It is by means of the cochlea that we discriminate pitch, hear beats, and are affected by quality of tone.

Since the size of the membranous labyrinth is so small, measuring, in man, not more than ½ in. in length by 1⁄8 in. in diameter at its widest part, and since it is a chamber consisting partly of conduits of very irregular form, it is impossible to state accurately the course of vibrations transmitted to it by impulses communicated from the base of the stirrup. In the cochlea vibrations must pass from the saccule along the scala vestibuli to the apex, thus affecting the membrane of Reissner, which forms its roof; then, passing through the opening at the apex (the helicotrema), they must descend by the scala tympani to the round window, and affect in their passage the membrana basilaris, on which the organ of Corti is situated. From the round window impulses must be reflected backwards, but how they affect the advancing impulses is not known. But the problem is even more complex when we take into account the fact that impulses are transmitted simultaneously to the utricle and to the semicircular canals communicating with it by five openings. The mode of action of these vibrations or impulses upon the nervous terminations is still unknown; but to appreciate critically the hypothesis which has been advanced to explain it, it is necessary, in the first place, to refer to some of the general characters of auditory sensation.

4. General Characters of Auditory Sensations.—Certain conditions are necessary for excitation of the auditory nerve sufficient to produce a sensation. In the first place, the vibrations must have a certain amplitude and energy; if too feeble, no impression will be produced.

Various physicists have attempted to measure the sensitiveness of the ear by estimating the amplitude of the molecular movements necessary to call forth the feeblest audible sound. Thus A. Töpler and L. Boltzmann, on data founded on experiments with organ pipes, state that the ear is affected by vibrations of molecules of the air not more in amplitude than .0004 mm. at the ear, or 0.1 of the wave-length of green light, and that the energy of such a vibration on the drum-head is not more than 1⁄543 billionth kilog., or 1⁄17th of that produced upon an equal surface of the retina by a single candle at the same distance (Ann. d. Phys. u. Chem., Leipzig. 1870, Bd. cxli. S. 321). Lord Rayleigh, by two other methods, arrived at the conclusion “that the streams of energy required to influence the eye and ear are of the same order of magnitude.” He estimated the amplitude of the movement of the aërial particles, with a sound just audible, as less than the ten-millionth of a centimetre, and the energy emitted when the sound was first becoming audible, at 42.1 ergs per second. He also states that in considering the amplitude or condensation in progressive aërial waves, at a distance of 27.4 metres from a tuning-fork, the maximum condensation was = 6.0 × 10−9 cm., a result showing “that the ear is able to recognize the addition or subtraction of densities far less than those to be found in our highest vacua” (Proc. Roy. Soc., 1877, vol. xxvi. p. 248; Lond. Edin. and Dub. Phil. Mag., 1894, vol. xxxviii. p. 366).

In the next place, vibrations must have a certain duration to be perceived; and lastly, to excite a sensation of a continuous musical sound, a certain number of impulses must occur in a given interval of time. The lower limit is about 30, and the upper about 30,000 vibrations per second. Below 30, the individual impulses may be observed, and above 30,000 few ears can detect any sound at all. The extreme upper limit is not more than 35,000 vibrations per second. Auditory sensations are of two kinds—noises and musical sounds. Noises are caused by impulses which are not regular in intensity or duration, or are not periodic, or they may be caused by a series of musical sounds occurring instantaneously so as to produce discords, as when we place our hand at random on the keyboard of a piano. Musical tones are produced by periodic and regular vibrations. In musical sounds three characters are prominent—intensity, pitch and quality. Intensity depends on the amplitude of the vibration, and a greater or lesser amplitude of the vibration will cause a corresponding movement of the transmitting apparatus, and a corresponding intensity of excitation of the terminal apparatus. Pitch, as a sensation, depends on the length of time in which a single vibration is executed, or, in other words, the number of vibrations in a given interval of time. The ear is capable of appreciating the relative pitch or height of a sound as compared with another, although it may not ascertain precisely the absolute pitch of a sound. What we call an acute or high tone is produced by a large number of vibrations, while a grave or low tone is caused by few. The musical tones which can be used with advantage range between 40 and 4000 vibrations per second, extending thus from 6 to 7 octaves. According to E. H. Weber, practised musicians can perceive a difference of pitch amounting to only the 1⁄64th of a semitone, but this is far beyond average attainment. In a few individuals, and especially in early life, there may be an appreciation of absolute pitch. Quality or timbre (or Klang) is that peculiar characteristic of a musical sound by which we may identify it as proceeding from a particular instrument or from a particular human voice. It depends on the fact that many waves of sound that reach the ear are compound wave systems, built up of constituent waves, each of which is capable of exciting a sensation of a simple tone if it be singled out and reinforced by a resonator (see [Sound]), and which may sometimes be heard without a resonator, after special practice and tuition. Thus it appears that the ear must have some arrangement by which it resolves every wave system, however complex, into simple pendular vibrations. When we listen to a sound of any quality we recognize that it is of a certain pitch. This depends on the number of vibrations of one tone, predominant in intensity over the others, called the fundamental or ground tone, or first partial tone. The quality, or timbre, depends on the number and intensity of other tones added to it. These are termed harmonic or partial tones, and they are related to the first partial or fundamental tone in a very simple manner, being multiples of the fundamental tone: thus—

Fundamental
Tone		 Upper Partials or Harmonics.
Notes do1 do2 sol2 do3 mi3 sol3 si♭3 do4 re4 mi4
Partial tones 1 2 3 4 5 6 7 8 9 10
Number of vibrations 33 66 99 132 165 198 231 264 297 330

When a simple tone, or one free from partials, is heard, it gives rise to a simple, soft, somewhat insipid sensation, as may be obtained by blowing across the mouth of an open bottle or by a tuning-fork. The lower partials added to the fundamental tone give softness combined with richness; while the higher, especially if they be very high, produce a brilliant and thrilling effect, as is caused by the brass instruments of an orchestra. Such being the facts, how may they be explained physiologically?

Little is yet known regarding the mode of action of the vibrations of the fluid in the labyrinth upon the terminal apparatus connected with the auditory nerve. There can be no doubt that it is a mechanical action, a communication of impulses to delicate hair-like processes, by the movements of which the nervous filaments are irritated. In the human ear it has been estimated that there are about 3000 small arches formed by the rods of Corti. Each arch rests on the basilar membrane, and supports rows of cells having minute hair-like processes. It would appear also that the filaments of the auditory nerve terminate in the basilar membrane, and possibly they may be connected with the hair-cells. At one time it was supposed by Helmholtz that these fibres of Corti were elastic and that they were tuned for particular sounds, so as to form a regular series corresponding to all the tones audible to the human ear. Thus 2800 fibres distributed over the tones of seven octaves would give 400 fibres for each octave, or nearly 33 for a semitone. Helmholtz put forward the hypothesis that, when a pendular vibration reaches the ear, it excites by sympathetic vibration the fibre of Corti which is tuned for its proper number of vibrations. If, then, different fibres are tuned to tones of different pitch, it is evident that we have here a mechanism which, by exciting different nerve fibres, will give rise to sensations of pitch. When the vibration is not simple but compound, in consequence of the blending of vibrations corresponding to various harmonics or partial tones, the ear has the power of resolving this compound vibration into its elements. It can only do so by different fibres responding to the constituent vibrations of the sound—one for the fundamental tone being stronger, and giving the sensation of a particular pitch to the sound, and the others, corresponding to the upper partial tones, being weaker, and causing undefined sensations, which are so blended together in consciousness as to terminate in a complex sensation of a tone of a certain quality or timbre. It would appear at first sight that 33 fibres of Corti for a semitone are not sufficient to enable us to detect all the gradations of pitch in that interval, since, as has been stated above, trained musicians may distinguish a difference of 1⁄64th of a semitone. To meet this difficulty, Helmholtz stated that if a sound is produced, the pitch of which may be supposed to come between two adjacent fibres of Corti, both of these will be set into sympathetic vibration, but the one which comes nearest to the pitch of the sound will vibrate with greater intensity than the other, and that consequently the pitch of that sound would be thus appreciated. These theoretical views of Helmholtz have derived much support from experiments of V. Hensen, who observed that certain hairs on the antennae of Mysis, a Crustacean, when seen with a low microscopic power, vibrated with certain tones produced by a keyed horn. It was seen that certain tones of the horn set some hairs into strong vibration, and other tones other hairs. Each hair responded also to several tones of the horn. Thus one hair responded strongly to d♯ and d′♯, more weakly to g, and very weakly to G. It was probably tuned to some pitch between d″ and d″♯. (Studien über das Gehörorgan der Decapoden, Leipzig, 1863.)

Histological researches have led to a modification of this hypothesis. It has been found that the rods or arches of Corti are stiff structures, not adapted for vibrating, but apparently constituting a support for the hair-cells. It is also known that there are no rods of Corti in the cochlea of birds, which are capable nevertheless of appreciating pitch. Hensen and Helmholtz suggested the view that not only may the segments of the membrana basilaris be stretched more in the radial than in the longitudinal direction, but different segments may be stretched radially with different degrees of tension so as to resemble a series of tense strings of gradually increasing length. Each string would then respond to a vibration of a particular pitch communicated to it by the hair-cells. The exact mechanism of the hair-cells and of the membrana reticularis, which looks like a damping apparatus, is unknown.

5. Physiological Characters of Auditory Sensation.—Under ordinary circumstances auditory sensations are referred to the outer world. When we hear a sound, we associate it with some external cause, and it appears to originate in a particular place or to come in a particular direction. This feeling of exteriority of sound seems to require transmission through the membrana tympani. Sounds which are sent through the walls of the cranium, as when the head is immersed in, and the external auditory canals are filled with, water, appear to originate in the body itself.