On the assumption that one piece of apparatus is tuned to resonate for every distinguishable sound, between 5,000 and 11,000 pieces of apparatus would be required. Taking one of Corti’s arches as the centre-piece of the resonator, although the rods are certainly not vibratile structures, we find the number to be 3,848 (the number of the outer rods); if either rod with a hair-cell, or hair-cells, is the analytical element, 9,438. Counting gives 3,487 inner, 11,700 outer, hair-cells. The fibres of the basilar membrane are estimated at 24,000; the fibres of the cochlear nerve at 14,000. It will be understood that the counting of structures as minute as these yields results which cannot be more than approximately accurate. Helmholtz, assuming that each arc of Corti indicates an analytical element, accounted for the apparent deficiency in their number by assuming that a tone of which the pitch fell between two arches set both in sympathetic vibration, the arch which was nearest in pitch to the tone vibrating the more strongly. In this way he anticipated an objection which has often been brought against his theory of a long series of resonators.
In opposition to Helmholtz’s theory it is pointed out that when a violinist runs his finger up a bowed string, the pitch rises with perfect smoothness; it does not bump along from resonator to resonator. Especially in the case of very high tones given out by a siren, it is urged that at the rare intervals at which a resonator in the ear is tuned for the tone which the siren is emitting it should sound much louder than when the tone falls midway between two resonators. But the whole question of the nature of the response of the analytical elements is too obscure at present for the discussion of points so nice as this.
Many who think that Helmholtz’s theory of resonators is based upon principles of physics and of physiology which must be regarded as the starting-points of any explanation of the analysis of sounds by the ear and the mind, hold that it goes too far in searching for a separate resonator for every distinguishable tone. The cochlea, as we have already said, does not offer anything like so extensive a choice as this, if regard be had to the tension or length of its elements, and not to their numbers. Those who accept it as an axiom that the cochlea contains a series of responding instruments—but a series far more limited in range than the gamut of our sound-perceptions—seek to discover in musical tones qualities which unite them in groups. Just as in the case of colour-sensations they recognize four (or six) elementary qualities which excite four (or six) pieces of responding apparatus, so also in the case of hearing they seek for a limited number of tone-qualities and a correspondingly limited number of elementary sensations. The ideal of those who take this view is an octave of qualities and of elementary sensations sounded in the middle of the scale when x nerve-endings are stimulated, as the octave above when 2x nerves respond, the octave below with x/2. Such a conception seems to guide thought round insurmountable barriers. There is, however, a risk of making too much of the periodic intervals, because they take so important a place in music. At one side of the gap which sound bridges between the individual and his environment is an elastic body shaking at any possible rate within the range of hearing. At the other side of the gap is the ear. If, having arranged several thousands of stones along the side of the road in order of size, I were to state, picking up No. 512, “This is the fundamental of which No. 1,024 is the octave,” answer would be made to me: “It may be that the larger could be broken into halves, each as heavy as the smaller stone; but I recognize no difference between the stones in shape, colour, or hardness.” A vibrating string divides into equal segments, each of which vibrates within the vibrations of the whole string, sounding the octave. We recognize a similarity in quality between tones and their octaves because we are accustomed to hear the octave, the most prominent of overtones, in all musical sounds. Hence, from association, it has become more difficult to distinguish a note from its octave than it is to distinguish it from its fifth; but it does not follow that the effect of 1,024 vibrations upon the sensory cells more nearly resembles the effect of 512 than does that of 768. But at this point we are compelled to construct some hypothesis as to the way in which the vibrations affect the sensory cells. The protoplasm of the cells is not directly sensitive to them. We can account for the generation of impulses in the nerve connected with a particular cell, or group of cells, only on the supposition that a resonating mechanism which responds to vibrations of a certain frequency shakes the cell. Even then it seems necessary to suppose that there is an accessory mechanism which disturbs the cell-protoplasm sufficiently to render the shake effective, probably the hairs rubbing against the tectorial membrane. Anatomical study gives us no confidence in the theory of the existence of several thousands of resonators tuned to as many notes of different pitch. It remains for the physicists to say whether or not we may picture one of these minute resonators as responding to a given note in 10 separate octaves, another in 9 ... another in only 1. The physicists, on their part, may very properly ask the anatomists to point out the resonators, and even to reproduce them in models of dimensions which allow of experimental investigation.
It is generally agreed that the sensation of a chord is compounded of the sensations to which each of its constituent tones gives rise, and that our power of analysing the compound is a question of attention. A musician can direct his attention to either sensation at will. It is not equally certain that a person who has no knowledge of music can do the same. Familiarity with musical instruments gives us so exact a knowledge of the way in which compound tones are produced that it becomes a difficult matter to decide whether, when we say that we can pick out the E or the G of the common chord, it means that we can hear it as distinct from C and C′, or whether it means that, knowing the constitution of the chord, we think about the E or the G when we hear the compound tone, to the exclusion of its other constituents. Then, again, the several strings which we try to strike simultaneously do not actually “toe the line.” Their vibrations are not in the same phase, even though the strings be in absolute tune. Discrepancy of phase may favour the singling out of the several constituents of the chord. There we touch upon a problem which we passed over in silence when attempting to give an idea of the nature of the pulsations which reach the ear. We then ([p. 405]) described the partial pulsations which are superimposed upon the main pulsation as if they necessarily started simultaneously with it. We assumed that the phase difference of the partials was zero. But it is clear that differences of phase of its constituent tones may produce an almost infinite number of variations in the form of a compound “wave” of sound. Is the ear variously affected by different forms of wave? Does difference of phase result in difference of sensation? In broad terms, the answer to this question must be in the negative; although it can be shown that in certain cases a change in phase of the several constituents of a compound tone, without any alteration in their number or their loudness, makes a change in its acoustic quality. Any attempt to correlate physical changes—the movements of air in the outer ear—with the effects which they may be supposed to have upon the organ of Corti must take into account this wide range of variation of wave-form. We have called attention to the difficulties which it introduces; but have no hope of indicating the way in which they may be overcome.
Nothing connected with the physiology of the sense of hearing is more remarkable than its capacity for education. The cochlea of one human being is as extensive and as elaborate in structure as that of another, yet some men can make an infinitely more refined use of it as an analytical apparatus than can others. A native of the Torres Straits cannot distinguish as two separate notes sounds which are less than a semitone apart. Sir Michael Costa could distinguish sounds into the sixty-fourth parts of semitones. The cochlea of a cat is not less elaborate than that of a man, yet Man’s mental life is based upon the analysis of auditory sensations. His supreme advance in the animal scale has depended upon the invention of language, by means of which he communicates and receives information, thus rendering experience eternal, notwithstanding the transience of the individuals who acquire and transmit it. An animal is born, finds out, dies. A man starts with the wisdom of the race beneath his feet.
Hearing has a nebulous origin in sensations of movement or displacement. The connection between the two special senses—the sense of orientation and the sense of hearing, properly so-called—remains always intimate. David danced before the Ark of the Lord. All people, savage and civilized, associate music with movement. High in the animal scale appears the sense-organ which enables its possessor to discriminate musical tones. By its use Man has developed with great rapidity—as secular time is reckoned—an intelligence which removes him from all other animals a planet’s space. The sounding of his organ of Corti by pure tones and combinations of pure tones gives him extreme pleasure, although it in no way ministers to his intelligence. Yet there is in the enjoyment of music a quality of pleasure which makes it near akin to the satisfaction which we experience in exercising the intellect.
CHAPTER XV
SKIN-SENSATIONS
The senses, according to a time-honoured classification, are five in number—smell, sight, taste, hearing, and common sensation, or touch; but such a classification of our sensations and of the organs which originate them is too crude for modern needs. Already we have shown that, whereas the nose and the tongue afford the same kind of information, the ear affords information of two, perhaps of three, different kinds. Within the realm of common sensation we pick out three special senses served by specialized sense-organs—touch, cold and heat—and, possibly, a fourth, served by non-specialized nerves, to which alone the epithet “common” properly applies.