Sensier, Vie et Oeuvre de J.-F. Millet.

The idea is, as I said, from this point of view, a means to new beauty; and the stranger and subtler the idea, the more original the forms. The more unrestrained the expression of emotion in the figures, the more chance to surprise them in some new lovely pattern. It is thus, I believe, that we may interpret the seeming trend of modern sculpture, and so much, indeed, of all modern art, to the "expressive beauty" path. "The mediocre artist" will lose beauty in seeking expression, the great artist will pursue his idea for the sake of the new beauty it will yield.

Thus it seems that the stumbling blocks in the way of our theory are not insurmountable after all. From every point of view, it is seen to be possible to transmute the idea into a helpmeet to the form. Visual beauty is first beauty to the eye and to the frame, and the mind cherishes and enriches this beauty with all its own stored treasures. The stimulation and repose of the psychophysical organism alone can make one thrill to visual form; but the thrill is deeper and more satisfying if it engage the whole man, and be reinforced from all sources.

VII

But we ought to note a borderland in which the concern is professedly not with beauty, but with ideas of life. Aristotle's lover of knowledge, who rejoiced to say of a picture "This is that man," is the inspirer of drawing as opposed to the art of visual form.

It is not beauty we seek from the Rembrandt and Durer of the etchings and woodcuts, from Hogarth, Goya, Klinger, down to Leech and Keene and Du Maurier; it is not beauty, but ideas,— information, irony, satire, life-philosophy. Where there is a conflict, beauty, as we have defined it, goes to the wall. We may trace, perhaps, the ground of this in the highly increased amount of symbolic, associative power given, and required, in the black and white. Even to understand such a picture demands such an enormous amount of unconscious mental supplementation that it is natural to find the aesthetic centre of gravity in that element.

The first conditions of the work, that is, determine its trend and aim. The part played by imagination in our vision of an etching is and must be so important, that it is, after all, the imaginative part which outweighs the given. Nor do we desire the given to infringe upon the ideal field. Thus do we understand that for most drawings a background vague and formless is the desideratum. "Such a tone is the foil for psychological moments, as they are handled by Goya, for instance, with barbarically magnificent nakedness. On a background which is scarcely indicated, with few strokes, which barely suggest space, he impales like a butterfly the human type, mostly in a moment of folly or wickedness.... The least definition of surrounding would blunt his (the artist's) keenness, and make his vehemence absurd."

Max Klinger, Malerei u. Zeichnung, 1903, p. 42.

This theory of the aim of black and white is confirmed by the fact that while a painting is composed for the size in which it is painted, and becomes another picture if reproduced in another measure, the size of drawings is relatively indifferent; reduced or enlarged, the effect is approximately the same, because what is given to the eye is such a small proportion of the whole experience. The picture is only the cue for a complete structure of ideas.

Here is a true case of Anders-Streben, that "partial alienation from its own limitations, by which the arts are able, not indeed to supply the place of each other, but reciprocally to lend each other new forces." It is by its success as representation that the art of the burin and needle—Griffelkunst, as Klinger names it—ought first to be judged. This is not saying that it may not also possess beauty of form to a high degree,—only that this beauty of form is not its characteristic excellence.

W. Pater, The Renaissance: Essay on Giorgione.

In what consists the beauty of visual form? If this question could be answered in a sentence our whole discussion of the abstract formula for beauty would have been unnecessary. But since we know what the elements of visual form must do to bring about the aesthetic experience, it has been the aim of the preceding pages to show how those elements must be determined and related. The eye, the psychophysical organism, must be favorably stimulated; these, and such colors, combinations, lines as we have described, are fitted to do it. It must be brought to repose; these, and such relations between lines and colors as we have set forth, are fitted to do it, for reasons we have given. It is to the eye and all that waits upon it that the first and the last appeal of fine art must be made; and in so far as the emotion or the idea belonging to a picture or a statue waits upon the eye, in so far does it enter into the characteristic excellence, that is, the beauty of visual form.

B. SPACE COMPOSITION AMONG THE OLD MASTERS

I

THE preceding pages have set forth the concrete facts of visible beauty, and the explanation of our feelings about it. It is also interesting, however, to see how these principles are illustrated and confirmed in the masterpieces of art. A statistical study, undertaken some years ago with the purpose of dealing thus with the hypothesis of substitutional symmetry in pictorial composition, has given abundance of material, which I shall set forth, at otherwise disproportionate length, as to a certain extent illustrative of the methods of such study. It is clear that this is but one of many possible investigations in which the preceding psychological theories may be further illuminated. The text confines itself to pictures; but the functions of the elements of visual form are valid as well for all visual art destined to fill a bounded area. The discussion will then be seen to be only ostensibly limited in its reference. For picture might always be read space arrangement within a frame.

In the original experimental study of space arrangements, the results of which were given at length on page 111, the elements of form in a picture were reduced to SIZE or MASS, DEPTH in the third dimension, DIRECTION, and INTEREST. Direction was further analyzed into direction of MOTION or ATTENTION (of persons or objects in the picture), an ideal element, that is; and direction of LINE. For the statistical study, a given picture was then divided in half by an imaginary vertical line, and the elements appearing on each side of this line were set off against each other to see how far they lent themselves to description by substitutional symmetry. Thus: in B. van der Helst's "Portrait of Paul Potter," the head of the subject is entirely to left of the central line, as also his full face and frontward glance. His easel is right, his body turned sharply to right, and both hands, one holding palette and brushes, are stretched down to right. Thus the greater mass is to the left, and the general direction of line is to the right; elements of interest in the head, left; in implements, right. This may be schematized in the equation (Lt.)M.I.=(Rt.)I.L.

Pieter de Hooch, "The Card-Players," in Buckingham Palace, portrays a group completely on the right of the central line, all facing in to the table between them. Directly behind them is a high light window, screened, and high on the wall to the extreme right are a picture and hanging cloaks. All goes to emphasize the height, mass, and interest of the right side. On the left, which is otherwise empty, is a door half the height of the window, giving on a brightly lighted courtyard, from which is entering a woman, also in light clothing. The light streams in diagonally across the floor. Thus, with all the "weight" on the right, the effect of this deep vista on the left and of its brightness is to give a complete balance, while the suggestion of line from doorway and light makes, together with the central figure, a roughly outlined V, which serves to bind together all the elements. Equation, (Lt.)V.I. =(Rt.)M.I.

The thousand pictures on which the study was based were classified for convenience into groups,—Religious, Portrait, Genre, and Landscape. It was found on analysis that the functions of the elements came out clearly, somewhat as follows.

One thousand reproductions of old masters from F. Bruckmann's Classischer Bilderschatz, Munich, omitting frescoes and pictures of which less than the whole was given.

Of the religious pictures, only the "Madonnas Enthroned" and other altar-pieces are considered at this point as presenting a simple type, in which it is easy to show the variations from symmetry. In all these pictures the balance comes in between the interest in the Infant Christ, sometimes together with direction of attention to him, on one side, and other elements on the other. When the first side is especially "heavy" the number of opposing elements increases, and especially takes the form of vista and line, which have been experimentally found to be powerful in attracting attention. Where there are no surrounding worshipers, we notice remarkable frequency in the use of vista and line, and, in general, balance is brought about through the disposition of form rather than of interests. The reason for this would appear to be that the lack of accessories in the persons of saints, worshipers, etc., and the consequent increase in the size of Madonna and Child in the picture, heightens the effect of any given outline, and so makes the variations from symmetry greater. This being the case, the compensations would be stronger; and as we have learned that vista and line are of this character, we see why they are needed.

The portrait class is an especially interesting object for study, inasmuch as while its general type is very simple and constant, for this very reason the slightest variations are sharply felt, and have their very strongest characteristic effect. The general type of the portrait composition is, of course, the triangle with the head at the apex, and this point is also generally in the central line; nevertheless, great richness of effect is brought about by emphasizing variations. For instance, the body and head are, in the great majority of cases, turned in the same way, giving the strongest possible emphasis to the direction of attention,—especially powerful, of course, where all the interest is in the personality. But it is to be observed that the very strongest suggestion of direction is given by the direction of the glance; and in no case, when most of the other elements are directed in one way, does the glance fail to come backward. With the head on one side of the central line, of course the greatest interest is removed to one side, and the element of direction is brought in to balance. Again, with this decrease in symmetry, we see a significant increase in the use of the especially effective elements, vista and line. In fact, the use of the small deep vista is almost confined to the class with heads not in the middle. The direction of the glance also plays an important part. Very often the direction of movement alone is not sufficient to balance the powerful M.+I. of the other side, and the eye has to be attracted by a definite object of interest. This is usually the hand, with or without an implement,—like the palette, etc., of our first examples,—or a jewel, vase, or bit of embroidery. This is very characteristic of the portraits of Rembrandt and Van Dyck.

In general, it may be said that (1) portraits with the head in the centre of the frame show a balance between the direction of suggested movement on one side, and mass or direction of attention, or both together, on the other; while (2) portraits with the head not in the centre show a balance between mass and interest on one side, and direction of attention, or of line, or vista, or combinations of these, on the other.

Still more unsymmetrical in their framework than portraits, in fact the most unfettered type of all, are the genre pictures. As these are pictures with a human interest, and full of action and particular points of interest, it was to be expected that interest would be the element most frequently appearing. In compositions showing great variations from geometrical symmetry, it was also to be expected that vista and line, elements which have been noted comparatively seldom up to this point, should suddenly appear strongly; for, as being the most strikingly "heavy" of the elements, they serve to compensate for other variations combined.

The landscape is another type of unfettered composition. It was of course to be expected that in pictures without action there should be little suggestion of attention or of direction of movement. But the most remarkable point is the presence of vista in practically every example. It is, of course, natural that somewhere in almost every picture there should be a break to show the horizon line, for the sake of variety, if for nothing else; but what is significant is the part played by this break in the balancing of the picture. In about two thirds of the examples the vista is inclosed by lines, or masses, and when near the centre, as being at the same time the "heaviest" part of the picture, it serves as a fulcrum or centre to bind the parts—always harder to bring together than in the other types of pictures—into a close unity. The most frequent form of this arrangement is a diagonal, which just saves itself by turning up at its far end. Thus the mass, and hence usually the special interest of the picture, is on the one side, on the other the vista and the sloping line of the diagonal. In very few cases is the vista behind an attractive or noticeable part of the picture, the fact showing that it acts in opposition to the latter, leading the eye away from it, and thus serving at once the variety and richness of the picture, and its unity. A complete diagonal would have line and vista both working at the extreme outer edge of the picture, and thus too strongly,— unless, indeed, balanced by very striking elements near the outer edge.

This function of the vista as a unifying element is of interest in connection with the theory of Hildebrand, that the landscape should have a narrow foreground and wide background, since that is most in conformity with our experience. He adduces Titian's "Sacred and Profane Love" as an example. But of the general principle it may be said that not the reproduction of nature, but the production of beauty, is the aim of composition, and that this aim is best reached by focusing the eye by a narrow background, i.e. vista. No matter how much it wanders, it returns to that central spot and is held there, keeping hold on all the other elements. Of Hildebrand's example it may be said that the pyramidal composition, with the dark and tall tree in the centre, effectually accomplishes the binding together of the two figures, so that a vista is not needed. A wide background without that tree would leave them rather disjointed.

Op cit., p. 55.

In general, it may be said that balance in landscape is effected between mass and interest on one side and vista and line on the other; and that union is given especially by the use of vista.

II

The experimental treatment of the isolated elements detected the particular function of each in distributing attention in the field of view. But while all are possibly operative in a given picture, some are given, as we have seen, much more importance than others, and in pictures of different types different elements predominate. In those classes with a general symmetrical framework, such as the altar and Madonna pieces, the elements of interest and direction of attention determine the balance, for they appear as variations in a symmetry which has already, so to speak, disposed of mass and line. They give what action there is, and where they are very strongly operative, they are opposed by salient lines and deep vistas, which act more strongly on the attention than does mass. Interest keeps its predominance throughout the types, except in the portraits, where the head is usually in the central line. But even among the portraits it has a respectable representation, as jewels, embroideries, beautiful hands, etc., count largely too in composition.

The direction of attention is most operative among the portraits. Since these pictures represent no action, it must be given by those elements which move and distribute the attention; in accordance with which principle we find line also unusually influential. As remarked above, altar-pieces and Madonna pictures, also largely without action, depend largely for it on the direction of attention.

The vista, as said above, rivets and confines the attention. We can, therefore, understand how it is that in the genre pictures it appears very numerous. The active character of these pictures naturally requires to be modified, and the vista introduces a powerful balancing element, which is yet quiet; or, it might be said, inasmuch as energy is certainly expended in plunging down the third dimension, the vista introduces an element of action of counterbalancing character. In the landscape it introduces the principal element of variety. It is always to be found in those parts of the picture which are opposed to other powerful elements, and the "heavier" the other side, the deeper the vista. Also in pictures with two groups it serves as a kind of fulcrum, or unifying element, inasmuch as it rivets the attention between the two detached sides.

The direction of suggestion by means of the indication of a line, quite naturally is more frequent in the Madonna picture and portrait classes. Both these types are of large simple outline, so that line would be expected to tell. In a decided majority of cases, combined with vista—the shape being more or less a diagonal slope—it is clear that it acts as a kind of bond between the two sides, carrying the attention without a break from one to the other.

The element of mass requires less comment. It appears in greatest number in those pictures which have little action, i.e. portraits and landscapes, and which are not yet symmetrical,— in which last case mass is, of course, already balanced. In fact, it must of necessity exert a certain influence in every unsymmetrical picture, and so its percentage, even for genre pictures, is large.

Thus we may regard the elements as both attracting attention to a certain spot and dispersing it over a field. Those types which are of a static character (landscapes, altar-pieces) abound in elements which disperse the attention; those which are of a dynamic character (genre picture), in those which make it stable. The ideal composition seems to combine the dynamic and static elements,—to animate, in short, the whole field of view, but in a generally bilateral fashion. The elements, in substitutional symmetry, are then simply means of introducing variety and action. As a dance in which there are complicated steps gives the actor and beholder a varied and thus vivified "balance," and is thus more beautiful than the simple walk, so a picture composed in substitutional symmetry is more rich in its suggestions of motor impulse, and thus more beautiful, than an example of geometrical symmetry.

III

The particular functions of the elements which are substituted for geometrical symmetry have been made clear; their presence lends variety and richness to the balance of motor impulses. But this quality of repose, or unity, given by balance, is also enriched by a unity for intuition,—a large outline in which all the elements are held together. Now this way of holding together varies; and I believe that it bears a very close relation to the subject and purpose of the picture.

Examples of these types of composition may best be found by analyzing a few well-known pictures. We may begin with the class first studied, the Altar-piece, choosing a picture by Botticelli, in the Florence Academy. Under an arch is draped a canopy held up by angels; under this, again, sits the Madonna with the Child on her lap, on a throne, at the foot of which, on each side, stand three saints. The outline of the whole is markedly pyramidal; in fact, there are, broadly speaking, three pyramids, —of the arch, the canopy, and the grouping. A second, much less symmetrical example of this type, is given by another Botticelli in the Academy,—"Spring." Here the central female figure, topped by the floating Cupid, is slightly raised above the others, which, however, bend slightly inward, so that a triangle, or pyramid with very obtuse angle at the apex, is suggested; and the whole, which at first glance seems a little scattered, is at once felt, when this is grasped, as closely bound together.

Closely allied to this is the type of the Holbein "Madonna of Burgomaster Meyer," in the Grand Ducal Castle, Darmstadt. It is true that the same pyramid is given by the head of the Madonna against the shell-like background, and her spreading cloak which envelops the kneeling donors. But still more salient is the diamond form given by the descending rows of these worshiping figures, especially against the dark background of the Madonna's dress. A second example, without the pyramid backing, is found in Rubens's "Rape of the Daughters of Leucippus," in the Alte Pinakothek at Munich. Here the diamond shape formed by the horses and struggling figures is most remarkable,—an effect of lightness which will be discussed later in interpreting the types.

A third type, the diagonal, is given in an "Evening Landscape" by Cuyp, in the Buckingham Palace, London. High trees and cliffs, horsemen and others, occupy one side, and the mountains in the background, the ground and the clouds, all slope gradually down to the other side.

It is a natural transition from this type to the V-shape of the landscapes by Aart van der Neer, "Dutch Villages," in the London National Gallery and in the Rudolphinum at Prague, respectively. Here are trees and houses on each side, gradually sloping to the centre to show an open sky and deep vista. Other examples, of course, show the opening not exactly in the centre.

In the "Concert" by Giorgione, in the Pitti Gallery, Florence, is seen the less frequent type of the square. The three figures turned toward each other with heads on the same level make almost a square space-shape, although it might be said that the central player gives a pyramidal foundation. This last may also be said of Verrocchio's "Tobias and the Archangels" in the Florence Academy, for the square, or other rectangle, is again lengthened by the pyramidal shape of the two central figures. The unrelieved square, it may here be interpolated, is not often found except in somewhat primitive examples. Still less often observed is the oval type of "Samson's Wedding Feast," Rembrandt, in the Royal Gallery, Dresden. Here one might, by pressing the interpretation, see an obtuse-angled double-pyramid with the figure of Delilah for an apex, but a few very irregular pictures seem to fall best under the given classification.

Last of all, it must be remarked that the great majority of pictures show a combination of two or even three types; but these are usually subordinated to one dominant type. Such, for instance, is the case with many portraits, which are markedly pyramidal, with the double-pyramid suggested by the position of the arms, and the inverted pyramid, or V, in the landscape background. The diagonal sometimes just passes over into the V-shape, or into the pyramid; or the square is combined with both.

What types are characteristic of the different kinds of pictures? In order to answer this question we must ask first, What are the different kinds of pictures? One answer, at least, is at once suggested to the student on a comparison of the pictures with their groupings according to subjects. All those which represent the Madonna enthroned, with all variations, with or without saints, shepherds, or Holy Family, are very quiet in their action; that is, it is not really an action at all which they represent, but an attitude,—the attitude of contemplation. This is no less true of the pictures we may call "Adorations," in which, indeed, the contemplative attitude is still more marked. On the other hand, such pictures as the "Descents," the "Annunciations," and very many of the miscellaneous religious, allegorical, and genre pictures, portray a definite action or event. Now the pyramid type is characteristic of the "contemplative" pictures in a much higher degree. A class which might be supposed to suggest the same treatment in composition is that of the portraits, —absolute lack of action being the rule. And we find, indeed, that no single type is represented within it except the pyramid and double-pyramid, with eighty-six per cent. of the former. Thus it is evident that for the type of picture which expresses the highest degree of quietude, contemplation, concentration, the pyramid is the characteristic type of composition. Among the so-called "active" pictures, the diagonal and V-shaped types are most numerous.

The landscape picture presents a somewhat different problem. It cannot be described as either "active" or "passive," inasmuch as it does not express either an attitude or an event. There is no definite idea to be set forth, no point of concentration, as with the altar-pieces and the portraits, for instance; and yet a unity is demanded. An examination of the proportions of the types shows at once the characteristic type to be here also the diagonal and V-shaped.

It is now necessary to ask what must be the interpretation of the use of these types of composition. Must we consider the pyramid the expression of passivity, the diagonal or V-shape, of activity? But the greatly predominating use of the second for landscapes would remain unexplained, for at least nothing can be more reposeful than the latter. It may aid the solution of the problem to remember that the composition taken as a whole has to meet the demand for unity, at the same time that it allows free play to the natural expression of the subject. The altar-piece has to bring about a concentration of attention to express or induce a feeling of reverence. This is evidently accomplished by the suggestion of the converging lines to the fixation of the high point in the picture,—the small area occupied by the Madonna and Child,—and by the subordination of the free play of other elements. The contrast between the broad base and the apex gives a feeling of solidity, of repose; and it seems not unreasonable to suppose that the tendency to rest the eyes above the centre of the picture directly induces the associated mood of reverence or worship. Thus the pyramidal form serves two ends; primarily that of giving unity, and secondarily, by the peculiarity of its shape, that of inducing the feeling-tone appropriate to the subject of the picture.

Applying this principle to the so-called "active" pictures, we see that the natural movement of attention between the different "actors" in the picture must be allowed for, while yet unity is secured. And it is clear that the diagonal type is just fitted for this. The attention sweeps down from the high side to the low, from which it returns through some backward suggestion of lines or interest in the objects of the high side. Action and reaction—movement and return of attention—is inevitable under the conditions of this type; and this it is which allows the free play,—which, indeed, CONSTITUTES and expresses the activity belonging to the subject, just as the fixation of the pyramid constitutes the quietude of the religious picture. Thus it is that the diagonal composition is particularly suited to portray scenes of grandeur, and to induce a feeling of awe in the spectator, because only here can the eye rove in one large sweep from side to side of the picture, recalled by the mass and interest of the side from which it moves. The swing of the pendulum is here widest, so to speak, and all the feeling-tones which belong to wide, free movement are called into play. If, at the same time, the element of the deep vista is introduced, we have the extreme of concentration combined with the extreme of movement; and the result is a picture in the "grand style" —comparable to high tragedy—in which all the feeling-tones which wait on motor impulses are, as it were, while yet in the same reciprocal relation, tuned to the highest pitch. Such a picture is the "Finding of the Ring," Paris Bordone, in the Venice Academy. All the mass and the interest and the suggestion of the downward lines and of the magnificent perspective toward the left, and the effect of the whole space composition is of superb largeness of life and feeling. Compare Titian's "Presentation of the Virgin," also the two great compositions by Veronese, "Martyrdom of St. Mark," etc., in the Doge's Palace, Venice, and "Esther before Ahaseurus," in the Uffizi, Florence. In these last two, the mass, direction of interest, movement, and attention are toward the left, while all the lines tend diagonally to the right, where a vista is also suggested,—the diagonal making a V just at the end. Here, too, the effect is of magnificence and vigor.

If, then, the pyramid belongs to contemplation, the diagonal to action, what ca be said of landscape? It is without action, it is true, and yet does not express that positive quality, that WILL not to act, of the rapt contemplation. The landscape uncomposed is negative, and it demands unity. Its type of composition, then, must give it something positive besides unity. It lacks both concentration and action; but it can gain them both from a space composition which shall combine unity with a tendency to movement. And this is given by the diagonal and V-shaped type. This type merely allows free play to the natural tendency of the "active" picture; but it constrains the neutral, inanimate landscape. The shape itself imparts motion to the picture: the sweep of line, the concentration of the vista, the unifying power of the inverted triangle between two masses, act, as it were, externally to the suggestion of the object itself. There is always enough quiet in a landscape,— the overwhelming suggestion of the horizontal suffices for that; it is movement that is needed for richness of effect, and, as I have shown, no type imparts the feeling of movement so strongly as the diagonal and V-shaped type of composition. Landscapes need energy to produce "stimulation," not repression, and so the diagonal type is proportionately more numerous.

The rigid square is found only at an early stage in the development of composition. Moreover, all the examples are "story" pictures, for the most part scenes from the lives of the saints, etc. Many of them are double-centre,—square, that is, with a slight break in the middle, the grouping purely logical, to bring out the relations of the characters. Thus, in the "Dream of Saint Martin," Simone Martini, a fresco at Assisi, the saint lies straight across the picture with his head in one corner. Behind him on one side stand the Christ and angels, grouped closely together, their heads on the same level. These are all, of course, in one sense symmetrical,— in the weight of interest, at least,—but they are completely amorphous from an aesthetic point of view. The forms, that is, do not count at all,—only the meanings. The story is told by a clear separation of the parts, and as, in most stories, there are two principal actors, it merely happens that they fall into the two sides of the picture. On the other hand, a rigid geometrical symmetry is also characteristic of early composition, and these two facts seem to contradict each other. But it is to be noted, first, that the rigid geometrical symmetry belongs only to the "Madonna Enthroned," and general "Adoration" pieces; and secondly, that this very rigidity of symmetry in details can coexist with variations which destroy balance. Thus, in a "Madonna Enthroned" of Giotto, where absolute symmetry in detail is kept, the Child sits far out on the right knee of the Madonna.

It would seem that the symmetry of these early pictures was not dictated by a conscious demand for symmetrical arrangement, or rather for real balance, else such failures would hardly occur. The presence of geometrical symmetry is more easily explained as the product, in large part, of technical conditions: of the fact that these pictures were painted as altar-pieces to fill a space definitely symmetrical in character—often, indeed, with architectural elements intruding into it. We may even connect the Madonna pictures with the temple images of the classic period, to explain why it was natural to paint the object of worship seated exactly facing the worshiper. Thus we may separate the two classes of pictures, the one giving an object of worship, and thus taking naturally, as has been said, the pyramidal, symmetrical shape, and being moulded to symmetry by all other suggestions of technique; the other aiming at nothing except logical clearness. This antithesis of the symbol and the story has a most interesting parallel in the two great classes of primitive art—the one symbolic, merely suggestive, shaped by the space it had to fill, and so degenerating into the slavishly symmetrical; the other descriptive, "story-telling," and without a trace of space composition. On neither side is there evidence of direct aesthetic feeling. Only in the course of artistic development do we find the rigid, yet often unbalanced, symmetry relaxing into a free substitutional symmetry, and the formless narrative crystallizing into a really unified and balanced space-form. The two antitheses approach each other in the "balance" of the masterpieces of civilized art—in which, for the first time, a real feeling for space composition makes itself felt.



V THE BEAUTY OF MUSIC

V THE BEAUTY OF MUSIC

I

THERE is a story, in Max Muller's amusing reminiscences, of how Mendelssohn and David once played, in his hearing, Beethoven's later sonatas for piano and violin, and of how they shrugged their shoulders, and opined the old man had not been quite himself when he wrote them. In the history of music it seems to be a rule almost without exceptions, that the works of genius are greeted with contumely. The same is no doubt true, though to a much less degree, of other arts, but in music it seems that the critics proposed also excellent reasons for their vehemence. And it is instructive to observe that the objections, and the reasons for the objections, recur, after the original object of wrath has passed into acceptance, nay, into dominance of the musical world. One may also descry one basic controversy running through all these utterances, even when not explicitly set forth.

It was made a reproach to Beethoven, as it has been made a reproach to Richard Strauss, that he sacrificed the beauty of form to expression; and it was rejoined, perhaps less in the old time than now, that expression was itself the end and meaning of music. Now the works of genius, as we have seen, after all take care of themselves. But it is of greatest significance for the theory of music, as of all art, that in the circle of the years, the same contrasting views, grown to ever sharper opposition, still greet the appearance of new work. It was with Wagner, as all the world knows, that the question came first to complete formulation. His invention of the music-drama rested on his famous theory of music as the heightened medium of expression, glorified speech, which accordingly demands freedom to follow all the varying nuances of feeling and emotion. Music has always been called the language of the emotions, but Wagner based his views not only on the popular notion, but on the metaphysical theories of Schopenhauer; in particular, on the view that music is the objectification of the will. Herbert Spencer followed with the thesis that music has its essential source in the cadences of emotional speech. In opposition primarily to Wagner, the so-called formalists were represented by Hanslick, who wrote his well-known "The Beautiful in Music" to show that though music ha a limited capacity of expression, its aim is formal or logical perfection alone. The expressionist school could not contradict the undoubted fact that chords and intervals which are harmonious show certain definite physical and mathematical relationships, that, in other words, our musical preferences appear to be closely related to, if not determined by, these relationships. Thus each school seemed to be backed by science. The emotional-speech theory has been held in a vague way, indeed, by most of those theorists whose natural conservatism would have drawn them in the other direction, and is doubtless responsible for the attempts at mediation, first made by Ambros, and now met in almost all musical literature. Music may be, and is, expressive, it is said, so long as each detail allows itself to be entirely derived from and justified by the mere formal element. The "centre of gravity" lies in the formal relations.

The Boundaries of Music and Poetry.

To this, after all, Hanslick himself might subscribe. Other writers seek to balance form and expression, insisting on "the dual nature of music," while resting ultimately on the emotional-speech theory. "The most universal composers, recognizing the interdependence of the two elements, produce the highest type of pure music, music in which beauty is based upon expression, and expression transfigured by beauty."

D.G. Mason, From Grieg to Brahms, 1902, p. 30.

This usual type of reconciliation, however, is a perfectly mechanical binding together of two possibly conflicting aesthetic demands. The question is of the essential nature of music, not whether music may be, but whether it must be, expressive; not whether is has expressive power, but whether it is, in its essence, expression,—a question which is only obscured by insisting on the interdependence of the two elements. If music has its essential source in the cadences of speech, then it must develop and must be judged accordingly. Herbert Spencer is perfectly logical in saying "It may be shown that music is but an idealization of the natural language of emotion, and that, consequently, music must be good or bad according as it conforms to the laws of this natural language." But what, then, of music which, according to Ambros, is justified by its formal relations? Is music good because it is very expressive, and bad because it is too little expressive? or is its goodness and badness independent of its expressiveness? Such a question is not to be answered by recognizing two kinds of goodness. Only by an attempt to decide the fundamental nature of the musical experience, and an adjustment of the other factors in strict subordination to it, can the general principle be settled.

On Educaiton, p. 41.

The excuse for this artificial yoking together of two opposing principles is apparent when it is seen that form and expression are taken as addressing themselves to two different mental faculties. It seems to be the view of most musical theorists that the experience of musical form is a perception, while the experience of musical expression, disregarding for the moment the suggestion of facts and ideas, is an emotion. Thus Mr. Mason: "In music we are capable of learning, and knowledge of the principles of musical effect can help us to learn, that the balance and proportion and symmetry of the whole is far more essential than any poignancy, however great, in the parts. He best appreciates music...who understands it intellectually as well as feels it emotionally;" and again, "We feel in the music of Haydn its lack of emotional depth, and its lack of intellectual subtlety."

Op. Cit., p. 6.

It is just this contrast and parallelism of structure as balance, proportion, symmetry, addressed to the mind, with expression as emotional content, that a true view of the aesthetic experience would lead us to challenge. If there is one thing that our study of the general nature of aesthetic experience has shown, it is that aesthetic emotion is unique— neither a perception nor an intellectual grasp of relations, nor an emotion within the accepted rubric—joy, desire, triumph, etc. Whether or not music is an exception to this principle, remains to be seen; but the presumption is at least in favor of a direct, immediate, unique emotion aroused by the true beauty of music, whatever that may prove to be.

With a great literature in the form of special studies, we must yet, on the whole, admit that we possess no general formula in the philosophy or psychology of music which covers the whole ground. Schopenhauer has said that music is the objectification of the will—not a copy or a picture of it, but the will itself; a doctrine which however illuminating when it is modified in various ways is obviously no explanation of our experience. Hanslick has but shown what music is not; Edmund Gurney's eloquent book, "The Power of Sound," is completely agnostic in its conclusion that music is a unique, indefinable, indescribable phenomenon, which possesses, indeed, certain analogues with other physical and psychical facts, but is coextensive with none. Spencer's theory of music as glorified speech is not only in a yet unexplained conflict with many facts, but has never been formulated so that it could apply to concrete cases. The same is true of Wagner's "music as the utterance of feeling."

But there is a body of scientific facts respecting the elements of music, in which we may well seek for clues. As facts alone they are of no value. They must be explained as completely as possible; and it is probable that if we are able to reach the ultimate nature and origin of these elements of music they will prove significant, and a way will be opened to a theory of the whole musical experience. The need of such intensive understanding must excuse the more or less technical discussions in the following pages, without which no firm foundation for a theory of music could be attained.

II

The two great factors of music are rhythm and tone-sensation, of which rhythm appears to be the more fundamental.

Rhythm is defined in general as a repeating series of time intervals. Events which occur in such a series are said to have rhythm. In aesthetics, it is the periodic recurrence of stress, emphasis, or accent in the movements of dancing, the sounds of music, the language of poetry. Subjectively it is the quality of stimulation due to a succession of impressions (tactual and auditory are most favorable) which vary regularly in objective intensity. We desire to understand the nature, and the source of the pleasing quality, of this phenomenon.

It is only by a complete psychological description, however, even a physiological explanation, that we can hope to fathom the tremendous significance of rhythm in music and poetry. Those treatments which expose its development in the dance and song really beg the question; they assume the very fact for which we have to find the ground, namely, the natural impulse to rhythm. Even those theories which explain it as a helpful social phenomenon, as regulating work, etc., fail to account for its peculiar psychological character—that compelling, intimate force, the "Zwang" of which Nietszche speaks, which we all feel, and which makes it helpful. This compelling quality of rhythm would lead us to look behind the sociological influences, for the explanation in some fundamental condition of consciousness, some "demand" of the organism. For this reason we must find superficial the views which connect rhythm with the symmetry of the body as making rhythmical gesture necessary; or more particularly with the conditions of work, which, if it is skilled and well carried out, proceeds in equal recurring periods, like the swinging of a hammer or an axe. But it appears that primitive effort is not carried on in this way, and proceeds, not from regularity to rhythm, but rather, through, by means of rhythm, which is made a help, to regularity. Again, it is said that work can be well carried out by a large number of people, only in unison, only by simultaneous action, and that rhythm is a condition of this. The work in the cotton fields, the work of sailors, etc. requires something to give notice of the moment for beginning action. Rhythm would then have arisen as a social function. Against this it may be said that signals of this kind might assist common action without recurring at regular intervals, while periodicity is the fundamental quality of rhythm. Thus this theory would explain a natural tendency by its effect.

Looking then, in accordance with the principle stated above, for deeper conditions, we find rhythm explained in connection with such rhythmical events as the heart beat and pulse, the double rhythm of the breath; but these are, for the most part, unfelt; and moreover, they would hardly explain the predominance of rhythms quite other than the physiological ones. Another theory, closely allied, connects rhythm with the conditions of activity in general, but attaches itself rather to the effect of rhythm than to its cause. Thus we are reminded of the "heightened sense of expansion, or life, connected with the augmentation of muscular movements induced by the more extensive nervous discharges following rhythmic stimulation." But why should it be just rhythmic stimulation that produces this effect? We are finally thrown back on physiology for the answer that in rhythmical stimulation there are involved recurrent activities of organs refreshed by immediately preceding periods of repose. Here again, however, we must ask, why on this hypothesis the periods themselves must be exactly equal. For within the periods the greatest variety obtains. One measure of a single note may be succeeded by another containing eight; within the periods, that is, the minor moments of activity and repose are quite unequal.

H.R. Marshall, Pain, Pleasure, and Aesthetics.

Last of all, we must note the view of rhythm as a phenomenon of expectation (Wundt). But while we can undoubtedly describe rhythm in terms of expectation and its satisfaction, rhythm is rhythm just through its difference from other kinds of expectation.

All these explanations seem either merely to describe the facts we seek to explain, or to fail to notice the peculiar intimate nature of the rhythmical experience. But if it could be shown not only that in all stimulation there must be involved an alternation of activity and repose, but also that an equality of such periods was highly favorable to the organism, we should have the conditions for a physiological theory of rhythm. Now the important psychological facts of so-called subjective rhythmizing seem to supply just this need.

It has been shown that we can neither receive objectively equal sense-stimuli, nor produce regular movements, without injecting into these a rhythmical element. A series of objectively equal sound-stimuli—the ticking of a clock, for instance—is heard in groups, within each of which one element is of greater intensity. A series of movements are never objectively equal, but grouped in the same way. Now this subjective rhythm, sensory and motor, is explained as follows from the general physiological basis of attention.

T.L. Bolton, Amer. Jour. Of Psychol., vol. vi. The classical historical study of theories of rhythm remains that of Meumann, Phil. Studien, vol. x.

Attention itself is ultimately a motor phenomenon. Thus: the sensory aspect of attention is vividness, and vividness is explained physiologically as a brain-state of readiness for motor discharge; in the case of a visual stimulus, for instance, a state of readiness to carry out movements of adjustment to the object; in short, the motor path is open. Now attention, or vividness, is found to fluctuate periodically, so that in a series of objectively equal stimuli, certain ones, regularly recurring, would be more vividly sensed. This is exemplified in the well-known facts of the fluctuation of the threshold of sensation, of the so-called retinal rivalry, and of the subjective rhythmizing of auditory stimuli, already mentioned. There is a natural rhythm of vividness. Here, therefore, in the very conditions of consciousness itself, we have the conditions of rhythm too. The case of subjective motor rhythm would be still clearer, since vividness is only the psychical side of readiness for motor discharge; in other words, increased readiness for motor discharge occurs periodically, giving motor rhythm.

Munsterberg, Grundzuge d. Psychologie, 1902,. P. 525.

It has been said that this periodicity of the brain-wave cannot furnish the necessary condition for rhythm, inasmuch as it is itself a constant, and could at most be applied to a series which was adapted to its own time. But this objection does not fit the facts. The "brain-wave," or "vividness," or attention period, is not a constant, but attaches itself to the contents of consciousness. In other words, it does not function without material. It is itself conditioned by its occasion. In the case of a regularly repeated stimulus, it is simply adjusted to what is there, and out of the series chooses, as it were, one at regular periods.

J.B. Miner, "Motor, Visual, and Applied Rhythms," Psychol. Rev., Mon. Suppl., No. 21. Facts, too technical for reproduction here, quoted by R.H. Stetson (Harvard Psychol. Studies, vol. i, 1902) from Cleghorn's and Hofbauer's experiments seem to be in harmony with this view.

Closely connected with these facts, perhaps only a somewhat different aspect of them, is the phenomenon of motor mechanization. Any movement repeated tends to become a circular reaction, as it is called; that is, the end of one repetition serves as a cue for the beginning of the next. Now, in regularly recurring stimuli, giving rise, as will be later shown, to motor reactions, which are differentiated through the natural periodicity of the attention (physiologically the tendency to motor discharge), we have the best condition for this mechanization. In other words, a rhythmical grouping once set up naturally tends to persist. The organism prepares itself for shocks at definite times, and shocks coming at those times are pleasant because they fulfill a need. Moreover, every further stimulus reinforces the original activity; so that rhythmical grouping tends not only to persist, but to grow more distinct,—as, indeed, all the facts of introspection show.

All this, however, is true of the repetition of objectively equal stimuli. It shows how an impulse to rhythm would arise and persist subjectively, but does not of itself explain the pleasure in the experience of objective rhythm. It may be said in general, however, that changes which would occur naturally in an objectively undifferentiated content give direct pleasure when they are artificially introduced,—when, that is, the natural disposition is satisfied. This we have seen to be true in the of color contrast; and it is perhaps even more valid in the realm of motor activity. Whatever in sense stimulation gives the condition for, helps, furthers, enhances the natural function, is felt both as pleasing and as furthering the particular activity in question. Now, the objective stress in rhythm is but emphasis on a stress that would be in any case to some degree subjectively supplied. Rhythm in music, abstracting from all other pleasure-giving factors, is then pleasurable because it is in every sense a favorable stimulation.

In accordance with the principle that complete explanation of psychical facts is possible only through the physiological substrate, we have so far kept rather to that field in dealing with the foundations of our pleasure in rhythm. But further description of the rhythmical experience is most natural in psychological terms. There seems, indeed, on principle no ground for the current antithesis, so much emphasized of late, of "psychical" and "motor" theories of rhythm. Attention and expectation are not "psychical" as opposed to "motor." Granting, as no doubt most psychologists would grant, that attention is the psychical analogue of the physiological tendency to motor discharge, then a motor automatism of which one is fully conscious could be described as expectation and its satisfaction. Indeed, the impossibility of a sharp distinction between ideas of movement and movement sensations confirms this view. When expectation has reference to an experience with a movement element in it, the expectation itself contains movement sensations of the kind in question. To say, then, that rhythm is expectation based on the natural functioning of the attention period, is simply to clothe our physiological explanation in terms of psychological description. The usual motor theory is merely one which neglects the primary disposition to rhythm through attention variations, in favor of the sensations of muscular tension (kinaesthetic sensations) which arise IN rhythm, but do not cause it. To say that the impression of rhythm arises only in kinaesthetic sensations begs the question in the way previously noted. Undoubtedly, the period once established, the rhythmic group is held together, felt as a unit, by means of the coordinated movement sensations; but the main problem, the possibility of this first establishment, is not solved by such a motor theory. In other words, the attention theory is the real motor theory.

C.M. Hitchcock, "The Psychol. Of Expectation," Psychol. Rev., Mon. Suppl., No. 20.

Expectation is the "set" of the attention. Automatism is the set of the motor centres. Now as attention is parallel to the condition of the motor centres, we are able to equate expectation and automatic movement. Rhythm is literally embodied expectation, fulfilled. It is therefore easily to be understood that whatever other emotions connect themselves with satisfied expectation are at their ideal poignance in the case of rhythm.

It is from this point of view that we must understand the helpfulness of rhythm in work. That all definite stimulus, and especially sound stimulus, rhythmical or not, sets up a diffusive wave of energy, increasing blood circulation, dynamogenic phenomena, etc., is another matter, which has later to be discussed. But the essential is that this additional stimulus is rhythmical, and therefore a reinforcement of the nervous activity, and therefore a lightening and favorable condition of work itself. So it is, too, that we can understand the tremendous influence of rhythm just among primitive peoples, and those of a low degree of culture. Work is hard for savages, not because bodily effort is hard, but because the necessary concentration of attention is for them almost impossible; and the more, that in work they are unskilled, and without good tools, so that generally every movement has to be especially attended to. Now rhythm in work is especially directed to lighten that effort which they feel as hardest; it rests, renews, and frees the attention. Rhythm is helpful not primarily because it enables many to work together by making effort simultaneous, but rhythm rests and encourages the individual, and working together is most naturally carried out in rhythm.

To this explanation all the other facts of life-enhancement, etc., can be attached. Rhythm is undoubtedly favorable stimulation. Can it be brought under the full aesthetic formula of favorable stimulation with repose? A rhythm once established has both retrospective and prospective reference. It looks before and after, it binds together the first and the last moments of activity, and can therefore truly be said to return upon itself, so as to give a sense of equilibrium and repose.

But when we turn from the fundamental facts of simple rhythm to the phenomena of art we find straightway many other problems. It is safe to say that no single phrase of music or line of poetry is without variation; more, that a rhythm without variation would be highly disagreeable. How must we understand these facts? It is impossible within the natural limitations of this chapter to do more than glance at a few of them.

First of all, then, the most striking thing about the rhythmical experience is that the period, or group, is felt as a unit. "Of the number and relation of individual beats constituting a rhythmical sequence there is no awareness whatever on the part of the aesthetic subject....Even the quality of the organic units may lapse from distinct consciousness, and only a feeling of the form of the whole sequence remains." Yet the slightest deviation from its form is remarked. Secondly, every variation creates not only a change in its own unit, but a wave of disturbance all along the line. Also, every variation from the type indicates a point of accentual stress; the syncopated measure, for instance, is always strongly accented. All these facts would seem to be connected with the view of the importance of movement sensations in building up the group feeling. The end of each rhythm period gives the cue for the beginning of the next, and the muscle tensions are coordinated within each group; so that each group is really continuous, and would naturally be "felt" as one,—but being automatic, would not be perceived in its separate elements. On the other hand, it is just automatic reaction, a deviation from which is felt most strongly. The syncopated measure has to maintain itself against pressure, as it were, and thus by making its presence in consciousness felt more strongly, it emphasizes the fundamental rhythm form.

R. MacDougall, "The Structure of Simple Rhythm Forms," Harv. Psychol. Studies, vol. i, p. 332.

This is well shown in the following passage from a technical treatise on expression in the playing of music. "The efforts which feeling makes to hold to...the shape of the first rhythm, the force which it is necessary to use to make it lose its desires and its habits, and to impose others on it, are naturally expressed by an agitation, that is, by a crescendo or greater intensity of sound, by an acceleration in movement." If a purely technical expression may be pardoned here, it could be said that the motor image, that is, the coordinated muscular tensions which make the group feeling of the fundamental rhythm, is always latent, and becomes conscious whenever anything conflicts with it. Thus it is that we can understand the tremendous rhythmical consciousness in that music which seems most to contradict the fundamental rhythm, as in negro melodies, and rag-time generally; and in general, the livening effect of variation. The motor tension, the "set" becomes felt the moment there is objective interference—just as we feel the rhythm of our going downstairs only when we fail to get the sensation we expect.

M. Lussy, Traite de l'Expression Musicale, Paris, 1874, p. 7. Gestaltsqualitat, literally form-quality.

This principle of the motor image is of tremendous significance, as we shall see, for the whole theory of music. Let it be sufficient to note here that expression, in the form of Gestaltsqualitat, or motor image, is, as a principle, sufficient for the explanation of the most important factors in the experience of rhythm.

III

But we have dwelt too long on the general characteristics. Although our examples have been drawn mostly from the field of music, the preceding principles apply to all kinds of rhythm, tactual and visual as well as auditory. It is time to show why the rhythm out of all comparison the strongest, most compelling, most full of emotional quality, is the rhythm of music.

It has long been known that there is especially close connection between sounds and motor innervations. All sorts of sensorial stimuli produce reflex contractions, but the auditory, apparently, to a much higher degree. Animals are excited to all sorts of outbreaks by noise; children are less alarmed by visual than by auditory impressions. The fact that we dance to sound rather than to the waving of a baton, or rhythmical flashes of light for instance—the fact that this second proposition is felt at once to be absurd, shows how intimately the two are bound together. The irresistible effects of dance, martial music, etc., are trite commonplaces; and I shall therefore not heap up instances which can be supplied by every reader from his own experience. Now all this is not hard to understand, biologically. The eye mediated the information of what was far enough away to be fled from, or prepared for; the ear what was likely to be nearer, unseen, and so more ominous. As more ominous, it would have to be responded to in action more quickly. So that if any sense was to be in especially close connection with the motor centres, it would naturally be hearing.

The development of the auditory functions points to the same close connection of sound and movement. Sounds affect us as tone, and as impulse. The primitive sensation was one of impulse alone, mediated by the "shake-organs." These shake- organs at first only gave information about the attitude and movements of the body, and were connected with motor centres so as to be able to reestablish equilibrium by means of reflexes. The original "shake-organ" developed into the organs of hearing and of equilibrium (that is, the cochlea and the semicircular canals respectively), but these were still side by side in the inner ear, and the close connection with the motor centres was not lost. Anatomically, the auditory nerve not only goes to those parts of the brain whence the motor innervation emanates, and to the reflex centres in the cerebellum, but passes close by the vagus or pneumogastric nerve, which rules the heart and the vasomotor functions. We have then multiplied reasons for the singular effect of sound on motor reactions, and on the other organic functions which have so much to do with feeling and emotion.

Every sound-stimulus is then much more than sound-sensation. It causes reflex contractions in the whole muscular system; it sets up some sort of cardiac and vascular excitation. This reaction is in general in the direction of increased amplitude of respiration, but diminution of the pulse, depending on a peripheral vaso-constriction. Moreover, this vasomotor reaction is given in a melody or piece of music, not by its continuity, but for every one of the variations of rhythm, key, or intensity,—which is of interest in the light of what has been said of the latent motor image. The obstacle in syncopated rhythm is physiologically translated as vaso-constriction. In general, music induces cardiac acceleration.

All this is of value in showing how completely the attention- motor theory of rhythm applies to the rhythm of sounds. Since sound is much more than sound, but sound-sensation, movement, and visceral change together, we can see that the rhythmical experience of music is, even more literally and completely than at first appeared, an EMBODIED expectation. No sensorial rhythm could be so completely induced in the psychological organism as the sound-rhythm. In listening to music, we see how it is that we ourselves, body and soul, seem to be IN the rhythm. We make it, and we wait to make it. The satisfaction of our expectation is like the satisfaction of a bodily desire or need; no, not like it, it IS that. The conditions and causes of rhythm and our pleasure in it are more deeply seated than language, custom, even instinct; they are in the most fundamental functions of life. This element of music, at least, seems not to have arisen as a "natural language."

IV

The facts of the relations of tones, the elements, that is, of melody and harmony, are as follows. We cannot avoid the observation that certain tones "go together," as the phrase is, while others do not. This peculiar impression of belonging together is known as consonance, or harmony. The intervals of the octave, the fifth, the third, for instance, that is, C-C', C-G, C-E, in the diatonic scale, are harmonious; while the interval of the second, C-D, is said to be dissonant. Consonance, however, is not identical with pleasingness, for different combinations are sometimes pleasing, sometimes displeasing. In the history of music we know that the octave was to the Greeks the most pleasing combination, to medieval musicians the fifth, while to us, the third, which was once a forbidden chord, is perhaps most delightful. Yet we should never doubt that the octave is the most consonant, the fifth and the third the lesser consonant of combinations. We see, thus, that consonance, whatever its nature, is independent of history; and we must seek for its explanation in the nature of the auditory process.

Various theories have been proposed. That of Helmholtz has held the field so long that, although weighty objections have been raised to it, it must still be treated with respect. In introducing it a short review of the familiar facts of the physics and physiology of hearing may not be out of place.

The vibration rates per second of the vibrating bodies, strings, steel rods, etc., which produce those musical tones which are consonant, are in definite and small mathematical ratios to each other. Thus the rates of C-C' are as 1:2; of C-G, C-E, as 2:3, 4:5. In general, the simpler the fraction, the greater the consonance.

But no sonorous body vibrates in one single rate; a taut string vibrates as a whole, which gives its fundamental tone, but also in halves, in fourths, etc., each giving out a weaker partial tone, in harmony with the fundamental. And according to the different ways in which a sonorous body divides, that is, according to the different combination of partial tones peculiar to it, is its especial quality of tone, or timbre. The whole complex of fundamental and partial tones is what we popularly speak of as a tone,—more technically a clang. These physical agitations or vibrations are transmitted to the air. Omitting the account of the anatomical path by which they reach the inner ear, we find them at last setting up vibrations in a many-fibred membrane, the basilar membrane, which is in direct connection with the ends of the auditory nerve. It is supposed that to every possible rate of vibration, that is, every possible tone, or partial tone, there corresponds a fibre of the basilar membrane fitted by its length to vibrate synchronously with the original wave-elements. The complex wave is thus analyzed into its constituents. Now when two tones, which we will for clearness suppose to be simple, unaccompanied by partial tones, sounding together, have vibration rates in simple ratios to each other, the air- waves set in motion do not interfere with each other, but combine into a complex but homogeneous wave. If they have to each other a complicated ratio, such as 500:504, the air- waves will not only not coalesce, but four times in the second the through of one wave will meet the crest of the other, thus making the algebraic sum zero, and producing the sensation of a momentary stoppage of the sound. When these stoppages, or beats, as they are called, are too numerous to be heard separately, as in the interval, say, 500:547, the effect is of a disagreeable roughness of tone, and this we call discord. In other words, any tones which do not produce beats are harmonious, or harmony is the absence of discord. In the words of Helmholtz, consonance is a continuous, dissonance an intermittent, tone-sensation.

Lehre v.d. Tonempfindungen, p. 370, in 4th edition.

Aside from the fact that consonance, as a psychological fact, seems positive, while this determination is negative, two very important facts can be set up in opposition. As a result of experimental investigation, we know that the impression of consonance can accompany the intermittent or rough sound- sensations we know as beating tones; and, conversely, tones can be dissonant when the possibility of beats is removed. Briefly, it is possible to make beats without dissonance, and dissonance without beats.

The other explanation makes consonance due to the identity of partial tones. When two tones have one or more partial tones in common they are said to be related; the amount of identity gives the degree of relationship. Physiologically, one or more basilar membrane fibres are excited by both, and this fact gives the positive feeling of relationship or consonance. Of course the obvious objection to this view is that the two tones should be felt as differently consonant when struck on instruments which give different partial tones, such as organ and piano, while in fact they are not so felt.

But it is not after all essential to the aesthetics of music that the physiological basis of harmony should be fully understood. The point is that certain tones do indeed seem to be "preordained to congruity," preordained either in their physical constitution or their physiological relations, and not to have achieved congruity by use or custom. Consonance is an immediate and fundamental impression,—psychologically an ultimate fact. That it is ultimate is emphasized by Stumpf in his theory of Fusion. Consonance is fusion, that is, unitary impression. Fusion is not identical with inability to distinguish two tones from each other in a chord, although this may be used as a measure of fusion. Consonance is the feeling of unity, and fusion is the mutual relation of tones which gives that feeling.

Beitrage zur Akustik u. Musikwissenschaft, Heft I, Konsonanz u. Dissonanz, 1898.

The striking fact of modern music is the principle of tonality. Tonality is said to be present in a piece of music when every element in it is referred to, gets its significance from its relation to, a fundamental tone, the tonic. The tonic is the beginning and lowest note in the scale in question, and all notes and chords are understood according to their place in that scale. But the conception of the scale of course does not cover the ground, it merely furnishes the point of departure,— the essential is in the reference of every element to the fundamental tone. The tonic is the centre of gravity of a melody.

The feeling of tonality grew up as follows. Every one was referred to a fundamental, whether or not it made with it an harmonious interval. The fundamental was imaged TOGETHER WITH every other note, and when a group of such references often appeared together, the feelings bound up with the single reference (interval-feelings) fused into a single feeling,— the tonality-feeling. When this point is once reached, it is clear that every tone is heard not as itself alone, but in its relations; it is not that we judge of tonality, it is a direct impression, based on a psychological principle that we have already touched on in the theory of rhythm. The tonality- feeling is a feeling of form, or motor image, just as the shape of objects is a motor image. We do not now need to go through all possible experiences in relation to these objects, we POSSESS their form in a system of motor images, which are themselves only motor cues for coordinated movements. So every tone is felt as something at a certain distance from, with a certain relation to, another tone which is dimly imagined. In following a melody, the notes are able to belong together for us by virtue of the background of the tone to which they are related, and in terms of which they are heard. The tonality is indeed literally a "funded content,"—that is, a funded capital of relation.

These are the general facts of tonality. But what is its meaning for the nature of music? Why should all notes be referred to one? Is this, too, an ultimate psychological fact? In answer there may be pointed out the original basic quality of certain tones, and the desire we have to return to them. Of two successive tones, it is always the one which is, in the ratio of their vibration rates, a power of two, with which we wish to end. When neither of two successive tones contains a power of two, we have no preference as to the ending. Thus denoting any tone by 1, it is always to 1 or 2, or 2n that we wish to return, from any other possible tone; while 3 and 5, 5 and 7, leave us indifferent as to their succession. In general, when two tones are related, as 2n:3, 5, 7, 9, 15—in which 2n denotes every power of two, including 2o=1, with the progression from the first to the second, there is bound up a tendency to return to the first. Thus the fundamental fact of melodic sequence may be said to be the primacy of 2 in vibration rates. But 2n, in a scale containing 3, 5, etc., is always what we know as the tonic. The tonic, then, gives a sense of equilibrium, of rest, of finality, while to end on another tone gives a feeling of restlessness or striving.

Now tone-relationship alone, it is clear, would not of itself involve this immediate impulse to end a sequence of notes on one rather than on another. Nor is tonality, in the all- pervasive sense in which we understand it, a characteristic of ancient, or of mediaeval music, while the tendency to end on a certain tone, which we should to-day call the tonic, was always felt. Thus, since complete tonality was developed late in the history of music, while the closing on the tonic was certainly prior to it, the finality of the tonic would seem to be the primary fact, out of which the other has been developed.

We speak to-day, for instance, of dissonant chords, which call for a resolution—and are inclined to interpret them as dissonant just because they do so call. But the desire for resolution is historically much later than the distinction between consonance and dissonance.... "What we call resolution is not change from dissonant to consonant IN GENERAL, but the transition of definite tones of a dissonant interval into DEFINITE TONES of a consonant." The dissonance comes from the device of getting variety, in polyphonic music, by letting some parts lag behind, and the discords which arose while they were catching up were resolved in the final coming together; but the STEPS were all PREDETERMINED. Resolution was inevitably implied by the very principle on which the device is founded. That is, the understanding of a chord as something TO BE RESOLVED, is indeed part of the feeling of tonality; but the ending on the tonic was that out of which this resolution- feeling grew.

Stumpf, op. Cit., p. 33. Grove, Dict. Of Music and Musicians. Art. "Resolution."

Must we, then, say that the finality of the tonic is a unique, inexplicable phenomenon? giving up the nature of melody as a problem if not insoluble, at least unsolved?

The feeling of finality in the return to 2n is explained by Lipps and his followers, from the fact that the two-division is most natural, and so tones of 2n vibrations would have the character of rest and equilibrium. This explanation might hold if we were ever conscious of the two-division as such, in tones —which we are not; so that it would seem to depend on the restful character of a perception which by hypothesis is never present to the mind at all.

The experience is, on the contrary, immediate,—an impression, not a perception; and this immediacy points to the one ultimate fact in musical feeling we have so far discovered. The whole development of the scale, and the complex feeling of tonality, is an expression of the desire for consonance. Every change and correction in the scale has gone to make every note more consonant with its neighbors. And naturally the tonic is the tone with which all other tones have the most unity. Now this "return" phenomenon is a simpler case of the desire for the feeling of unity. The tonic is the epitome of all the most perfect feelings of consonance or unity which are possible in any particular sequence of tones, and is therefore the goal or resting-place after an excursion. The undoubted feeling of equilibrium or repose which we have in ending on the tonic is thus explained. Not that consonance itself, the feeling of unity, is explained. But at any rate consonance is the root of the "return," and of its development into complete tonality.

The history of music is then the explicit development of acoustic laws implicit in every stage of musical feeling. That feeling covers an ever wider field. When Mr. Hadow says that the terms concord and discord are wholly relative to the ear of the listener, and that the distinction between them is not to be explained on any mathematical basis, or by any a priori law of acoustics,—that it is not because a minor second is ugly that we dislike it, for it will be a concord some day,—he is only partly right. The minor second may be a "concord," that is, we may like it, some day; but that will be because w have extended our feeling of tonality to include the minor second. When that day comes the minor second will be so closely linked with other fully consonant combinations that we shall hear it in terms of them, just as to-day we hear the chord of the dominant seventh in terms of its resolution. But the basis will not be convention or custom, except in so far as custom is the unfolding of natural law. The course of music, like that of every other art, is away from arbitrary—though simple—convention, to a complexity which satisfies the natural demands of the organism. The "natural persuasion" of the ear is omnipotent.

W.H. Hadow, Studies in Modern Music, 1893.

V

It has been said that the feeling of tonality is a motor image or "form-quality" and that the image of the tonic persists throughout every sequence of tones in a melody. Now these are not only felt as having a certain relation to the tonic; that relation is an active one. It was said that we had a positive desire to end on a certain tone, and that a tendency to pass to that tone was bound up with the hearing of another tone. The degree of this tendency is determined by their relation. The key, the tonality, is determined by the consensus of intervals which have been felt as more or less consonant. Then steps in this scale which come near to the great salient points—that is, the points of greatest consonance, which is unity, which is rest—are felt as suggesting them. This is the reason why a semitone progression is felt as so compelling. In taking the scale upward, C to C', that element in the tone- Space already clearly foreshadowed by the previous tones is C'; B is so near that it is almost C'—it seems to cry aloud to be completed by C'. Then the tendency to move from B to C' is especially strong. In the same way a chromatic note suggests most strongly the salient point in the scheme to which it is nearest—and "tends" to it as to a point of comparative rest. The difference between the major and minor scales may be found in the lesser definiteness with which the tendency to progression, in the latter, is felt—"a condition of hovering, a kind of ambiguity, of doubt, to which side the movement shall proceed." We may then understand a melody as ever tending with various degrees of urgency, of strain, to its centre of gravity, the tonic.

F. Weinmann, Zeitschr. f. Psychol., Bd. 35, p. 360.

It is from this point of view that we can see the cogency of Gurney's remark, that when music seems to be yearning for unutterable things, it is really yearning only for the next note. "In this step from the state of rest into movement and return, the coming again to rest; on what circuitous ways, with what reluctances and hesitations; whether quick and decisively or gradually and unnoticed—therein consists the nature of melody."

Weinmann, op. cit.

Or in Gurney's more eloquent description, "The melody may begin by pressing its way through a sweetly yielding resistance to a gradually foreseen climax; whence again fresh expectation is bred, perhaps for another excursion, as it were, round the same centre but with a bolder and freer sweep,...to a point where again the motive is suspended on another temporary goal; till after a certain number of such involutions and evolutions, and of delicately poised leanings and reluctances and yieldings, the forces so accurately measured just suffice to bring it home, and the sense of potential and coming integration which has underlain all our provisional adjustments of expectation is triumphantly justified."

Op. cit., p. 165.

This should not be taken as a more or less poetical account under the metaphor of motion. These "leanings" are literal in the sense that one note does imply another as its natural complement and satisfaction and we seek to reach or make it. The striving is an intrinsic element, not a by-product for our understanding.

There is another point to note. The "sense of potential and coming integration" is a strong factor of melody. If it cannot be said that the first note implies the last, it is at least true that from point to point the next step is dimly foreseen, and this effect is cumulative. If melody is an ever-hindered striving for the goal, at least the hindrances themselves are stations on the way, each one as overcome adding to the final momentum with which the goal is reached. It is like an accumulation of evidence, a constellation of associations. AB foretells C; but ABCDEF rushes yet more strongly upon G. So it is that the irresistibleness, the "unalterable rightness" of a piece of music increases from beginning to end.

The significance of this essential internal necessity of progression cannot be overestimated. The unalterable rightness of music is founded on natural acoustic laws, and this "rightness" is fundamental. A melody is not right because it is beautiful, it is beautiful because it is right. The natural tendencies point out different paths to the goal; and thus different ways of being beautiful; but the nature of the relation between point and point, the nature of the progression, that is, the nature of melody, is the same.

Up to this point we have consistently abstracted from the element of rhythm in melody. Strictly speaking, however, it is impossible to do so. The individuality of a melody is absolutely dependent on its rhythm, that is, on the relative time-value of its tones. Gurney has devoted some amusing pages to showing the trivial, dragging, lustreless tunes that result from ever so slight a change in the rhythm of noble themes, or even in the distribution of rhythmical elements within the bar. The reason for this is evident. The nature of melody in the sense of sequence consists in the varied answers to the demands of the ear as felt at each successive point. Now it is clear that such "answer" can be emphasized, given indifferently, held in suspense, in short, subjected to all kinds of variation as well by the rhythmical form into which it is cast, as by the different choice of possibilities for the tone itself. The rhythm helps out the melody not only by adding to it an independently pleasing element, but, and this is indeed the essential, by reinforcing the intrinsic relations of the notes themselves. Thus it is in the highest degree true that in melody and rhythm we do not have content and form, but that, strictly speaking, the melody is tone-sequence in rhythm.

The intimate bondage of tone-sequence and rhythm is grounded in the identity of their inner nature; both are varieties of the objective conditions of embodied expectation. It is not of the essence of music to satisfy explicit and conscious expectation—to satisfy the understanding. It meets on the contrary a subconscious, automatic need which becomes conscious only in the moment of its contenting. Every moment of progress in a beautiful melody is hailed like an instinctive action performed for the first time. Rhythm is the ideal satisfaction of attention in general with all its bodily concomitants and expressions. Tone-sequence is the satisfaction of attention directed to auditory demands. But the form-quality of rhythm, the form-quality of tonality, is an all but subconscious possession. Together, reinforcing each other in melody, they furnish the ideal arrangement of the most poignant of sense- stimulations.

VI

It is strange that those who would accept the general facts of musical logic as outlined above do not perceive that they have thereby cut away the ground from under the feet of the "natural language" argument. If the principle of choice in the progress of a melody is tone-relationship, the principle of choice cannot also be the cadences of the speaking voice. That musical intervals often RECALL the speaking voice is another matter, as we have said, and to this it may be added that they much more often do not. The question here is only of the primacy of the principle. Thus it would seem that the facts of musical structure constitute in themselves a refutation of the view we have disputed. To say that music arose in "heightened speech" is irrelevant; for the occasion of an aesthetic phenomenon is never its cause. It might as well be said that music arose in economic conditions,— as indeed Grosse, in his "Anfange der Kunst," conclusively shows, without attempting to make this social occasion intrude into the nature of the phenomenon. Primitive decorative art arose in the imitation of the totemic or clan symbols, mostly animal forms; but we have seen that the aesthetic quality of the decoration is due to the demands of the eye, and appears fully only in the comparative degradation of the representative form. In exactly the same way might we consider the "degradation" of speech cadences into real music,—supposing this were really the origin of music. As a matter of fact, however, the best authorities seem to be agreed that the primitive "dance-song" was rather a monotonous, meaningless chant, and that the original pitch- elements were mechanically supplied by the first musical instruments; these being at first merely for noise, and becoming truly vibrating, sonorous bodies because they were more easily struck if they were hard or taut. The musical tones which these hard vibrating bodies gave out were the first determinations of pitch, and of the elements of the scale, which correspond to the natural partial vibrations of such bodies. "The human voice," Wallaschek tells us, "equally admits of any pentatonic or heptatonic intervals, and very likely we should never have got regular scales if we had depended upon the ear and voice only. The first unique cause to settle the type of a regular scale is the instrument." To this material we have to apply only that "natural persuasion of the ear" which we have already explained, to account for the full development of music.

Primitive Music, 1893, p. 156.

The beauty of music, in so far as beauty is identical with pleasantness, consists in its satisfaction of the demands of the ear, and of the whole psychophysical organism as connected with the ear. It is now time to return to a thread dropped at the beginning. It was said that a common way of settling the musical experience was to make musical beauty the object of perception, and musical expression the object, or source, of emotion. This view seems to attach itself to all shades of theory. Hanslick always contrasts intellectual activity as attaching to the form, and emotion as attaching to the sensuous material (that is, the physical effects of motion, loud or soft sound, tempo, etc.). He speaks of the aesthetic criterion of INTELLIGENT gratification. "The truly musical listener" has "his attention absorbed by the particular form and character of the composition," "the unique position which the INTELLECTUAL ELEMENT in music occupies in relation to FORMS and SUBSTANCE (subject)." M. Dauriac in the same way separates the emotion of music as a product of nervous excitations, from the appreciation of it as beautiful. "It is probably that the pleasure caused by rhythm and color prevails with a pretty large number, with the greatest number, over the pleasure in the musical form, pleasure too exclusively PSYCHOLOGICAL for one to be content with it alone....The musical sense implies the intelligence....The theory...applies to a great number of sonorous sensations, and not at all to any musical perceptions." Mr. W.H. Hadow tells us that it is the duty of the musician not to flatter the sense with an empty compliment of sound, but to reach through sensation to the mental faculties within. And again we read "the art of the composer is in a sense the discovery and exposition of the INTELLIGIBLE relations in the multifarious material at his command."

"Le Plaisir et l'Emotion Musicale," Rev. Philos., Tome 42, No. 7. Op. cit., p. 47. Grove's Dict. Art. "Relationship."

Now it is not hard to see how this antithesis has come about. But that the work of a master is always capable of logical analysis does not prove that our apprehension of it is a logical act. And the preceding discussion has wholly failed to make its point, if it is not now clear that the musical experience is an impression and not a judgment; that the feeling of tonality is not a judgment of tonality, and that though the aesthetic enjoyment of music extends only to those limits within which the feeling of tonality is active, that feeling is more likely than not to be quite unintelligible to the listener. Indeed, if it were not so, we should have to restrict, by hypothesis, the enjoyment of music to those able to give a technical report of what they hear,—which is notoriously at odds with the facts. That psychologist is quite right who holds that psychology, in laying down a principle explaining the actual effect of a musical piece, is not justified in confining itself to skilled musicians and taking no notice of more than nine tenths of those who listen to the piece. But on the understanding that the tonality-feeling acts subconsciously, that our satisfaction with the progression of notes is unexplained by the laws of acoustics and association, we are enabled to bring within the circle of those who have the musical experience even those nine tenths whose intellects are not actively participant.

Lazarus, Das Leben der Seele, ii, p. 323.

The fact is that musical form, in the sense of structure, balance, symmetry, and proportion in the arrangement of phrases, and in the contrasting of harmonies and keys, is different from the musical form which is felt intimately, intrinsically, as the desired, the demanded progress from one note to another. Structure is indeed perceived, understood, enjoyed as an orderly unified arrangement. Form is felt as an immediate joy. Structure it is which many critics have in mind when they speak of form, and it is the confusion between the two which makes such an antithesis of musical beauty and sensuous material possible. The real musical beauty, it is clear, is in the melodic idea; in the sequence of tones which are indissolubly one, which are felt together, one of which cannot exist without the other. Musical beauty is in the intrinsic musical form. And yet here, too, we must admit, that, in the last analysis, structure and form need not be different. The perfect structure will be such a unity that it, too, will be FELT as one—not only "the orderly distribution of harmonies and keys in such a manner that the mind can realize the concatenation as a complete and distinct work of art." The ideal musical consciousness would have an ideally great range; it would not only realize the concatenation, but it would take it in as one takes in a single phrase, a simple tune, retaining it from first not to last. The ordinary musical consciousness has merely a much shorter breath. It can "feel" an air, a movement; it cannot "feel" a symphony, it can only perceive the relation of keys and harmonies therein. With repeated hearing, study, experience, this span of beauty may be indefinitely extended—in the individual, as in the race. But no one will deny that the direct experience of beauty, the single aesthetic thrill, is measured exactly by the length of this span. It is only genius—hearer or composer—who can operate "a longue haleine."

So it is that we must understand the development in musical form from the cut and dried sonata form to the wayward yet infinitely greater beauty of Beethoven; and thence to the "free forms" of modern music. "Infinite melody" is a contradiction in terms, because when the first term cannot be present in consciousness with the last there is nothing to control and direct the progression; and our musical memory is limited. Yet we can conceive, theoretically, the possibility of an indefinite widening of the memory.

It was on some such grounds as these that Poe laid down his famous "Poetic Principle,"—that a long poem does not exist; that "a long poem" is simply a flat contradiction in terms. He says, indeed, that because "elevating excitement," the end of a poem, is "through a psychical necessity" transient, therefore no poem should be longer than the natural term of such excitement. It is clearly possible to substitute for "elevating excitement," immediate musical feeling of the individual. What is the meaning of "feeling," "impression," here? It is the power of entering into a Gestaltsqualitat— a motor group, a scheme in which every element is the mechanical cue to the following. Beauty ceases for the hearer where this carrying power, the "funded capital" of tone- linkings ceases. In just the same way, if rhythm were a perception rather than an impression, we ought to be able to apprehend a rhythm of which the unit periods were hours. Yet we may so bridge over the moments of beauty in experience that we are enabled, without stretching to a breaking-point, to speak of a symphony or an opera as a single beautiful work of art.

VII

But what of the difficulties which such a theory must meet? The most obvious one is the short life of musical works. If musical beauty is founded in natural laws, why does music so quickly grow old? The answer is that music is a phenomenon of expectation as founded on these natural laws. It is the tendency of one note to progress to another which is the basis of the vividness of our experience. We expect, indeed, what belongs objectively to the development of a melody, but only that particular variety of progression to which we have become accustomed. So it is that music which presents only the old, simple progressions gives the greatest sense of ease, but the least sense of effort—the ideal motion not being hindered on its way. Intensity, vividness, would be felt where the progression is less obvious, but felt as "fitting in" when it is once made; and where it is not obvious at all—where the link is not felt, a sense of dissatisfaction and restlessness arises. So it is with music which we know by heart. It is not that we know each note, and so expect it, but that it is felt as necessarily issuing out of the preceding. A piece of poor music, really heterogeneous and unconnected, might be thoroughly familiar, and yet never, in this sense, felt as SATISFYING expectation. In the same way, music in which the progressions were germane to the existing tonality-feeling, while still not absolutely obvious, would not be less quickening to the musical sense, even if learned by heart. It is clear that there is an external and an internal expectation—one, imposed by memory, for the particular piece; the other constituted partly by intrinsic internal relations, partly by the degree to which these internal relations have been exploited. That is, the possibility of musical expectation, and pleasure in its satisfaction, is conditioned by the possession of a tonality- feeling which covers the constituents of the piece of music, but which has not become absolutely mechanical in its action. Just as rhythm needs an obstacle to make the structure felt, so melody needs some variation from the obvious set of relations already won and possessed. If that possession is too complete, the melody becomes as stale and uninteresting as would a 3-4 rhythm without a change or a break.

The test of genius in music, of the width and depth of mastery, is to be able to become familiar without ceasing to be strange. On the other hand, if in music to be great is always to be misunderstood, it is no less true, here as elsewhere, that to be misunderstood is not always to be great. And music may be merely strange, and pass into oblivion, without ever having passed that stage of surprised and delighted acceptance which is the test of its truth to fundamental laws.

But how shall music advance? How shall it set out to win new relations? It is at least conceivable that it takes the method of another art which we have just studied. To get new beauties, it does not say,—Go to, I will add to the beauties I already have! It makes new occasions, and by way of these finds the impulse it seeks. Renoir paints the baigneuse of Montmartre, and finds "the odd, beautiful huddle of lines" in so doing; Rodin portrays ever new subtleties of situation and mood, and by way of these comes most naturally to "the unedited poses." So a musician, we may imagine, comes to new and strange utterances by way of a new and strange motion or cry that he imitates. Out of the various bents and impulses that these give him he chooses the ones that chance to be beautiful. And in time these new beauties have become worn away like the trite metaphors that are now no longer metaphors, but part of the "funded capital." That was a ridiculous device of Schumann's, who found a motif for one of his loveliest things by using the letters of his temporary fair one's name—A B E G G; but it may not be so utterly unlike the procedure by which music grows.