own note as an overtone. It is unaffected by other notes. Conversely, if the tuningfork is struck in the neighbourhood of the wires of a piano, those wires will vibrate in response to it, which are specially adjusted to the same tone, or to any of the notes which contain this as an overtone. In the second case they do not vibrate along their whole length, but in segments. The wire which corresponds to the lower octave of the tone sounded on the tuningfork responds by a vibration of which the wavelength is half the length of the wire. Now, the theory of Helmholtz is that the basilar membrane consists of a series of strands, each of which, like the wires of a piano or like a tuningfork, is adapted to its own peculiar tone, and vibrates in response to this. Thus, however complex the physical soundwave may be, it produces in the basilar membrane not a single complex vibration, but a number of distinct vibrations, and each of these constitutes a separate stimulus affecting the terminations of the auditory nerve.

Though the theory of Helmholtz is very simple and plausible, it is not without difficulty. In particular, it does not in its present form satisfactorily explain differencetones (see § 8 Difference-Tones). Attempts have been made to find a substitute for it: but in all probability it only needs modification and development. Recently facts have come to light analogous to colour-blindness which appear strongly to support it. There are cases in which the mechanism for conducting soundimpulses is intact, and yet the sensibility for greater or smaller portions of the scale of tones is absent or much impaired. In some instances the tonedeafness extends to the greater part of the scale, leaving sensibility only to a fragmentary portion of it. One tone of moderate intensity may be clearly distinguished, while another neighbouring tone is indistinguishable, even when it is very loud. It is difficult to explain these phenomena unless we suppose in the ear a system of separate elements, each adjusted to its own peculiar tone, some of which may be absent or incapable of discharging their function while the rest behave in a normal manner.

In this chapter I have followed Ebbinghaus very closely. For further reading in English the student is referred to Foster's TextBook of Physiology, part iv., book iii., pp. 13611378, and to The Power of Sound, by E. Gurney. In German there is the great work of Karl Stumpf in two vols., entitled Tonpsychologie.