space and time
(rest and motion)
Space and time are the prime elements of the cosmos. The genesis of Nature may be attributed to time acting on space. What they are, what may be their true essence, whether they be real of ideal, whether they be things or merely names, whether they exist or be nothings — all these questions concerning them in the absolute do not come within the scope of the present little work. I shall merely consider them from the relative point of view, and only so far as is necessary to define the position of music in the cosmos. For this purpose let us cast a glance at their fundamental characteristics.
Space is rest, time is motion. Space is lifeless, time is life. Space is rest, lifeless, yet in consequence knows no death. Time is motion, life, yet what is life but change, and what is change but death? And still — eternal antithesis! — though in all things the contrary of each other, they are yet the counterparts of one another; though, by their very definitions, the opposites, they are yet wonderfully similar; though, subjectively, essentially antagonistic, they are, objectively, but different manifestations of an identical idea! For what is time? It is the space of motion, the space of existence!
Both exist forever. In space, this forever is called “infinity;” in time, “eternity.” Yet each particle of space is infinitesimal but eternal while each particle of time is eternitesimal, [2] but infinite. Each particle of space is infinitely small, but it remains the same, unchanged through all ages; each particle of time is infinitely short, yet it extends through the whole universe, immeasurable even in the imagination — it is infinite! Space is the limitation of matter; all things material must occupy some space. Time, however, is the limitation of the spiritual; our very thoughts are bounded by it. Space may therefore be considered as the essential limitation of all things material; time, the essential limitation of all things whatsoever. Ideas, consequently, do not exist in space. Matter is lifeless, inactive, put in motion by forces. Forces are ideal; they exist in time. Consequently, time and space constantly act upon each other. But time is but another name for space — it is the space of motion.
Now, what is music? The beautifier of time, is the simple and categorial answer; an answer, too, from which further answers to all questions springing from the original questions may be deduced; an answer that serves as the corner-stone of the fundamental theory of music itself. It is to adorn the ever-moving space of existence that music was generated and the germs of its development were placed within it. In the space of rest, in visible Nature, Nature itself has undertaken the task of beautifying. And there she has lavished beauties untold and unnumbered. Beauty reigns on the mountain and in the valley, on the hill and in the dale. It is present in the gentle grove as well as in the mighty forest. It is in the little brook and in the magnificent ocean. It is in man and woman, in the birds, in the plants; anywhere, everywhere, it meets our eyes if we will but see. There are beauties of all kinds and degrees, from the sublime to the graceful, from the magnificent to the picturesque. All this has Nature done for space; and to do something similar for time is the grand and holy object of music.
The materials of which music is composed exist only in time, and here we have the explanation of many of the characteristics of music. Time is motion, is life, yet the sure bringer of change, of death. As it is motion, its influence upon us is emotional, agitating; as it constantly tells us of change and death, it awakens the feeling of melancholy within us. Music, as it beautifies the passing moments, yet tells us that they are passing, and consequently it is so prone to cause sadness.
We may divide the pleasures arising from the contemplation of the beautiful into two classes — pleasures productive of joy, and those productive of sadness. There is nothing paradoxical in this division. A thing that is beautiful will give pleasure at all times, though it may at the same time cause sadness. A great tragedy will give pleasure, though it may not put us in a joyful mood. So it is with a beautiful poem on a tragic subject. In tact, intense and exquisite delight is perfectly compatible with a frame of mind strongly tinged with the melancholy. Nay, even more, joyful sensations, when they become ecstatic, generally have a background in deep sadness.
Now, the characteristic state of mind accompanying the contemplation of things in space is that of serene joy. Space, being rest, does not excite the more powerful emotions, it does not agitate. It has, on the contrary, the effect of calming and quieting the mind. I am, of course, speaking of the beautiful purely as such without admitting of associations of ideas. These, of course, often exercise a powerful influence, and cause emotion by their own force. But they exist as much for music as they do for things in visible Nature, and their consideration at present would only cause useless complications. That beauty in space has the tendency — and very strongly — to create a serene frame of mind, any one desirous of doing so can easily test. A landscape must be entirely covered with clouds, be exceedingly gloomy, before it causes us to be sad. Let but the sun appear and shine upon the clouds, and they will be tinged with bright colors; the scene will appear more cheerful even than were there no clouds. The opposite is the case in music. Often a single minor or diminished chord, introduced into a gay melody, will change its entire expression, rendering it melancholy. Space know naught of death, it particles exist forever; its beauties are, therefore, prone to create joy. Time speaks constantly of change and death; its particles are infinitely short, it beauties create sadness.
Then, again, as Aristotle has already said, what are the emotions but motions? And as music is motion, its effect on them must be great, for motions exercise an enormous influence on like motions, and have a very great tendency to respond to like motions. This is a fact well known to all familiar with the operation of vibrations. “But,” it may be objected, “the eye is also an organ capable of discerning motion.” To this I answer, that we are at present concerned only about the beautiful in motion, and that this is chiefly the province of the ear. The beauties of motion open to the perception of the eye are of an inferior kind. The pleasures in viewing dancing or marching do not really come with the range of those caused by the contemplation of the beautiful in the highest sense. In the motion of the waves of the sea, we are more impressed by the natural association of ideas than by the beauty of the motion itself.
There is, indeed, another, higher ind of motion in visible Nature — the motions of the heavenly bodies. Daily the run rises, and tranquility and majestically pursues its course in the firmament, to set amid splendor and glory. Then the stars appear, and with equal majesty traverse the skies, set the rise until the kind of day again ascends from the horizon, and eclipses them by the exceeding power of his light. Nor is this motion limited to the day and night; as the year moves on, sun and stars move with it. This month the sun rises in one sign, the next month in another, until he has traversed the whole circle of the zodiac. This month Arcturus is the proudest of the starry host shining high above; in the next he is already dethroned, and bright Antares for a brief time assumes his honor. But the beautiful, imperial Lyra follows in the wake, and in her turn claims homage as chief of the stars. Less steady wanderers, too, are there in the heavens; the planet moving unconcerned in their orbits, now visible here, now there. The lovely moon, queen of the night, pursues her tranquil course. Now seen but as a silver thread in the west, she waxes lovelier and prouder as she approaches the east, until she almost rivals the sun in the refulgency of her light; but it is only to wane and wane again, until she is seen no more.
There is, too, the subtle motion of the seasons. Now the forest is the garb of a beautiful green, the garden is fragrant with flowers, the trees are loaded with fruits, the fields teem with the heaving corn. Soon the green changes into numerous varieties of color, the leaves fall and strew and ground, the flowers are plucked from the garden, the corn is gathered from the fields. Then comes Winter; snow covers the ground, the water courses of the mountains and the rivers of the valleys are turned into ice, cold and bright, the mild breezes give way to the fierce blasts of the storm. But Spring follows close behind, and wafts and breath of life before him. The now melts, the ice thaws, the mountain torrents tear on with renewed and tenfold increased vigor; the pulse of Nature throbs with the freshness of youth. Soon all is again in bloom, the trees are white, the plants begin to shoot forth. The Summer is here once more, and the course of the year begins anew.
The motions of the spheres and of the seasons are, indeed, full of sublimity. The ancient philosophers and their followers unto recent times, however, saw in them yet the workings of music. All these motions were to them but the visible manifestations of a transcendental harmony. Therefore does the Pythagorean say, “It is the business of music, not only to preside over the voice and the musical instruments, but even to harmonize all things contained in the universe.”
A similar sentiment inspired Shakespeare when he wrote:
“Look how the floor of heaven
Is thick inlaid with patines of bright gold;
There's not the smallest orb, which thou beholdst,
But in his motion like an angel sings,
Still quiring to the young-eyed cherubins.
Such harmony is in immortal souls;
But, whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it.”
If I where asked to give my own views on these motions, I should say that I do not believe that they properly come under the head of the beautiful in motion. If we admire the landscape, or look up to the starry vault of heaven, our purely aesthetical pleasure does not take in the factor of motion. It is continuous and imperceptible to the eye — it is only by the aid of memory that we know that it exists, and the feeling of awe connected with it arises solely from the association of ideas. Indeed, if we wish thoroughly to examine an object in space, we require it to be perfectly at rest — its motion, as a rule, has a tendency to confuse us; [3] and, if the motion be rapid, the object becomes blurred. The very life of the beautiful in audible Nature, however, is motion — it exists in time and not in space.
As time and space — visible and audible Nature — are the counterparts of each other, there must be great analogies in the manner in which beauty is perceive and produced in either. Of the analogies of perception I shall now treat, under the heading of Vibrations.
vibrations
We perceive things in visible Nature by means of light; things in audible Nature by means of sound. To one unacquainted with physics, light and sound are entirely different phenomena, having no connection whatever with each other, and yet they are intrinsically very nearly related to each other, being but different manifestations of the same cause. Vibrations of a certain rapidity are perceived by the instrument constructed to respond to them — the ear, as sound; vibrations of greater rapidity are perceived by the instrument constructed to respond to them — the eye, as light. And not only are they produced by the same cause, they are also propagated by the same means — undulations. Entering into details, we find the analogies between the two phenomena in almost all of the principal manifestations. Some bodies are transparent, others translucent, others again opaque to light; in like manner, some bodies permit sound to pass on through them without practically enfeebling it; others, like thick walls, transmit it much weakened; while other again do not transmit it to any appreciable degree. An instance of the last cause is a tunnel. To any one standing at a distance, the roar of a train entering it is hushed, and remains so until the cars merge, when it is immediately renewed.
Some of the principal properties of light are absorption, reflection, refraction, and diffraction. These are also the properties of sound. That is may be absorbed can easily be tested, by comparing the sound of a musical instrument in a carpeted and furnished room with that of one heard in an empty room. The echo is a familiar illustration of reflection of sound. The experiments of Sondhauss and Jajeck prove conclusively that is is refracted when it enters a medium whose density differs from the one it leaves, in the same manner and under the same conditions as is light. The diffraction of sound has been demonstrated by Seebeck.
It is, however, not only in the physical manifestations of sound and light that we discover great analogies; the construction of the instruments for their perception — the eye and ear, is essentially based on analogous plans. Like the ear, the eye is a membranous structure. The ear is composed of three parts — the auditory canal, with the tympanum, the tympanic cavity, and the labyrinth. The corresponding parts of the eye are the sclerotic coat, the choroid coat, and the iris. The aqueous and vitreous humors present strong points of resemblance with the water of the labyrinth. The difference between light and sound is not in kind, but in degree. Extremely rapid vibrations produce light; slower ones, sound. The rapid vibrations have, however, a proportionately small amplitude; slower vibrations, a proportionately large amplitude. Hence the difference in the anatomy of the eye and the ear. The first is prepared to receive and respond to vibrations of enormous rapidity and small amplitude; the latter, to receive and respond to vibrations of comparative slowness, but with a relatively large amplitude.
Tones and colors are essentially the same things. Colors are tones of tremendous height of pitch. Tones are colors of tremendous depth of pitch. The ear perceives as tones from 8 (Savart) to 38,016 (Dupretz) vibrations in a second. The ye perceives as light from 458,000,000,000,000 (extreme red) to 727,000,000,000,000 (extreme violet) vibrations per second. From the most acute tone capable of being perceived by the ear to the extreme red color there is, therefore, an interval of about thirty-four octaves. To give an illustration of the enormity of such an interval, let us take the length of the string of the highest C of a seven and a quarter octave piano-forte, which is about 1 3/4 inch, and it will be easy to calculate that a string of the same material and thickness, in order to produce the extreme red light, would have to be but down to about 1/10000000000 of an inch! The rapidity of the vibrations defines the length of the undulations; the length of a sonorous wave produced by 8 vibrations per second is 140 feet; the length of a luminiferous undulation in the extreme violet ray is 167/10000000 of an inch; otherwise expressed, while of the former there would be but 37 5/7 in a mile, in the latter there are 59,150 in an inch!
Rapidity of vibrations is, however, the means of distinguishing tones from tones and colors from colors, as well as tones from colors; and consequently, difference in rapidity of vibrations solely, cannot be considered an intrinsic difference.
The principal phenomena connected with colors — analysis and interference — are also proper to tones.
For colors the triangular prism acts as analyzer; for tones that office is performed by resonators. Prof. Helmholtz has constructed a series of the latter, which serve as analyzers for isolated tones — by resolving them into the fundamental and overtones — as well as for those tones of combination produced by the simultaneous existence of two or more independent tones. Interference in sonorous waves has been demonstrated ocularly as well as auricularly by numerous apparatus.
Having now sufficiently illustrated the identity of the manner of perception of the beautiful in visible and audible Nature, I shall proceed to the consideration of the fundamental analogies regarding the production of the beautiful in space and time.
colors and forms
The elements of the beautiful in space are colors and forms. The counterpart of colors having been found in tones, there remains but the question: “Is there also a counterpart of forms to be found in music?” This question I answer categorically in the affirmative: Rhythm is the shape, form or proportion of things in time; and shape, form or proportion is the rhythm of things in space. And this answer is not based on any arbitrary ideas, but on incontestable facts — facts as indisputable as is the theorem that colors are the tones of space. Time is but the space of motion, and rhythm defines that space in the same manner that the space of rest is defined by forms. The lines of space are translated, as it were, into time, by its means. On entering into an investigation of the prime principles of morphology, we find that the straight line and the curve are the fundamental types of form. In like manner the fundamental types of rhythm are found in the dual and in the triple metre. The geometrical point is an impossibility — so is single metre. The reason is plain. Rhythm, like form, is based on proportion; in other words, on relativity. We have no perception of rhythm on hearing a single beat. A beat must be defined and bounded by a second one to become a metre - i.e., a measure of time. The analogy between dual metre and the straight line, and triple metre and the curved line, is by no means a fanciful conception — it has been intuitively felt by musical composers in all times; and tones spread over rhythms as colors do over forms.
We cannot, however, overlook the remarkable fact that, while in visible Nature colors play the subordinate and form the principal part, the order is reversed in audible Nature, where rhythm is subordinate to tones. Well, this is necessitated by the fundamental characteristics of space and time, rest and motion. In space, things may remain at rest; our eyes can take in a great variety of forms simultaneously. They have time to examine beauty — extend comparisons over a wide field. Forms and proportions may establish themselves in unlimited variety; for we have co-existence on a large scale. Time, however, is motion. In it, proportions and forms are perceptible by their very motion, and only by motion; one tone vanishes as the next comes on. Here there is no room such an extreme variety of forms; rhythms (though they may yet be infinitely varied and complicated) must be much simpler than the forms of visible Nature.
On the other hand, the tones, which constitute the material of melody, embrace about seven and a half octaves, good for practical purposes; while the colors do not extend over more than one octave. This octave, even, is not entirely visible under ordinary circumstances, its eighth degree being that which is called the lavender light of Herschel, and only produced by concentration. [4] Practically, the whole combination of colors does not exceed the interval of a seventh. There are, therefore, conclusive reasons why the chief riches of visible Nature lie in forms, while the chief riches of audible Nature are in tones.
There is, however, another factor besides melody and rhythm that enters into the composition of music — harmony; and it may be asked whether any analogy for it can be found in visible Nature. To this question I reply that the fundamental theory of musical harmony lies in the very nature of time. Each particle of space is infinitely small; consequently, not two things can occupy the same space. Each particle of time, on the contrary, is infinitely large, embracing the whole cosmos; consequently, an infinite number of things can occur at the same time. Space, however, is rest, and the mind can therefore take in a large number of particles of space at once. Time, being motion, does not admit of perceiving more than one of its particles at once; and, therefore, the simultaneity compatible with it acts as a certain compensation for those advantages which, by its definition, rest has over it. I am, of course, using the word “harmony” in its narrow signification, in the sense of counterpoint, and not in its spiritual meaning. In the latter higher sense it pervades the whole universe, existing both in space and in time. The soul of the cosmos, says Plato, is musical harmony. The whole topic of colors, and forms, and rhythms, and tones, and harmony, together with them any analogies of detail in these matters, is a tempting and prolific subject for speculation. I shall, however, resist the temptation of going any further into the matter, for it is beyond my scope in this little work to introduce any but plain demonstrable facts. One thing only I must yet allude to, and this is that, in instituting comparisons between the beautiful in space and in time, we should never forget that, in the former case, the task of beautifying has been undertaken by Nature itself with the unbounded resources at its command, while in the latter it is left to the limited means of man. Were Nature to beautify time as it does space — could we hear, for instance, such a thing as the harmony of the spheres — the sublimity of such music might transcend all possible conceptions.
And now we leave the field of the material analogies, respecting the perception and the production of the beautiful in space and time, to enter into that of what may be termed the “spiritual analogies.” Those of production I shall class under Internal Government; those of perception under States of Mind.
internal government
Several of the great forces which we see manifested in visible Nature have the counterparts in audible Nature; and prime among these are the forces of gravity and attraction and the centrifugal force. I am not aware that any writer has ever had the boldness to make this assertion in so positive a manner, but certainly the influence of the first over music has been instinctively felt in all times and among all nations; while that of the last two was discovered as soon as it could have been — namely, in the first stages of the development of the science of harmony.
The center of gravity of the musical scale is the tonic. The whole history of music tends to confirm this in an unequivocal manner. I have before me, as I write, a volume of August Wilhelm Ambros, wherein I find scraps of melodies from the land of the Esquimaux and from the Friendly Islands, from New Zealand and from Abyssinia, from Corea and from Senegal. Besides these, a number of finished Chinese melodies, and number of beautiful songs of Hindostan, together with Arabian, Persian, and Turkish airs, and two of the three ancient Greek nomoi that have come down to us; and in each one of them, from tutored and from untutored people, the audible manifestation of the principle of gravity is unmistakably discernible; all the tones gravitate toward their common centre — the tonic. A characteristic passage from the writings of Aristotle proves indeed, beyond doubt, that the consciousness of the force of the tonic was not only apparent in the practice of music of the ancients, but that they were also aware of its spiritual relation to the other degrees of the scale, and attempted to account for it philosophically. “Why is it,” he asks, “that, when the tonic [mese] is changed [sharpened or flattened], all the other strings sound out of tune; but, if the tonic is in tune, and one of the other strings is changed, on only the changed string sounds out of tune? Is it because not only all the strings are tuned, but also that they are tuned with respect to the tonic, and that the latter defines the order in which they appear? But, when the basis of the tuning and that which keeps [the melody] together is taken away, there can no longer be the same kind of order.” But should the reader be disinclined to accept the testimony of a single person, no matter of what importance it may be, I have still another powerful proof in support of my argument to bring forward. Let us cast a glance in pre-Ptolemaic astronomy, and what do we find? That the prime principles of modern astronomy — those contained in the Copernican system — were essentially known and taught in the sixth century B.C. by Pythagoras. His doctrine was that the sun is the centre of the universe, and that the earth has a diurnal motion around its axis, and an annual motion around the sun! Now, we have already seen (in an earlier part of this little work) that the planets and the sun were compared and considered mysteriously related to the tones pf the scale. And the sun, the central sphere, was supposed to be the mese of the scale — the manifestation of the principles embodied in the tonic. Cicero, however, did not believe in the Pythagorean doctrine of the revolution of the planets around the sun. He was of the opinion that the sun and planets revolve around the earth, which remains stationary. And in consequence, too, he change the Pythagorean division of the scale among the heavenly bodies — the sun was not longer mese, it became simply the lichanos hypaton. But what did he do with the mese? It could not be given to the earth, because she, being stationary, represented silence; so he made mese symbolical of the whole expanse of the firmament!
In the ninth century, Huebald de St. Amand worked out his “Organum,” the first step toward modern harmony. One of the first results of his discovery was the introduction of the leading note into the musical scale — the forced recognition of the second great governing principle of the scale — attraction. By-and-by retards came into use, and showed that this attraction acted in a dual manner — upward and downward. The analogy between it and magnetic attraction, with its two poles must, I think, strike every one — the attraction of the one pole manifested in the retard and the resolution of the seventh, that of the other in the alteration and leading note.
The dominant, which is in all respects the contrary of the tonic, is the audible manifestation of the centrifugal force. In our modern system of harmony, where the principle of tonality is fully understood and recognized, the intensity of this force is even considerably increased by the fact that the dominant is likewise the tonic of the next related key, and consequently as such exercises as extraneous attraction, tending to oppose, by a secondary gravity, the force of gravity in the tonic.
And now, remembering that the emotions are motions, we cannot but be convinced that the foregoing facts serve as explanation for many of the characteristic effects which music has on our emotions. The centre of gravity, manifested in the tonic of the musical scale, is likewise manifested in the emotions expressive of satisfaction. I am using this word, not in the sense of contentment, but in contradistinction to the term suspense; the satisfaction need, of course, not have any gay or even cheerful sentiments connected with it, it may in fact be accompanied by extreme despondency: it is but the relief from suspense, or typifying suspense as the question — it is the answer. The centrifugal force is manifested in the dominant, and likewise in the emotions expressive of suspense; it is typified in the question. The perfect cadence is universally, and I may say intuitively, recognized as the only manner in which a composition can be satisfactorily closed. But what is the perfect cadence? It is a chord built on the dominant of a key followed by on on its tonic. And what is the reason that it is the most satisfactory manner of closing a composition? This question is easily answered by a consideration of the data we have just been adduced. The satisfaction is most intense when we have tasted the suspense to its extreme limit, the answer is most complete when it follows the question directly, taking it in to its fullest extent.
Of course, there are different degrees of satisfaction. If the tonic alone is employed and merely doubled in the higher parts, the satisfaction is perfect; if the tonic occurs in the highest part, as well as the lowest, it is nearly perfect; if the mediant is heard in the highest part, a feeling of vagueness — often charming — is superadded; and if the dominant is sounded in the highest part, the vagueness is considerably augmented; the mixture of suspense with the ground feeling of satisfaction creates, in fact, a peculiar weird impression, easily and (as I believe) only explicable by considering the forces that I have asserted to be manifested in the tonic and the dominant.
Before closing this part of my argument, let me refer the reader to two powerful passages taken at random from the works of Beethoven, where he will find a remarkable corroboration of my conception the tonic, dominant and attraction. The first consists in the closing measures of the “Largo Appassionato” of the Sonata Opus II, No. 2. It is impossible to describe the apathy expressed in that cadence. Yet, by analyzing it, according to the principles which I have set forth, we can explain its effect on natural grounds. The A in the bass is the dominant of the key — the manifestation of suspense — and the mind expects it to move on to the tonic toward which it gravitates. It does not do so, however; and, though the upper parts have already entered the domains of the tonic, the bass still clings to the dominant as though in complete abstraction. The upper parts attempt to console — to urge it to abandon the dominant. It does so, but only to return to it as though to a forlorn hope. Then the upper parts finally move on to the tonic and remain there, and so nothing is left for the bass but to follow. But it does so reluctantly, tardily, as if awakening from a reverie. The emotions of the hearer respond to all these movements, and hence are affected as they are. The second passage occurs near the close of the first movement of the Seventh Symphony. It is expressive of an intense longing that can never be satisfied, of a passionate yearning for the unattainable, or to use a magnificent figure of a modern German poet, [5] it is like “the love of the sea for the moon.” This is due to the conflict between the forces of attraction and of the tonic. A seventh is attracted to the degree below it. Here we find the seventh inverted in the bass, and in consequence the chord cannot resolve itself on the tonic, but must do so on the chord of the sixth on the mediant. This chord, however, unsatisfactory, and can never be the concluding one; and the vain attempts of the inverted seventh to resolve itself satisfactorily, repeated and repeated with obstinate fervor, though warned and entreated by the pleading tones fo the upper part, constantly obtaining the same discontenting answer, which it is fated to receive, and which it knows that it must receive, is the picture of fervent hope doomed to eternal disappointment.
Let us now pass on to the consideration of the analogies between the spiritual perception of the beautiful in visible and in audible Nature.
states of mind
The beautiful in Nature, whether visible or audible, is perceived as a state of mind. The contemplation of a beautiful landscape impresses our mind directly, primarily, without the intervention of thought; a certain mood takes possession of us, we know not how, pervades us, masters us, and gives rise to sentiments and thoughts. By listening to a great composition, our mind undergoes the same process — first the mood, then the sentiment, then the definite thought. This order is characteristic of the perception of the beautiful in Nature.
Things in space will be apt to produce the state of mind in which calmness is the predominating feature — things in time those in which agitation will be more perceptible. It is true that music can also affect us with calmness, but even then it will be what might be called emotional calmness, it will be more powerful, more intense.
Yet the very capability of music to produce this cheerful and tender calmness is the reason why it can depict pastoral scenes, for by its means it produces a state of mind analogous to the one produced by such scenes; but this depicting must solely depend on the spiritual analogies manifested in the states of mind; if it resorts to other means it will have a degrading effect. This remark applies with no less force to the description of passions and actions by music; such description, to be true and elevated, must look to the analogies in the spiritual perception, to the creation of similar moods, by purely musical means. The mission of music is to create, not to imitate.