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.