That this mathematical turn of expression is no vagary, but perfectly germane to the subject, and accurate in application, we propose to prove to those who love coincidences and analogies sufficiently to fish them out of a little dilute science.
Light and sound are the daughters of motion. Color and music, the ethereal and aërial offspring of this ancestry, born with the world, fostered in Biblical times, expanded in China and Egypt, living on the painted jar, and breathing in the oaten reed, deified in Greece, and analyzed to-day, are natural cousins at the least, and they have come from the spacious home of their progenitor, upon our dusky and silent sphere, like Peace and Goodwill, with hands bound in an oath and contract never to part. We will spare a dissertation on chaos; we will not speak of matter and inertia; but as our greatest and purest fountain of light is the sun, we may be allowed a modest exposition of his philosophical state, as a granite gate to the garden beyond. Ninety-five millions of miles to the north, east, south, or west of us, up or down, as the case may be, stands the molten centre of our system—an orb, whose atoms, turbulent with electricity, gravity, or whatever mechanists please to call the attraction of particle for particle, are forever urging to its centre, forever meeting with repulsions when they slide within the forbidden limits of molecular exclusiveness, and eternally vibrating with a quake and quiver which lights and heats the worlds around. In other words, this agitation is one that, transmitted to an ethereal medium, produces therein corresponding vibrations or waves, which are light and heat.
As sound is the symmetrical aërial motion, if our atmosphere embraced our sun, and extended throughout space, we should perhaps hear in the ambient the fundamental chord, resolvable into the diatonic scale—as we look upon the beam of white which the prism decomposes into the solar spectrum, and in the ghostly watches of the night, we might recognize the 'music of the spheres' as the planets rushed around their airy orbits, with a noise like the 'noise of many waters,' no longer a poetic illusion, but a harmonic fact.
Light, whether white or colored, is transmitted through ether in waves of measurable length: each atom of the medium, when disturbed, moves around its place of rest in an orbit of variable dimension and eccentricity. On the character of the orbit depends the character of the light; and on the velocity of orbit motion, its intensity. Like the gentle pulsations which circle from the point where fell the pebble in the purple lake, come the grateful twilight waves, red with the last kiss of day; like the fierce struggles of the storm-beaten ocean floods come the lightning waves, blazing through the thunder clouds, howling in riven agony: so great is the variety of character in these orbicular disturbances, which, acting upon the optic nerves, produce the sensation of multiform light and color.
Waves of light, like waves of sound, are of different lengths, and while the eye prefers some single waves to others, it recognizes a harmony in certain combinations, which it cannot discover in different ones.
While, however, the constitution of individual eyes acknowledges one color more pleasing than another, there is none, perhaps, which does not prefer the coldest monochromatic to entire absence of color, as in blank white, or to an absolute vacancy of light, as in black.
Sepia pieces are more agreeable than the neatest drawings in China ink, or the most graceful curves done in chalk upon a blackboard. But however the eye may admire a severe and simple unity, it relishes still more a harmonious complexity; and a very mediocre little pensée in water colors, will prove more generally attractive than the monochromatic copies in the Liber Veritatis.
But to this complexity there must be limits—an endless and incongruous variety teases and revolts; the discordant effect of innumerable tints, among which some are sure to be uncongenial to each other, is always extremely irritating. There ought, then, to be a scale of color, it would seem, within whose limits the purest harmonies are to be found, and beyond which subdivisions should be no more allowed than in constant musical notes. When this idea strikes, as it must have, many artists, reason, consideration, instinct, and all, refer at once to the solar spectrum as such an one. The analogy between this scale, which governs the chromatics of the sunset and thunderstorm, and that which the science of man has established, empirically, for harmonies, is remarkable, and we shall try to make it patent. They are both scales of seven: the tonic, mediant, and dominant, find their types in red, yellow, and blue, while the modifications on which the diatonic scale is constructed, resemble, numerically and esthetically, the well-known variations in the spectrum.
The theory of harmonies in optics is the same as in acoustics, the same as in everything—it is based on simplicity. Those colors, like those notes, the number of whose vibrations or waves in the same time bear some simple ratio to each other, are harmonious; an absolute equality produces unison; and a group of harmonies is melody both in music and in color. At this point we cannot but hint at the analogy already discovered between the elements of music and the elements of form. Angles harmonize in simple analysis, or intricate synthesis, whose circular ratios are simple.
Numerical proportions are the roots of that shaft of harmony which, springing from motion, rises and spreads into the nature around us, which the senses appreciate, the spirit feels, and the reason understands. Beauty is order, and the infinity of the law is testified in the ever-swelling proofs of an unlimited consonance in creation, of which these analogies are the smallest types. But the idea of numerical analogy is not new to our age, now that the atomic theory is established, and people are turned back to the days when the much bescouted alchemist pored with rheumy eyes over the crucible, about to be the tomb of elective affinity, and whence a golden angel was to develop from a leaden saint: when they are reminded of the Pythagorean numbers, and the arithmetic of the realists of old, they may very well imagine that the vain world, like an empty fashion, has cycled around to some primitive phase, and look for the door of that academy 'where none could enter but those who understood geometry.'