By the side of magnitudes perceived by sight there are magnitudes perceived by the hearing,—I mean the velocities of sonorous vibrations; and these vibrations being magnitudes may also form aggregates of parts connected by mathematical laws. In the first place, as you are aware, a musical sound is composed of continuous vibrations of equal velocity, and this equality already places between them a mathematical relationship; in the second place, two sounds being given, the second may be composed of vibrations, two, three, or four times the rapidity of the first; accordingly, there is between these two sounds a mathematical relationship, which is figured by placing them at an equal distance from each other on the musical stave. If, consequently, instead of taking two, we take a number of sounds, and place them at equal distances,—we form a scale, which scale is the gamut, all the sounds being thus bound together according to their relative position on the gamut. You can now establish these connections either between successive or simultaneous sounds, the first order of sounds constituting melody, and the second harmony. This is music: it has two essential parts, based, like architecture, on mathematical relationships, which the artist is free to combine and modify.
Music, however, possesses a second property, and this new element gives it a peculiar quality and no ordinary scope. Besides its mathematical qualities, sound is analogous to the cry, and by this title it directly expresses with unrivalled precision, delicacy and force, suffering, joy, rage, indignation—all the agitations and emotions of an animated sensitive being, even to the most secret and most subtle gradations. From this point of view it is similar to poetic declamation, furnishing a specific type of music, called the music of expression, like that of Gluck and the Germans, in opposition to the music of melody, that of Rossini and the Italians. Let the composer's point of view be what it may, the two styles of music are nevertheless related to each other, sounds always forming aggregates of parts linked together at once by their mathematical relationship and by the correspondence which they have with the passions and the various internal states of the moral being. The musician, therefore, who conceives a certain salient, important feature of things, let it be sadness or joy, tender love or passionate rage, any idea or sentiment whatever, may freely select and combine in such a way in these mathematical and moral relationships as to manifest the character which he has conceived.
All the arts are thus included in the definition above presented. In architecture and music, as in sculpture, painting, and poetry, it is the object of a work of art to manifest some essential character, and to employ as means of expression an aggregate of connected parts, the relationship of which the artist combines and modifies.
[VII.]
Now that we know the nature of art, we can comprehend its importance. Previously we were only sensible of its effect; it was a matter of instinct, and not of reason: we were conscious of respecting and esteeming art, but were not qualified to account for our respect and esteem. Our admiration for art can now be justified, and we can mark its place in the order of life.
Man, in many respects, is an animal endeavoring to protect himself against nature and against other men. He is obliged to provide himself with food, clothing, and shelter, and to defend himself against climate, want, and disease. To do this he tills the ground, navigates the sea, and devotes himself to different industrial and commercial pursuits. Furthermore, he must perpetuate his species, and secure himself against the violence of his fellow-men; to this end, he forms families and states, and establishes magistracies, functionaries, constitutions, laws, and armies. After so many inventions and such labor, he is not yet emancipated from his original condition; he is still an animal, better fed and better protected than other animals; he still thinks only of himself, and of his kindred. At this moment a superior life dawns on him—that of contemplation, by which he is led to interest himself in the creative and permanent causes on which his own being and that of his fellows depend, in the leading and essential characters which rule each aggregate, and impress their marks on the minutest details. Two ways are open to him for this purpose. The first is Science, by which, analyzing these causes and these fundamental laws, he expresses them in abstract terms and precise formula; the second is Art, by which he manifests these causes and these fundamental laws no longer through arid definitions, inaccessible to the multitude, and only intelligible to a favored few, but in a sensible way, appealing not alone to reason, but also to the heart and senses of the humblest individual. Art has this peculiarity, that it is at once noble and popular, manifesting whatever is most exalted, and manifesting it to all.