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:
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:
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.
We have already mentioned the chord of the tonic, and the corresponding eye-music, red, yellow, and blue; let us consider the chord of the dominant or 5th note, whose analogue is blue. This chord is constructed on the 5th of the diatonic as a fundamental note, and consists of the 5th, 7th, and 9th, or returning the 9th an octave, the 5th, 7th, and 2d. The parallel harmony among the spectral colors is blue, violet, and orange. The name 'dominant' indicates the nature of this chord; its often recurring importance in harmonic combinations of a certain key make it easily recognized, and it is even more pleasing than the tonic in its subdued character.
Out of doors this chord is preëminent in the sunset key, and the western skies ever chant their evening hymn in the 5th, 7th, and 2d of the ethereal music. The correspondence of the sub-dominant would be red, green, and indigo; of the chord of the 6th, red, yellow, and indigo; and so on, the curious mind may elicit the symmetrical to any notes, half notes, or combinations of notes. It is evident that as a note may be interpolated between any two of the scale, for reach or variety, and called, e.g. ♯F or ♭G, so a half tint between green and blue is a kind of analogical ♯ green or ♭ blue.
It seems to us that the elementary angles which Mr. Hay conceives to be the tonic, mediant, and dominant, in formal symmetry, will soon be proved to decompose into a scale of linear harmony, forming another beam in this glory of natural analogy. These angles are the fundamental ones of the pentagon square, and equilateral triangle—respectively 108°, 90°, and 60°. Some such scale it is known existed when art was at its culmination in buried Greece, and it was less the stupendous genius of her designers than the soul of the universe which their rules taught them how to infuse into form, which rendered the marbles of Hellas synonymes for immortality.
The most beautiful and conclusive, and yet most mysterious sign, that points the seeker to the prosecution of this last analogy, remains yet for us to remark, and for some investigator yet to take advantage of. It is the nodal figures which arrange themselves upon an elastic plate (as of glass), when it is made to vibrate (strewed with sand) by a fiddle bow drawn across its edge, so as to produce a pitch of some intensity. These