THE CELESTIAL HARMONY.
Nature presents herself to us under various aspects. At times, it may be, she presents to us the appearance of discord, and we fail to perceive the unity that pervades the whole of her actions. At others, however, and most often to an instructed mind, there is a concord between her various powers, a harmony even in her sounds, that will not escape us. Even the wild notes of the tempest and the bass roll of the thunder form themselves into part of the grand chorus which in the great opera are succeeded by the solos of the evening breeze, the songs of birds, or the ripple of the waves. These are ideas that would most naturally present themselves to contemplative minds, and such must have been the students of the silent, but to them harmonious and tuneful, star-lit sky, under the clear atmosphere of Greece. The various motions they observed became indissolubly connected in their minds with music, and they did not doubt that the heavenly spheres made harmony, if imperceptible to human ears. But their ideas were more precise than this. They discovered that harmony depended on number, and they attempted to prove that whether the music they might make were audible or not, the celestial spheres had motions which were connected together in the same way as the numbers belonging to a harmony. The study of their opinions on this point reveals some very curious as well as very interesting ideas. We may commence by referring to an ancient treatise by Timæus of Locris on the soul of the universe. To him we owe the first serious exposition of the complete harmonic cosmography of Pythagoras. We must premise that, according to this school, God employed all existing matter in the formation of the universe—so that it comprehends all things, and all is in it. "It is a unique, perfect, and spherical production, since the sphere is the most perfect of figures; animated and endowed with reason, since that which is animated and endowed with reason is better than that which is not."
So begins Timæus, and then follows, as a quotation from Plato, a comparison of the earth to what would appear to us nowadays to be a very singular animal. Not only, says Plato, is the earth a sphere, but this sphere is perfect, and its maker took care that its surface should be perfectly uniform for many reasons. The universe in fact has no need of eyes, since there is nothing outside of it to see; nor yet of ears, since there is nothing but what is part of itself to make a sound; nor of breathing organs, as it is not surrounded by air: any organ that should serve to take in nourishment, or to reject the grosser parts, would be absolutely useless, for there being nothing outside it, it could not receive or reject anything. For the same reason it needs no hands with which to defend itself, nor yet of feet with which to walk. Of the seven kinds of motion, its author has given it that which is most suitable for its figure in making it turn about its axis, and since for the execution of this rotatory motion no arms or legs are wanted, its maker gave it none.
With regard to the soul of the universe, Plato, according to Timæus, says that God composed it "of a mixture of the divisible and indivisible essences, so that the two together might be united into one, uniting two forces, the principles of two kinds of motion, one that which is always the same, and the other that which is always changing. The mixture of these two essences was difficult, and was not accomplished without considerable skill and pains. The proportions of the mixture were according to harmonic numbers, so chosen that it is possible to know of what, and by what rule, the soul of the universe is compounded."
By harmonic numbers Timæus means those that are proportional to those representing the consonances of the musical scale. The consonances known to the ancients were three in number: the diapason, or octave, in the proportion of 2 to 1, the diapent, or fifth, in that of 3 to 2, and the diatessaron, or fourth, in that of 4 to 3; when to these are joined the tones which fill the intervals of the consonances, and are in the proportion of 9 to 8, and the semitones in that of 256 to 243, all the degrees of the musical scale is complete.
The discovery of these harmonic numbers is due to Pythagoras. It is stated that when passing one day near a forge, he noticed that the hammers gave out very accurate musical concords. He had them weighed, and found that of those which sounded the octave, one weighed twice as much as the other; that of those which made a perfect fifth, one weighed one third more than the other, and in the case of a fourth, one quarter more. After having tried the hammers, he took a musical string stretched with weights, and found that when he had applied a given weight in the first instance to make any particular note, he had to double the weight to obtain the octave, to add one third extra only to obtain a fifth, a quarter for the fourth, and eight for one tone, and about an eighteenth for a half-tone; or more simply still, he stretched a cord once for all, and then when the whole length sounded any note, when stopped in the middle it gave the octave, at the third it gave the fifth, at the quarter the fourth, at the eighth the tone, and at the eighteenth the semi-tone.
Since the ancients conceived of the soul by means of motion, the quantity of motion developed in anything was their measure of the quantity of its soul. Now the motion of the heavenly bodies seemed to them to depend on their distance from the centre of the universe, the fastest being those at the circumference of the whole. To determine the relative degrees of velocity, they imagined a straight line drawn outwards from the centre of the earth, as far as the empyreal heaven, and divided it according to the proportions of the musical scale, and these divisions they called the harmonic degrees of the soul of the universe. Taking the earth's radius for the first number, and calling it unity, or, in order to avoid fractions, denoting it by 384, the second degree, which is at the distance of an harmonic third, will be represented by 384 plus its eighth part, or 432. The third degree will be 432, plus its eighth part, or 486. The fourth, being a semitone, will be as 243 to 256, which will give 512; and so on. The eighth degree will in this way be the double of 384 or 768, and represents the first octave.
They continued this series to 36 degrees, as in the following table:—
The Earth.