The Continental Monthly , Vol. 2 No. 5, November 1862. Various

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СКАЧАТЬ 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.'

      But to return. When the ear accepts a tone, or the eye a single color, it is noticed that these organs, satiated finally with the sterile simplicity, echo, as it were, in a soliloquizing manner, to themselves, other notes or tints, which are the complementary or harmony-completing ones: so that if nature does not at once present a satisfaction, the organization of the senses allows them internal resources whereon to retreat. 'There is a world without, and a world within,' which may be called complementary worlds. But nature is ever liberal, and her chords are generally harmonies, or exquisite modifications of concord. The chord of the tonic, in music, is the primal type of this harmony in sound; it is perfectly satisfactory to the tympanum; and the ear, knowing no further elements (for the tonic chord combines them all), can ask for nothing more.

      This chord, constructed on the tonic C, or Do, as a key note, and consisting of the 1st, 3d, and 5th of the diatonic scale, or Do, Mi, Sol, is called the fundamental chord. The harmony in color which corresponds to this, and leaves nothing for the eye to desire, is, of course, the light that nature is full of—sunlight. White light is then the fundamental chord of color, and it is constructed on the red as the tonic, consisting of red, yellow, and blue, the 1st, 3d, and 5th of the solar spectrum.

      This little analogy is suggestive, but its development is striking.

      The diatonic scale in music, determined by calculation and actual experiment on vibrating chords, stands as follows. It will be easily understood by musicians, and its discussion appears in most treatises on acoustics:

      The intervals, or relative pitches of the notes to the tonic C, appear expressed in the fractions, which are determined by assuming the wave length or amount of vibration of C as unity, and finding the ratio of the wave length of any other note to it. The value of an interval is therefore found by dividing the wave length of the graver by that of the acuter note, or the number of vibrations of the acuter in a given time by the corresponding number of the graver. These fractions, it is seen, comprise the simplest ratios between the whole numbers 1 and 2, so that in this scale are the simple and satisfactory elements of harmony in music, and everybody knows that it is used as such. Now nature exposes to us a scale of color to which we have adverted; it is thus:

Red, Orange, Yellow, Green, Blue, Indigo, Violet

      Let us investigate this, and see if her science is as good as mortal penetration; let us see if she too has hit upon the simplest fractions between 1 and 2, for a scale of 7. We can determine the relative pitch of any member of this scale to another, easily, as the wave lengths of all are known from experiment.

      The waves of red are the longest; it corresponds, then, to the tonic. Let us assume it as unity, and deduce the pitch of orange by dividing the first by the second.

      The length of a red wave is 0.0000266 inches; the length of an orange wave is 0.0000240 inches; the fraction required then is 266/240; dividing both members of this expression by 30, it reduces to 9/8, almost exactly. This is encouraging. We find a remarkable coincidence in ratio, and in elements which occupy the same place on the corresponding scales. Again, the length of a yellow wave is 0.0000227 inches; its pitch on the scale is therefore 266/227; dividing both terms by 55, the reduced fraction approximates to 5/4 with great accuracy, when we consider the deviations from truth liable to occur in the delicate measurements necessary to determine the length of a light vibration, or the amount of quiver in a tense cord. A green wave is 0.0000211 inches in length; its pitch is then 266/211, which reduced, becomes 4/3; in like manner the subsequent intervals may be determined, which all prove to be complete analogues, except, perhaps, violet, whose fraction is 266/167, which reduces nearer 16/9 than 15/8. But these small discrepancies, which might be expected in the results of physical measurements, do not cripple the analogy which appears now in the two following scales:

DIATONIC OR NATURAL SCALE OF MUSIC

DIATONIC OR NATURAL SCALE OF COLOR

      Thus orange is to red what D is to C; and to resume the proportion we used before, red is to eye as C is to ear; yellow: eye: Mi: ear; and so on the proportion extends, till the analogy embraces chords, harmonies, melodies, and compositions even.

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