It has long been known that there is especially close connection between sounds and motor innervations. All sorts of sensorial stimuli produce reflex contractions, but the auditory, apparently, to a much higher degree. Animals are excited to all sorts of outbreaks by noise; children are less alarmed by visual than by auditory impressions. The fact that we dance to sound rather than to the waving of a baton, or rhythmical flashes of light for instance—the fact that this second proposition is felt at once to be absurd, shows how intimately the two are bound together. The irresistible effects of dance, martial music, etc., are trite commonplaces; and I shall therefore not heap up instances which can be supplied by every reader from his own experience. Now all this is not hard to understand, biologically. The eye mediated the information of what was far enough away to be fled from, or prepared for; the ear what was likely to be nearer, unseen, and so more ominous. As more ominous, it would have to be responded to in action more quickly. So that if any sense was to be in especially close connection with the motor centres, it would naturally be hearing.

The development of the auditory functions points to the same close connection of sound and movement. Sounds affect us as tone, and as impulse. The primitive sensation was one of impulse alone, mediated by the "shake-organs." These shake- organs at first only gave information about the attitude and movements of the body, and were connected with motor centres so as to be able to reestablish equilibrium by means of reflexes. The original "shake-organ" developed into the organs of hearing and of equilibrium (that is, the cochlea and the semicircular canals respectively), but these were still side by side in the inner ear, and the close connection with the motor centres was not lost. Anatomically, the auditory nerve not only goes to those parts of the brain whence the motor innervation emanates, and to the reflex centres in the cerebellum, but passes close by the vagus or pneumogastric nerve, which rules the heart and the vasomotor functions. We have then multiplied reasons for the singular effect of sound on motor reactions, and on the other organic functions which have so much to do with feeling and emotion.

Every sound-stimulus is then much more than sound-sensation. It causes reflex contractions in the whole muscular system; it sets up some sort of cardiac and vascular excitation. This reaction is in general in the direction of increased amplitude of respiration, but diminution of the pulse, depending on a peripheral vaso-constriction. Moreover, this vasomotor reaction is given in a melody or piece of music, not by its continuity, but for every one of the variations of rhythm, key, or intensity,—which is of interest in the light of what has been said of the latent motor image. The obstacle in syncopated rhythm is physiologically translated as vaso-constriction. In general, music induces cardiac acceleration.

All this is of value in showing how completely the attention- motor theory of rhythm applies to the rhythm of sounds. Since sound is much more than sound, but sound-sensation, movement, and visceral change together, we can see that the rhythmical experience of music is, even more literally and completely than at first appeared, an EMBODIED expectation. No sensorial rhythm could be so completely induced in the psychological organism as the sound-rhythm. In listening to music, we see how it is that we ourselves, body and soul, seem to be IN the rhythm. We make it, and we wait to make it. The satisfaction of our expectation is like the satisfaction of a bodily desire or need; no, not like it, it IS that. The conditions and causes of rhythm and our pleasure in it are more deeply seated than language, custom, even instinct; they are in the most fundamental functions of life. This element of music, at least, seems not to have arisen as a "natural language."

IV

The facts of the relations of tones, the elements, that is, of melody and harmony, are as follows. We cannot avoid the observation that certain tones "go together," as the phrase is, while others do not. This peculiar impression of belonging together is known as consonance, or harmony. The intervals of the octave, the fifth, the third, for instance, that is, C-C', C-G, C-E, in the diatonic scale, are harmonious; while the interval of the second, C-D, is said to be dissonant. Consonance, however, is not identical with pleasingness, for different combinations are sometimes pleasing, sometimes displeasing. In the history of music we know that the octave was to the Greeks the most pleasing combination, to medieval musicians the fifth, while to us, the third, which was once a forbidden chord, is perhaps most delightful. Yet we should never doubt that the octave is the most consonant, the fifth and the third the lesser consonant of combinations. We see, thus, that consonance, whatever its nature, is independent of history; and we must seek for its explanation in the nature of the auditory process.

Various theories have been proposed. That of Helmholtz has held the field so long that, although weighty objections have been raised to it, it must still be treated with respect. In introducing it a short review of the familiar facts of the physics and physiology of hearing may not be out of place.

The vibration rates per second of the vibrating bodies, strings, steel rods, etc., which produce those musical tones which are consonant, are in definite and small mathematical ratios to each other. Thus the rates of C-C' are as 1:2; of C-G, C-E, as 2:3, 4:5. In general, the simpler the fraction, the greater the consonance.

But no sonorous body vibrates in one single rate; a taut string vibrates as a whole, which gives its fundamental tone, but also in halves, in fourths, etc., each giving out a weaker partial tone, in harmony with the fundamental. And according to the different ways in which a sonorous body divides, that is, according to the different combination of partial tones peculiar to it, is its especial quality of tone, or timbre. The whole complex of fundamental and partial tones is what we popularly speak of as a tone,—more technically a clang. These physical agitations or vibrations are transmitted to the air. Omitting the account of the anatomical path by which they reach the inner ear, we find them at last setting up vibrations in a many-fibred membrane, the basilar membrane, which is in direct connection with the ends of the auditory nerve. It is supposed that to every possible rate of vibration, that is, every possible tone, or partial tone, there corresponds a fibre of the basilar membrane fitted by its length to vibrate synchronously with the original wave-elements. The complex wave is thus analyzed into its constituents. Now when two tones, which we will for clearness suppose to be simple, unaccompanied by partial tones, sounding together, have vibration rates in simple ratios to each other, the air- waves set in motion do not interfere with each other, but combine into a complex but homogeneous wave. If they have to each other a complicated ratio, such as 500:504, the air- waves will not only not coalesce, but four times in the second the through of one wave will meet the crest of the other, thus making the algebraic sum zero, and producing the sensation of a momentary stoppage of the sound. When these stoppages, or beats, as they are called, are too numerous to be heard separately, as in the interval, say, 500:547, the effect is of a disagreeable roughness of tone, and this we call discord. In other words, any tones which do not produce beats are harmonious, or harmony is the absence of discord. In the words of Helmholtz,<1> consonance is a continuous, dissonance an intermittent, tone-sensation.

<1> Lehre v.d. Tonempfindungen, p. 370, in 4th edition.