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rods of Corti (Co, Fig. 21), which are represented highly magnified in Fig. 22. These rods are stiff and arranged side by side in two rows, leaned against one another by their upper ends so as to cover in a tunnel; they are known respectively as the inner and outer rods, the former being nearer the lamina spiralis. The inner rods are more numerous than the outer, the numbers being about 6000 and 4500 respectively. Attached to the external sides of the heads of the outer rods is the reticular membrane (r, Fig. 22), which is stiff and perforated by holes. External to the outer rods come four rows of outer hair-cells, connected like the inner row with nerve-fibres; their bristles project into the holes of the reticular membrane. Beyond the outer hair-cells is ordinary columnar epithelium, which passes gradually into cuboidal cells lining most of the membranous cochlea. From the upper lip of the sulcus spiralis projects the tectorial membrane (t, Fig. 21) which extends over the rods of Corti and the hair-cells."*

[graphic]

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FIG. 23.-Sensory epithelium from ampulla or semicircua nerve-fibre pierces the wall, the two hair-cells, c. At ha

lar canal, and saccule. At n

and after branching enters

'columnar cell' with a long

being broken away from its

The hair-cells would thus seem to be the terminal organs for picking up' the vibrations which the airwaves communicate through all the intervening apparatus, solid and liquid, to the basilar membrane. Analogous hair-cells receive the terminal nerve-filaments in the walls of the saccule, utricle, and ampullæ (see Fig. 23). The Various Qualities of Sound.-Physically, sounds consist of vibrations, and these are, generally speaking, aërial When the waves are non-periodic the result is a

waves.

*Martin: op. cit.

hair is shown, the nerve-fibre base. The slender cells at cerves.

f seem unconnected with

noise; when periodic it is what is nowadays called a tone, or note. The loudness of a sound depends on the force of the waves. When they recur periodically a peculiar quality called pitch is the effect of their frequency. In addition to loudness and pitch tones have each, their voice or timbre, which may differ widely in different instruments giving equally loud tones of the same pitch. This voice depends on the form of the aërial wave.

Pitch. A single puff of air, set in motion by no matter what cause, will give a sensation of sound, but it takes at least four or five puffs, or more, to convey a sensation of pitch. The pitch of the note c, for instance, is due to 132 vibrations a second, that of its octave c' is produced by twice as many, or 264 vibrations; but in neither case is it necessary for the vibrations to go on during a full second for the pitch to be discerned. "Sound vibrations may be too rapid or too slow in succession to produce sonorous sensations, just as the ultra-violet and ultra-red rays of the solar spectrum fail to excite the retina. The highestpitched audible note answers to about 38,016 vibrations in a second, but it differs in individuals; many persons cannot hear the cry of a bat nor the chirp of a cricket, which lie near this upper audible limit. On the other hand, sounds of vibrational rate about 40 per second are not well heard, and a little below this they produce rather a 'hum’than a true tone-sensation, and are only used along with notes of higher octaves to which they give a character of greater depth." *

The entire system of pitches forms a continuum of one dimension; that is to say, you can pass from one pitch to another only by one set of intermediaries, instead of by more than one, as in the case of colors. (See p. 41.) The whole series of pitches is embraced in and between the terms of what is called the musical scale. The adoption of certain arbitrary points in this scale as 'notes' has an ex

*Martin: op. cit.

planation partly historic and partly æsthetic, but too complex for exposition here.

The timbre' of a note is due to its wave-form. Waves are either simple (pendular') or compound. Thus if a tuning-fork (which gives waves nearly simple) vibrate 132 times a second, we shall hear the note c. If simultaneously a fork of 264 vibrations be struck, giving the next higher octave, c', the aërial movement at any time will be the algebraic sum of the movements due to both forks; whenever both drive the air one way they reinforce one another; when on the contrary the recoil of one fork coincides with the forward stroke of another, they detract from each other's effect. The result is a movement which is still periodic, repeating itself at equal intervals of time, but no longer pendular, since it is not alike on the ascending and descending limbs of the curves. We thus get at the fact that non-pendular vibrations may be produced by the fusion of pendular, or, in technical phrase, by their composition.

Suppose several musical instruments, as those of an orchestra, to be sounded together. Each produces its own. effect on the air-particles, whose movements, being an algebraical sum, must at any given instant be very complex; yet the ear can pick out at will and follow the tones of any one instrument. Now in most musical instruments it is susceptible of physical proof that with every single note that is sounded many upper octaves and other harmonics' sound simultaneously in fainter form. On the relative strength of this or that one or more of these Helmholtz has shown that the instrument's peculiar voice de pends. The several vowel-sounds in the human voice also depend on the predominance of diverse upper harmonics accompanying the note on which the vowel is sung. When the two tuning-forks of the last paragraph are sounded together the new form of vibration has the same period as the lower-pitched fork; yet the ear can clearly distinguish the resultant sound from that of the lower fork alone, as a note of the same pitch but of different timbre; and within

the compound sound the two components can by a trained ear be severally heard. Now how can one resultant waveform make us hear so many sounds at once?

The analysis of compound wave-forms is supposed (after Helmholtz) to be effected through the different rates of sympathetic resonance of the different parts of the membranous cochlea. The basilar membrane is some twelve times broader at the apex of the cochlea than at the base where it begins, and is largely composed of radiating fibres which may be likened to stretched strings. Now the physical principle of sympathetic resonance says that when stretched strings are near a source of vibration those whose own rate agrees with that of the source also vibrate, the others remaining at rest. On this principle, waves of perilymph running down the scala tympani at a certain rate of frequency ought to set certain particular fibres of the basilar membrane vibrating, and ought to leave others unaffected. If then each vibrating fibre stimulated the hair-cell above it, and no others, and each such hair-cell, sending a current to the auditory brain-centre, awakened therein a specific process to which the sensation of one particular pitch was correlated, the physiological condition of our several pitchsensations would be explained. Suppose now a chord to be struck in which perhaps twenty different physical rates. of vibration are found: at least twenty different hair-cells or end-organs will receive the jar; and if the power of mental discrimination be at its maximum, twenty different 'objects' of hearing, in the shape of as many distinct pitches of sound, may appear before the mind.

The rods of Corti are supposed to be dampers of the fibres of the basilar membrane, just as the malleus, incus, and stapes are dampers of the tympanic membrane, as well as transmitters of its oscillations to the inner ear. There must be, in fact, an instantaneous damping of the physiological vibrations, for there are no such positive after-images, and no such blendings of rapidly successive tones, as the retina shows us in the case of light. Helmholtz's theory of

the analysis of sounds is plausible and ingenious. One objection to it is that the keyboard of the cochlea does not seem extensive enough for the number of distinct resonances required. We can discriminate many more degrees of pitch than the 20,000 hair-cells, more or less, will allow for.

The so-called Fusion of Sensations in Hearing.-A very common way of explaining the fact that waves which singly give no feeling of pitch give one when recurrent, is to say that their several sensations fuse into a compound sensation. A preferable explanation is that which follows the analogy of muscular contraction. If electric shocks are sent into a frog's sciatic nerve at slow intervals, the muscle which the nerve supplies will give a series of distinct twitches, one for each shock. But if they follow each other at the rate of as many as thirty a second, no distinct twitches are observed, but a steady state of contraction instead. This steady contraction is known as tetanus. The experiment proves that there is a physiological cumulation or overlapping of processes in the muscular tissue. It takes a twentieth of a second or more for the latter to relax after the twitch due to the first shock. But the second shock comes in before the relaxation can occur, then the third again, and so on; so that continuous tetanus takes the place of discrete twitching. Similarly in the auditory nerve. One shock of air starts in it a current to the auditory brain-centre, and affects the latter, so that a dry stroke of sound is heard. If other shocks follow slowly, the brain-centre recovers its equilibrium after each, to be again upset in the same way by the next, and the result is that for each shock of air a distinct sensation of sound occurs. But if the shock comes in too quick succession, the later ones reach the brain before the effects of the earlier ones on that organ have died away. There is thus an overlapping of processes in the auditory centre, a physiological condition analogous to the muscle's tetanus, to which new condition a new quality of feeling, that of pitch, directly corresponds. This latter

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