The Body at Work: A Treatise on the Principles of Physiology

by Alex Hill

The quality of a musical note depends upon the number and relative loudness of its overtones. When several notes are sounded simultaneously, they blend into a chord or harmony, provided the intervals which separate them are equal to the intervals which separate the simpler overtones. Each of the notes yields overtones. The tones blend into a concord. Their partials are in unison. The variations in air-pressure of the compound tone are strictly periodic. If the ratios of the frequencies of its constituent notes are simple the product is a rich, full sound, such as a common chord.

At least one other character of the pulsations of sound must be taken into consideration if we wish to picture the nature of the force to which the ear responds. Tones which reach it from several instruments simultaneously are not necessarily in unison, or even in harmony. The overtones of a single note sounded on a piano or violin—the statement does not hold good for bells, nor is it strictly true of flutes or horns—must necessarily bear a simple proportional relation to their prime tone. They divide the grand pulsation into fractions “without a remainder.” But the vibrations of two tuning-forks which are slightly out of unison interfere one with the other at regular intervals. They produce “beats.” Everyone is familiar with the curious effect which is produced upon the eye when one row of railings is seen through another, or one expanse of wire-netting behind another. Sets of lines which occupy nearly the same positions in the line of sight combine to make a large pattern, which overlies the smaller pattern of the rails or netting. The same thing happens with sounds which coincide at considerable intervals, although in the case of sounds interference is as marked as reinforcement. If whilst a tuning-fork yielding 101 vibrations per second is singing another of 100 vibrations is brought into play, the vibrations of the second fork are superposed on those of the first. At a certain moment the forward movement of molecules of air induced by the first fork is reinforced by a forward push from the second. But half a second after this coincidence of phase an opposite result is produced—50½ vibrations of No. 1 have passed, but only 50 of No. 2. No. 2 is going backwards (inwards), whilst No. 1 is moving forwards (outwards). The same molecules are impelled backwards by No. 2 and forwards by No. 1. The result is a pause. The compound sound produced by the two forks reaches the ear in throbs. If the forks were vibrating at the rates of 101 and 99, there would be two pauses and two beats in every second; if at the rate of 202 and 198, four. The number of beats per second equals the difference in frequency of vibration of the tones. A pianoforte tuner does his work best if he has a musical ear, yet he may discharge his duties with competence without one. Having struck a note, he sounds its octave, holding both keys down, and listens for the beat. If the first note gave no beat with his tuning-fork, the second is in time when it likewise gives no beat with the first. We have met a tuner who did his work in this way; but it must be admitted that his tempering of the intervals of the octave with which he commenced, and consequently of the other octaves above and below it, left something to be desired. The result might have been satisfactory had he been provided with twelve tuning-forks.

The question as to whether beats, when sufficiently rapid, blend into a tone has been much discussed, without a decision. Probably they do not. The complementary question as to the cause of dissonance is also not completely closed. Two notes harmonize, as we have seen, when the ratio of their frequencies is a simple fraction. Musicians are not quite agreed as to the level of numerical complexity at which a compound tone first produces a feeling of discomfort. A good deal depends upon its position in the scale and the instruments which are combining to produce it. A minor third (⁶/₅) is on the safe side. This is the first chord in our list of intervals in which a beat can be detected. Slow beats, however, do not distress us. It is the rapid beats of conflicting overtones which give a harsh, rough character to a compound note. The level at which a line is drawn between harmony and dissonance seems to depend to a considerable extent upon musical education, using the term in its widest sense. In primitive music—Hungarian, Scotch, Welsh—intricate minor chords predominate. The minute subdivision of the octave in Indian music is quite incomprehensible to a European ear. Musical cultivation tends to eliminate complex fractions. It is, however, to be noted that the history of Western music also shows the influence of an opposite tendency. Later generations have admitted as harmonies combinations which earlier generations could not tolerate.

Pitch, quality, harmony, and dissonance are distinguished by the human ear. These are the attributes of musical or periodic sounds. In a separate class must be included noises of all kinds, termed in acoustics “aperiodic,” because the vibrations which cause them are not rhythmic. The teeth of a policeman’s rattle may click a hundred times a second, but it does not make music. Even with a rapidity of interruption greater than this (at least 500 times per second) a succession of noises fails to blend into a smooth, continuous sound. The ear recognizes the loudness, duration, and even to a very high frequency the repetition of unmusical sounds.

The ear as a sense-organ can be followed down the zoological scale to jelly-fish. In its primitive form it is a chamber lined with epithelial cells bearing hairs, containing an otolith, or ear-stone. Otoliths are rounded calcareous masses which play an important part in the ears of all animals up to fishes. Even in man they are found in the more subdivided form of otoconia. Contact of the otoliths with the sensory hairs originates impulses in the nerves with which primitive ears are abundantly provided. Advisedly we use the word “ear” in place of “auditory organ.” In all animals this organ affords information of a double nature-movement of the external medium in which the animal lives, and movements of the animal in the medium. When the animal moves, its sensory hairs are displaced with regard to the otolith; when the water in which it is swimming pulsates, its otoliths are shaken against the sensory hairs. Displacements of the animal and agitations of the water produce similar effects. The ear in this stage is an organ of touch. It might well be questioned whether an animal fitted with a piece of sensory apparatus of this kind is endowed with a sense which we may properly, after reflecting upon our own sensations, term “hearing.” It is, however, stated that certain transparent crustaceans, in which the functioning of the ear-organs may be watched through a lens, show in these organs hairs of varying length which vibrate to tones of different frequency. This observation apart, it might be doubted whether fishes hear, if we mean by the word “hearing” the recognition and discrimination of tones of high frequency—musical tones. Their ears serve equally to inform them of the changes in position of their heads and of the tremblings of the sea. The shocks transmitted through the sea are near akin to the slower vibrations of sound, if the fishermen of the Mediterranean are justified in their practice of beating a wooden clapper which rests upon the seat of the boat as they row backwards and forwards in front of a curved net. They believe that the fish are frightened by the noise; but it matters little whether we describe the fish as hearing a noise, or as feeling the percussions of the clapper conducted through the water. To the more rapid vibrations of the clapper, the fish are probably insensitive. The cochlea, which we have every reason for regarding as the organ by which sound is analysed, is not possessed by fishes. It makes its first appearance in reptiles. Birds, it is evident, are able to distinguish musical tones. Their cochleæ are very short, and are destitute of “rods of Corti.” For a moment this appears surprising, but it must be remembered that the range of tones which any bird discriminates is very short, however nicely it may value the notes within its range. In mammals the ear is clearly divided into three parts, to which the three functions which have grown out of the specialization of the sense of touch are allocated. (1) The semicircular canals are concerned with the sense of orientation. (2) The utricle and saccule reverberate to noise—the rumbling of trains, the boom of guns, the beats of dissonant musical tones. We do not know how to classify the agitations of the atmosphere which surrounds us and of the earth on which we stand, nor can we point with any certainty to the groups of stimuli which for us have taken the place of the grinding of stones on the beach and slapping of rocks by waves. (3) The organ of Corti in the cochlea discriminates and analyses musical sounds. To these three sense-organs, which are situate in the inner ear, certain structures are accessory.

The concha, which enables a horse or a cat to collect sound and to localize its source, is in ourselves merely an ornament to the side of the head.

Fig. 38.—The External, Middle, and Internal Ear of the Left Side.

From right to left, the figure shows the concha and lobule of the ear in profile; the external meatus (abbreviated); the drum, divided vertically, its posterior half visible; the hammer-bone, with the tip of its long arm attached to the drum, an arrow indicating the point of attachment and line of action of the tensor tympani muscle; the anvil attached by a ligament to the bony wall of the middle ear; the stirrup, with its foot-plate almost filling the oval window; the labyrinth, with the three semicircular canals above, and the scala vestibuli below. The curled black line shows the situation of the scala media, or ductus cochleæ (which contains the organ of Corti). Pulsations of sound which move the membrana tympani are transmitted by the three bones to the oval window. They shake the perilymph, producing waves which travel along the scala vestibuli to the apex of the cochlea, whence they return by the scala tympani to the round window (if they do not take a shorter course through the ductus cochleæ). The Eustachian tube opens out of the lower part of the middle ear.