CHAPTER VII.

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 Timaeus 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 Timaeus, 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 Timaeus, 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 Timaeus 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.

Mi 384 + 1/8 = 432 Re 432 + 1/8 = 486 Ut 486 : 512 : : 243 : 256 Si 512 + 1/8 = 576 La 576 + 1/8 = 648 Sol 648 + 1/8 = 729 Fa 729 : 768 : : 243 : 256 Mi 768 + 1/8 = 864 Re 864 + 1/8 = 972 Ut 972 : 1024 : : 243 : 256 Si 1024 + 1/8 = 1152 La 1152 + 1/8 = 1296 Sol 1296 + 1/8 = 1458 Fa 1458 : 1536 : : 243 : 256 Mi 1536 + 1/8 = 1728 Re 1728 + 1/8 = 1944 Ut 1944 : 2048 : 243 : 256 Si 2048 + 139 = 2187 Si 2 2187 : 2304 : : 243 : 256 La 2304 + 1/8 = 2592 Sol 2592 + 1/8 = 2916 Fa 2916 : 3072 : : 243 : 256 Mi 3072 + 1/8 = 3456 Re 3457 + 1/8 = 3888 Ut 3888 + 1/8 = 4374 Si 4374 : 4608 : : 243 : 256 La 4608 + 1/8 = 5184 Sol 5184 + 1/8 = 5832 Fa 5832 : 6144 : : 243 : 256 Mi 6144 + 417 = 6561 Mi 2 6561 : 6912 : : 243 : 256 Re 6912 + 1/8 = 7776 Ut 7776 + 1/8 = 8748 Si 8748 : 9216 : : 243 : 256 La 9216 + 1/8 = 10368 Sol 10368 = 384 + 27

The empyreal heaven. Sum of all the terms, 114,695.

This series they considered a complete one, because by taking the terms in their proper intervals, the last becomes 27 times the original number, and in the school of Pythagoras this 27 had a mystic signification, and was considered as the perfect number.

The reason for considering 27 a perfect number was curious. It is the sum of the first linear, square, and cubic numbers added to unity. First there is 1, which represents the point, then 2 and 3, the first linear numbers, even and uneven, then 4 and 9, the first square or surface numbers, even and uneven, and the last 8 and 27, the first solid or cubic numbers, even and uneven, and 27 is the sum of all the former. Whence, taking the number 27 as the symbol of the universe, and the numbers which compose it as the elements, it appeared right that the soul of the universe should be composed of the same elements.

On this scale of distances, with corresponding velocities, they arranged the various planets, and the universe comprehended all these spheres, from that of the fixed stars (which was excluded) to the centre of the earth. The sphere of the fixed stars was the common envelope, or circumference of the universe, and Saturn, immediately below it, corresponded to the thirty-sixth tone, and the earth to the first, and the other planets with the sun and moon at the various harmonic distances.

They reckoned one tone from the earth to the moon, half a tone from the moon to Mercury, another half-tone to Venus, one tone and a half from Venus to the sun, one from the sun to Mars, a semitone from Mars to Jupiter, half a tone from Jupiter to Saturn, and a tone and a half from Saturn to the fixed stars; but these distances were not, as we shall see, universally agreed upon.

According to Timaeus, the sphere of the fixed stars, which contains within it no principle of contrariety, being entirely divine and pure, always moves with an equal motion in the same direction from east to west. But the stars which are within it, being animated by the mixed principle, whose composition has been just explained, and thus containing two contrary forces, yield on account of one of these forces to the motion of the sphere of fixed stars from east to west, and by the other they resist it, and move in a contrary direction, in proportion to the degree with which they are endowed with each; that is to say, that the greater the proportion of the material to the divine force that they possess, the greater is their motion from west to east, and the sooner they accomplish their periodic course. Now the amount of this force depends on the matter they contain. Thus, according to this system, the planets turn each day by the common motion with all the heavens about the earth from east to west, but they also retrograde towards the east, and accomplish their periods according to their component parts.

The additions which Plato made to this theory have always been a proverb of obscurity, and none of his commentators have been able to make anything of them, and very possibly they were never intended to.

So far the harmony of the heavenly bodies has been explained with reference to numbers only, and we may add to this that they reckoned 126,000 stadia, or 14,286 miles, to represent a tone, which was thus the distance of the earth to the moon, and the same measurement made it 500,000 from the earth to the sun, and the same distance from the sun to the fixed stars.

But Plato teaches in his _Republic_ that there is actual musical, harmony between the planets. Each of the spheres, he said, carried with it a Siren, and each of these sounding a different note, they formed by their union a perfect concert, and being themselves delighted with their own harmony, they sang divine songs, and accompanied them by a sacred dance. The ancients said there were nine Muses, eight of whom, according to Plato, presided over celestial, and the ninth over terrestrial things, to protect them from disorder and irregularity.

Cicero and Macrobius also express opinions on this harmonious concert. Such great motions, says Cicero, cannot take place in silence, and it is natural that the two extremes should have related sounds as in the octave. The fixed stars must execute the upper note, and the moon the base. Kepler has improved on this, and says Jupiter and Saturn sing bass, Mars takes the tenor, the earth and Venus are contralto, and Mercury is soprano! True, no one has ever heard these sounds, but Pythagoras himself may answer this objection. We are always surrounded, he says, by this melody, and our ears are accustomed to it from our birth, so that, having nothing different to compare it with, we cannot perceive it.

We may here recall the further development of the idea of the soul of the universe, which was the source of this harmony, and endeavour to find a rational interpretation of their meaning. They said that nature had made the animals mortal and ephemeral, and had infused their souls into them, as they had been extracts from the sun or moon, or even from one of the planets. A portion of the unchangeable essence was added to the reasoning part of man, to form a germ of wisdom in privileged individuals. For the human soul there is one part which possesses intelligence and reason, and another part which has neither the one nor the other.

The various portions of the general soul of the universe resided, according to Timaeus, in the different planets, and depended on their various characters. Some portions were in the moon, others in Mercury, Venus, or Mars, and so on, and thus they give rise to the various characters and dispositions that are seen among men. But to these parts of the human soul that are taken from the planets is joined a spark of the supreme Divinity, which is above them all, and this makes man a more holy animal than all the rest, and enables him to have immediate converse with the Deity himself. All the different substances in nature were supposed to be endowed with more or less of this soul, according to their material nature or subtilty, and were placed in the same order along the line, from the centre to the circumference, on which the planets were situated, as we have seen above. In the centre was the earth, the heaviest and grossest of all, which had but little if any soul at all. Between the earth and the moon, Timaeus placed first water, then the air, and lastly elementary fire, which he considered to be principles, which were less material in proportion as they were more remote and partook of a larger quantity of the soul of the universe. Beyond the moon came all the planets, and thus were filled up the greater number of the harmonic degrees, the motions of the various bodies being guided by the principle enunciated above.

When we carefully consider this theory we find that by a slight change of name we may bring it more into harmony with modern ideas. It would appear indeed that the ancients called that "soul" which we now call "force," and while we say that this force of attraction is in proportion to the masses and the inverse square of the distance, they put it that it was proportional to the matter, and to the divine substance on which the distance depended. So that we may interpret Timaeus as stating this proposition: _The distances of the stars and their forces are proportional among themselves to their periodic times._ "Some people," says Plutarch, "seek the proportions of the soul of the universe in the velocities (or periodic times), others in the distances from the centre; some in the masses of the heavenly bodies, and others more acute in the ratios of the diameters of their orbits. It is probable that the mass of each planet, the intervals between the spheres and the velocities of their motions, are like well-tuned musical instruments, all proportional harmonically with each other and with all other parts of the universe, and by necessary consequence that there are the same relative proportions in the soul of the universe by which they were formed by the Deity."

It is marvellous how deeply occupied were all the best minds in Greece and Italy on this subject, both poets and philosophers; Ocellus, Democritus, Timaeus, Aristotle, and Lucretius have all left treatises on the same subject, and almost with the same title, "The Nature of the Universe."

Though somewhat similar to that of Timaeus, it will be interesting to give an account of the ideas of one of these, Ocellus of Lucania.

Ocellus represents the universe as having a spherical form. This sphere is divided into concentric layers; above that of the moon they were called celestial spheres, while below it and inwards as far as the centre of the earth they were called the elementary spheres, and the earth was the centre of them all.

In the celestial spheres all the stars were situated, which were so many gods, and among them the sun, the largest and most powerful of all. In these spheres is never any disturbance, storm, or destruction, and consequently no reparation, no reproduction, no action of any kind was required on the part of the gods. Below the moon all is at war, all is destroyed and reconstructed, and here therefore it is that generations are possible. But these take place under the influence of the stars, and particularly that of the sun, which in its course acts in different ways on the elementary spheres, and produces continual variations in them, from whence arises the replenishing and diversifying of nature. It is the sun that lights up the region of fire, that dilates the air, melts the water, and renders fertile the earth, in its daily course from east to west, as well as in this annual journey into the two tropics. But to what does the earth owe its germs and its species? According to some philosophers these germs were celestial ideas which both gods and demons scattered from above over every part of nature, but according to Ocellus they arise continually under the influence of the heavenly bodies. The divisions of the heavens were supposed to separate the portion that is unalterable from that which is in ceaseless change. The line dividing the mortal from the immortal is that described by the moon: all that lies above that, inclusive, is the habitation of the gods; all that lies below is the abode of nature and discord; the latter tending constantly to destruction, the former to the reconstruction of all created things.

Ideas such as these, of which we could give other examples more remotely connected with harmony, whatever amount of truth we may discover in them, prove themselves to have been made before the sciences of observation had enabled men to make anything better than empty theories, and to support them with false logic. No better example of the latter can perhaps be mentioned here than the way in which Ocellus pretends to prove that the world is eternal. "The universe," he says, "_having_ always existed, it follows that everything in it and every arrangement of it must always have been as it is now. The several parts of the universe _having_ always existed with it, we may say the same of the parts of these parts; thus the sun, the moon, the fixed stars, and the planets have always existed with the heavens; animals, vegetables, gold, and silver with the earth; the currents of air, winds, and changes from hot to cold, from cold to hot, with the air. _Therefore_ the heaven, with all that it now contains; the earth, with all that it produces and supports; and lastly, the whole aerial region, with all its phenomena, have always existed." When this system of argument passed away, and exact observation took its place, it was soon found that so far from what the ancients had argued _must be_ really being the case, no such relation as they indicated between the distances or velocities of the planets could be traced, and therefore no harmony in the heavens in this sense. It is not indeed that we can say no sounds exist because we hear none; but considering harmony really to consist of the relations of numbers, no such relations exist between the planets' distances, as measured now of course from the sun, instead of being, as then, imagined from the earth.

The gamut is nothing else than the series of numbers:--

do re mi fa sol la si do 1 9/8 5/4 4/3 3/2 5/3 15/8 2

and is independent of our perception of the corresponding notes. A concert played before a deaf assembly would be a concert still. If one note is made by 10,000 vibrations per second, and another by 20,000, we should hear them as an octave, but if one had only 10 and the other 20, they would still be an octave, though inaudible as notes to us; so too we may speak even of the harmony of luminous vibrations of ether, though they do not affect our ears.

The velocities of the planets do not coincide with the terms of this series. The nearer they are to the sun the faster is their motion, Mercury travelling at the mean rate of 55,000 metres a second, Venus, 36,800, the earth 30,550, Mars 24,448, Jupiter 13,000, Saturn 9,840, Uranus 6,800, and Neptune 5,500, numbers which are in the proportion roundly of 100, 67, 55, 44, 24, 16, 12, 10, which have no sufficient relation to the terms of an harmonic series, to make any harmony obvious.

Returning, however, to the ancient philosophers, we are led by their ideas about the soul of the universe to discover the origin of their gods and natural religion. They were persuaded that only living things could move, and consequently that the moving stars must be endowed with superior intelligence. It may very well be that from the number seven of the planets, including the sun and moon, which were their earliest gods, arose the respect and superstition with which all nations, and especially the Orientals, regarded that number. From these arose the seven superior angels that are found in the theologies of the Chaldeans, Persians, and Arabians; the seven gates of Mithra, through which all souls must pass to reach the abode of bliss; the seven worlds of purification of the Indians, and all the other applications of the number seven which so largely figure in Judaism, and have descended from it to our own time. On the other hand, as we have seen, this number seven may have been derived from the number of the stars in the Pleiades.

We have noticed in our chapter on the History of the Zodiac how the various signs as they came round and were thought to influence the weather and other natural phenomena, came at last to be worshipped. Not less, of course, were the sun and moon deified, and that by nations who had no zodiac. Among the Egyptians the sun was painted in different forms according to the time of year, very much as he is represented in our own days in pictures of the old and new years. At the winter solstice with them he was an infant, at the spring equinox he was a young man, in summer a man in full age with flowing beard, and in the autumn an old man. Their fable of Osiris was founded on the same idea. They represented the sun by the hawk, and the moon by the Ibis, and to these two, worshipped under the names of Osiris and Isis they attributed the government of the world, and built a city, Heliopolis, to the former, in the temple of which they placed his statue.

The Phenicians in the same way, who were much influenced by ideas of religion, attributed divinity to the sun, moon, and stars, and regarded them as the sole causes of the production and destruction of all things. The sun, under the name of Hercules, was their great divinity.

The Ethiopians worshipped the same, and erected the famous table of the sun. Those who lived above Meroe, admitted the existence of eternal and incorruptible gods, among which they included the sun, moon, and the universe. Like the Incas of Peru, they called themselves the children of the sun, whom they regarded as their common father.

The moon was the great divinity of the Arabs. The Saracens called it Cabar, or the great, and its crescent still adorns the religious monuments of the Turks. Each of their tribes was under the protection of some particular star. Sabeism was the principal religion of the east. The heavens and the stars were its first object.

In reading the sacred books of the ancient Persians contained in the _Zendavesta_, we find on every page invocations addressed to Mithra, to the moon, the stars, the elements, the mountains, the trees, and every part of nature. The ethereal fire circulating through all the universe, and of which the sun is the principal focus, was represented among the fire-worshippers by the sacred and perpetual fire of their priests. Each planet had its own particular temple, where incense was burnt in its honour. These ancient peoples embodied in their religious systems the ideas which, as we have seen, led among the Greeks to the representation of the harmony of heaven. All the world seemed to them animated by a principle of life which circulated through all parts, and which preserved it in an eternal activity. They thought that the universe lived like man and the other animals, or rather that these latter only lived because the universe was essentially alive, and communicated to them for an instant an infinitely small portion of its own immortality. They were not wise, it may be, in this, but they appear to have caught some of the ideas that lie at the basis of religious thought, and to have traced harmony where we have almost lost the perception of it.