Victor A. Grauer

©Victor A. Grauer, 1982


Beyond Realism -- Fundamentals of Negative Syntax

Chapter 8

Space: Mondrian and the Archetypal Image

While its development is a vital element in the history we have traced, Cubism itself has serious drawbacks as a model for what we have called "negative syntax." Cubist paintings tend to be extremely complex and resistant to analysis. Cubism, moreover, is an almost completely intuitive art, an ad hoc process of observation and adjustment which its foremost practitioners have been understandably reluctant to discuss in any detail. The leading theoreticians of the early period tended, as we have seen, toward idealized notions involving multiple views and the "fourth dimension." Later scholars have concentrated on historical issues and/or the elucidation of particulars. Generalizations about Cubism as a whole have been offered with great caution, to the point that the ad hoc itself is often elevated to the status of a basic principle.

Even if our understanding of Cubism were complete, the implications of the structural principle to which it gave birth would carry us beyond the limitations of any one style and/or art form. Ultimately, as a mode of perceptual determination, negative syntax must be understood more generally, in terms of the two basic "fields" of perceptual experience: space and time. Fortunately, the fundamental spatial principles embodied in Cubism were adopted, simplified and carried to their logical goals by a major artist who was also a dedicated theoretician: Piet Mondrian. It is to the work and thought of this key figure that we must now turn.

The Essence of Disruption

In the words of Mondrian's friend and biographer, Michel Seuphor:

No other modern painter came from as far back, none went further [Mondrian] started from Van Gogh; more than that, he retraced the whole progress of Van Gogh; then, after painting like a Fauve before the Fauves, he overtook Cubism, [and] went beyond it. . . 1

Mondrian's earliest paintings dating from the 1890's, fuse a stark but conventional naturalism with the Dutch landscape tradition. From 1900 through 1907, his work reveals various influences, ranging from Van Gogh and Gauguin to Edvard Munch and the Fauves. 1908 is generally regarded as a turning point in his career, the beginning of a systematic development that was to continue till his death in 1944.

The "Tree'' Series

The crucial early stages of this development can be traced through a remarkable series of paintings involving an obsessive image: a solitary tree. The series begins in 1909 with two rather conventionally naturalistic studies of a particular tree, its trunk leaning heavily to the right.2 These lead to the highly expressionistic Red Tree,3 very much in the spirit of Van Gogh, but with even more intensified color. The tree is red striated with blue, on a blue background. Barren of leaves, the intricate network of branches stands out against the background as a dense interplay of expressively curving lines. Three more "portraits'' of the same tree, dating from 1909-10, are progressively more simplified and expressively symbolic.4 The third, called The Blue Tree, is a dark highly schematized dark silhouette with branches radiating out from the center. This design, combined with the intensity of the color, gives the tree a flamelike aspect. The overall effect is highly symbolic,as though the tree were being fragmented and consumed by its own life force.

Another sequence, 1910-12, involves a different tree, its trunk leaning to the left. An early study is detailed and naturalistic. The next two pictures in this sequence5 reveal a process of intensification and fragmentation recalling the earlier Red and Blue Tree paintings. There are some profound differences, however, reflecting the powerful and unmistakeable impact of Cubism.6 The second especially, known as The Gray Tree, seems poised midway between the schematized symbolism of the earlier expressionistic works and the analytic disjunctions of Cubism. Unlike the Blue Tree, which is systematically fragmented, according to a controlling scheme, The Gray Tree is fragmented (facetted) through a studied process of give and take, not clearly beholden to any single scheme, derived from idiosyncracies of the subject itself.

While the earlier works clearly set the tree off from its background in a striking figure-ground relation, The Gray Tree subjects both to a thorough fragmentation in which many figure-ground distinctions are lost in webs of facetting and passage. The controlling forces of the earlier paintings are strongly centric, a property emphasized with each progressive simplification to the point that The Blue Tree presents an unmistakeably geometrized gestalt. The Gray Tree, with its strikingly arcing central trunk and umbrella of middle branches, seems torn between a similarly centric force-field and the disruptive effects of Cubist facetting and passage, fusing figure and ground, liberating most of the lines from their sign-function as "branches'' and their consequent attachment to the trunk. While this work can still be "read'' as a tree, no really coherent gestalt unambiguously presents itself.

The final painting of this sequence, the Flowering Appletree of 1912,7 completes the process of representational disjunction. Though based on The Gray Tree, it is hardly identifiable as an image of a tree or anything else. The complex, sinuous branches of the earlier work are broken down into groups of lines, each a single, simple curve. Any but the subtlest hint of depth or modelling is gone. Lines deriving from contours of trunk and branches mingle imperceptibly with lines articulating "background'' space. "Empty'' passages between the lines, colored with great subtlety, also press forward toward the surface. While traces of a centric design remain, powerful centrifugal forces prevail, pulling the image literally to pieces.

The final sequence of tree paintings dates from 19I2-13. Stylistically these works are remarkably close to the most intricate of Braque and Picasso's "high analytic'' Cubist paintings of 1911. Each surface is totally fragmented into a clutter of small, irregular facets, saturated with em passage. Hardly a trace of the originating image remains. Nor is there a hint of any controlling scheme, geometric or otherwise: each facet relates only to its immediate neighbors and the surface itself.

While The Flowering Apple Tree consists almost exclusively of graceful curves, the later tree paintings are dominated by short straight lines. As the sequence progresses, diagonals too become rarer until, with Oval Composition (Trees), the culminating work, vertical and horizontal straight lines are overwhelmingly dominant.

The title of this painting, the last which can unequivocally be associated with trees, reinforces the impression that we have arrived at a point close to total abstraction. Other works of the same year (1913), very similar in general appearance, are titled simply Composition, Tableau, Composition in Brown and Gray, etc. The following year, completely rectilinear works appear with titles like Facade or Scaffolding. After 1914, titles with any but a purely formal reference are extremely rare. Mondrian's work is, in fact, no longer based on an external model of any kind.

Reduction and Resolution

The last of the tree paintings and the group of associated works of the same period combine an extreme simplification of the basic graphic means (reduced essentially to horizontal and vertical straiht lines) with a highly elaborate, even cluttered overall surface. From 1913 onward, following the example of synthetic Cubism, Mondrian begins to resolve his surfaces. Complex, tentative, linear interlockings, tentatively adjusted and linked by webs of passage become relatively simple, precisely and forcefully defined relationships. Horizontal and vertical lines which remained light and open begin to thicken and link, trapping rectangular planes within. (Compare Oval Composition (Trees), for example, with the Composition With Color Planes9 of 1914). By 1918, with Composition With Gray and Light Brown,10 Mondrian has arrived at the format which will pervade his work until the early Forties: an open, clearly articulated surface, giving the impression of order while, at the same time, lacking any sort of predictable or definable pattern, determined exclusively by intersecting thick horizontal and vertical lines and the rectangles enclosed by them.

Mondrian and the Icon

In the tree series, Mondrian, far more methodical than any the Cubists, has left us an extended meditation on the nature of the iconographic sign. The earliest sequence, culminating in the
Blue Tree, progressively fragments and schematizes the lower level paradigms (signifying the highly individualized branches) in such a way that every element finally becomes subordinate to the paradigm of the highest level (the tree as a whole). Exhibiting techniques already common in Symbolist pictorialism (techniques later to be revived by the Futurists), a painting like The Blue Tree disrupts only for the purpose of dramatizing and intensifying a "higher" unity. If we define the icon as "the sign which resembles," we must note how the progressive terms of the first tree sequence move from a true iconism (embodied in the initial, "naturalistic" attempts to render the tree in its unique individuality) to a largely conventional symbolism in which the tree becomes a universalized emblem, not many steps removed from the arbitrariness of the linguistic signifier.

When Mondrian first saw Cubist paintings, their reductivist, analytic fragmentations undoubtedly reminded him of his own efforts in a similar direction. Unlike the Futurists, however, who also discovered Cubism in 1911, the Dutch artist clearly must have sensed that the profoundly disruptive Cubist approach was as much a rejection of symbolist rhetoric as photographic naturalism. That this insight was decisive is essential to an understanding of his mature work. It is not until the second sequence of trees, unmistakeably reflecting Cubist influence that Mondrian sets out with real authority on the path that will be his consistently from then on.

From this point, Mondrian is no longer interested in the kind of quasi-linguistic fragmentations that lead to paradigmatic hierarchies. From the Gray Tree onward, his methodical analysis of the image reverses itself. He begins his years long search for the kind of structure that will exactly not sacrifice the idiosyncratic part to the meaningful whole. This is the only explanation for the enormously cluttered, even ungainly, tree paintings of the final phase (1912-13), works whose agglomerations of untamed detail could only be derived from an effort to interrelate the multiple contingencies of raw observation in a manner freed from any controlling scheme, iconographic language, or esthetic criterion. These paintings reach an extreme of visual analysis rivalling the most hermetic examples of late analytic Cubism.

In the works that follow, increasingly simplified and poised, less and less dependent on external observation, Mondrian is searching for the universal principle behind the Cubist obsession with contingency. In his realization that such a principle, a universal basis for the disruption of the universal itself, might exist, he goes beyond Cubism and abstraction as well into completely fresh territory.
According to Mondrian, "Cubism did not accept the logical consequences of its own discoveries; it was not developing abstraction toward its ultimate goal, the expression of pure reality."12 Having thoroughly disassembled it, robbed it of its signifying power and turned it into a simple design element, the Cubists remained fascinated by the visual sign. Indeed, the witty interplay of abstraction and defused iconographic signification is essentially the point of synthetic Cubism. Mondrian, on the other hand, clearly saw no point in continuing to dwell on the sign, a now superfluous remnant of a decoded, demystified, naturalism. It was the reality veiled by natural appearances, an ultimate truth released for the first time by the same forces that defeat signification, which he wished to confront.

Mondrian As Theoretician

Mondrian's notion of an apparently transcendent "pure reality" is one of the truly elusive artefacts in the history of verbalization about art, seeming, as with so many fundamental concepts, to partake equally of the naive and profound. While it is by no means clear that Mondrian himself fully and consistently grasped his own idea, he left an impressive body of theoretical writings which do clearly reflect certain of its key aspects. It is to these writings that we must turn if we wish to understand what he regarded as the "logical consequences" of Cubism.

Before we proceed, however, a word of explanation is necessary. Mondrian was a genuine thinker whose researches have produced theoretical works central to the very issues which most concern us. Unfortunately, Mondrian's dense, awkward literary style, coupled with the genuine complexity of his ideas, all too often leads to extreme confusion. There is also, to my knowledge, no one place where his overall position is presented as a continuous argument; vital aspects of his theoretical framework are spread out in various articles written over a period of more than forty years.

Because of the above situation, it would seem virtually impossible to attempt to "speak for" Mondrian with absolute authority. The strategy adopted here will be to carefully pick and choose among various key statements which have the virtue of being both relevant to our concerns and mutually consistent. The statements will be presented in the form of a coherent step by step argument, punctuated by a certain amount of paraphrase and explanation. While it is my sincere belief that the overall result does in fact reflect Mondrian's intentions, I may be wrong. Perhaps those who would accuse me of concocting a Mondrian of "my own," will also be willing to credit me with his insights.

A Dialectic of Form and Space

Nature reveals forms in space13...[yet] forms are part of space and the space between them appears as form, a fact which evidences the unity of form and space...14 Actually all is space, form as well as what we see as empty space... form is limited space concrete only through its determination. Art has to determine space as well as form and to create the equivalence of these two factors...15

Mondrian is speaking generally of the way real objects differentiate themselves from the space surrounding them. Objects are perceived as forms (figures or gestalts) in space (the ground). Under certain conditions the space between objects (negative space) appears as a form also, indicating an underlying unity which permits us to state that "all is space." Ultimately form may be regarded as "limited space."

While the limitation of forms could, from a very broad point of view, be regarded as a drawback (literally a "limitation"), forms gain in concreteness by being limited in a particular way (determined). Space is unlimited but also undetermined, thus insubstantial. The task of art must be to determine space and at the same time reveal (create) the equivalence of space and form. The implied goal is a space which is both determined (concrete) and unlimited.

the plastic relation is more alive precisely when it is not enveloped in the natural, but shows itself in the flat and rectilinear. In my opinion this gives us a far more intense expression than natural form and color. But, to use more general terms, the natural appearance veils the expression of relations. When one wants to express definite relations plastically, one must show them with greater precision than they have in nature...16
The more neutral the plastic means are, the more the unchangeable expression of reality can be established. We can consider all forms relatively neutral that do not show any relationship with the natural aspect of things or with any "idea." Abstract forms or dislocated parts of forms can be relatively neutral.17

The plastic relations which the artist must use in determining forms or space are veiled in the attempt to render natural appearance. In order to bring such relations forward, the "natural aspect" must be neutralized. This involves a process of simplification, reduction and abstraction leading to "flat, rectilinear" forms free of external reference. Note that in defining the "neutral," Mondrian rejects not only natural appearance but also "any `idea.' " He has turned his back on both conventional realism and symbolism.

According to our laws, it is a great mistake to believe that one is practising non-figurative art by merely achieving neutral forms or free lines and determinate relations. For in composing these forms one runs the risk of a figurative creation, that is to say, one or more particular forms...18
[I]n relation to the environment, simple forms show a static balance. They appear as entities separated from the whole. In order to establish universal unity, their proper unity has to be destroyed: their particular expression has to be annihilated...19

After one has neutralized the natural aspect of objects and transformed them into abstract forms, one is still faced with the problem that even the most abstract forms are still perceived statically as forms within an enclosing space. The equivalence of form and space will remain unexpressed.

In plastic art, the static balance has to be transformed into the dynamic equilibrium which the universe reveals...21 Non-figurative art is created by establishing a dynamic rhythm of determinate mutual relations which excludes the formation of any particular form...21
[Static balance] maintains the individual unity of particular forms, single or in plurality. [Dynamic equilibrium] is the unification of forms or elements of forms through continuous opposition. The first is limitation, the second is extension. Inevitably dynamic equilibrium destroys static balance ...22

The particular forms, static, limited, must be destroyed through a dynamic process of mutual opposition, which breaks them up and, in so doing, opens them to the enclosing space which is also established in the same process. This process Mondrian calls "dynamic equilibrium."

The equilibrium that neutralizes and annihilates the plastic means is achieved through the proportions within which the plastic means are placed and which create the living rhythm.23

Having neutralized and opened form, reducing all elements to a rectilinear opposition of lines and planes, all creative activity centers on the one element as yet undetermined, the "plastic relations" themselves, which must be made concrete (determined) by specific proportions. For Mondrian, the proportions must create that "living rhythm" which is the essence of dynamic equilibrium.

It is only after a long culture that within the plastic expression of the limiting form, one perceives another plastic expression closely allied with it, but, at the same time, opposed to it. Art today...has succeeded in establishing this plastic expression: it is the clear realization of liberated and universal rhythm distorted and hidden in the individual rhvthm of the limiting form.24

The proportions (rhythms) which annihilate the plastic means, open limited form, and make space concrete by determining it precisely, have their ultimate source in the same contingencies ("individual rhythms") which give rise to the particular, limiting form in the first place. Thus dynamic equilibrilium, while in one sense destroying the particular, in another sense preserves it by liberating its vital principle, usually veiled by natural appearance and limited form. Dynamic equilibrium is this principle, the equivalence of space and form, the universal which resides in the particular.

Far from ignoring our individual nature, far from losing "the human note" in the work of art, pure plastic art is the union of the individual with the universal. For liberated rhythm is composed of these two aspects of life in equivalence.25

A New Proportion

Ultimately, for Mondrian, the "logical consequences" of Cubism, the "expression of pure reality," are intimately connected with the "dynamic," "liberated," "universal," "rhythm of determinate mutual relations," that "living rhythm" "achieved through the proportions within which the plastic means are placed." One might go so far as to say that the thoroughgoing process of reduction and simplification, so evident in Mondrian's work from the second set of tree paintings to the rectilinear abstractions of the Twenties, is guided by an increasingly conscious need to clarify these proportions and bring them into the foreground of the viewer's awareness.

This is a process intimately connected with the "struggle for the surface" so crucial to the evolution of Cubism itself. Early Cubism, preoccupied with the opening out of representational space-in-depth, weakens the viewer's proportional sense through extreme fragmentation and continuous passage. There is, nevertheless, an important, if indirect,use of proportion as a tool for the disruption of positive space in the continual creation of effects of "reverse perspective." Such effects, largely dependent on the carefully calibrated proportions of the facets themselves,26 do much to activate the surface; which activation, in turn, simplifies and clarifies the viewer's awareness of proportion. As the surface emerges with ever greater clarity in synthetic Cubism, the proportional determination of this surface rivals the characteristically Cubist "play" with iconography for the attention of the viewer. With Mondrian, who eventually dispenses with every remnant of iconography, proportional determination becomes equivalent to the creative act itself.

What, we must now ask, is the basis for this proportional determination? A great deal of confusion has arisen from the common tendency to associate the rectilinearity of Mondrian and late Cubism with the systemizations of geometry. In such a context, any reference to "proportions" cannot escape association with the "harmonic" proportions first investigated by Pythagoras, based on symmetrical sets of whole number ratios and their rationally determined derivations. Such thinking has led to completely misguided speculations regarding Mondrian's employment of geometrically derived proportions.27

Such speculations are totally incompatible with the historical process we have outlined. It is the perspective system, thoroughly undermined by Mondrian and the Cubists, which is dependent on geometry. Cubism begins as a reaction against any such systemization, a return to direct observation of contingencies. Similarly, Mondrian's work, from the second set of tree pictures through the works of 1914, derives its proportions from careful observation of "individual rhythms" as manifested in a particular tree, building facade, etc. Unlike the Cubists, however, Mondrian is looking beyond contingencies for the "universal" principle linking them with the observer. After 1914, having ceased to depend on an external model, he does not then suddenly take up geometry, but clearly proceeds on the basis of his feeling for the same "universal residing in the particular" that he had sought in the earlier work. The extreme reductionism of his later paintings, their avoidance of any form of symmetry or regularity, their dependence on the rectilinear "opposition" of vertical and horizontal lines, can be regarded both as manifestations of this principle and, in a more subtle sense, clarifications of the sort that will permit the principle more readily to manifest itself.

Mondrian had explained to a young colleague, Charmion von Wiegand, "that he did not work with instruments nor through analysis, but by means of intuition and the eye. He tests each picture over a long period by eye: it is a physical adjustment of proportion through training, intuition and testing."28 In the light of Mondrian's writings, which continually stress the importance of objectivity and precision, such a statement can seem disappointing. The artist who works "intuitively," making crucial decisions "by eye," seems the very type of subjectivist whose outlook Mondrian rejected.

The contradiction is resolved only when we grasp the full extent of the dialectic entailed. Within the context of traditional pictorial syntax, the intuitive perception of the artist operates as a vaguely defined subjectivity opposing itself to a highly defined and objective overall controlling system (perspective). With Mondrian, not only is any such system opposed, but all the factors contributing to this opposition are ultimately reduced and clarified to the point that their guiding principle can be evaluated directly and completely by eye. In such a context, intuitive perception functions objectively and with precision.

This completely new situation would seem to throw theory into a crisis. In the complete absence of system (functioning either as a structural determinant or an object of resistance); in a context where the eye of the artist is the sole criterion of value; there is apparently nothing at all of a concrete nature to be said about that "dynamic rhythm of determinate mutual relations," that "dynamic equilibrium" which is the ultimate product of Mondrian's search for the universal principle residing in the particular.

Open Structure

Given the finality of the above conclusion, respecting always the fact that the precisions of any given Mondrian painting can ultimately be neither explained nor even stated (in language), it is still possible, nevertheless, for theory to speculate regarding the conditions satisfied by such precisions. Basic to Mondrian's "classic" works (dating from the period 1925 through, roughly, 1939) is the manner in which their rectilinear lines and planes "annihilate" (to use Mondrian's term) each other. In other words, the proportional relations of both (and we must remember that Mondrian's lines, thick enough to carry planar "weight," often vary in thickness) are such that no element is present as a figure against a ground, no gestalt emerges. While technically the lines contain rectangles, these do not come forward perceptually as isolated forms. Neither does any particular configuration of lines come forward. Most important, the total design, thoroughly non-centric, does not form a gestalt , but remains open to the space around it.

The whole is not greater than the sum of its parts. Each part, clearly differentiated (by shape, position and, more rarely, color) from every other part, is nevertheless equivalent to every other part and to the whole. While each element is clearly articulated, none is rigidly circumscribed -- all is in flux.

The Seeing of Seeing

The evolution of Mondrian's work and thought may be compared with the preliminary simplifications of Euclid or Descartes, leading backwards toward that which can have no other basis than intuition itself: the axiom. But there is a profound difference between conceptual and perceptual intuition. The axioms of Euclid and Descartes can be stated as propositions. Those of Mondrian, as we have seen, cannot. His ultimate decisions regarding the precise proportions (and, of course, colors of any given canvas must be regarded as "axiomatic" (thus, in some sense self-evident) to the eye alone. This unveiling of the "perceptual axiom" at the heart of "the universal which resides in the particular" confirms what we may call "sensory determination" as the ultimate goal, not only of Mondrian's "completion" of Cubism, but the long evolution of realism as well.

"Sensory determination" -- this phrase must be understood in two ways, both of which are equally valid in the present context: determination by means of the senses; determination of the senses. Mondrian's systematic reductionism is a journey to the heart, not simply of "realism", painting or artistic experience, but seeing itself. His precise determination of proportion is equivalent to the opening out of limited form (the "figure" or gestalt) to the space of the surface. Once limited form is thus disrupted, any possibility of seeing in iconographic, thus conceptual, terms is fatally weakened. For, as we have seen, there is an intimate connection between the sign and the gestalt: every sign must be perceptible as a distinguishable figure before it can signify (and, as has apparently been demonstrated by Piercean semiotics, anything distinguishable as a figure must signify).

Mondrian's "classic" canvasses, in destroying the figure liberate vision from meaning, freeing visual perception to be experienced more or less completely in its own terms. Proportional determination, originating as the disruption of the sign, achieved by means of sensory judgement, is thus equivalent to determination of the senses. In this light, what Mondrian has been calling "space" must be regarded both as the surface and the perceptual field. In determining "space" Mondrian is determining this field, articulated (brought into existence) on the painted surface, where it may be said that seeing itself is made visible.

B. The Disruption of Essence

In tracing the development of pictorial negative syntax, we have stressed problems stemming from the most coldly objectivist aspirations of realism in its reaction against Romantic idealism. Yet it should be clear that the more critical realism of Cézanne and the Cubists is characterized by an awareness that the "struggle to see" has a profoundly subjective component. If Mondrian may be characterized as the coldest of the cold objectivists, it must also be acknowledged that the work of few artists has been permeated with a warmer subjectivity. The Romantic, indeed Expressionist, element which so obvious]y pervades his earlier paintings is still, in fact, strongly present (albeit greatly transformed) in the later. Unless we examine this paradox, our understanding of negative syntax will be incomplete.

Mondrian and the Romantic Tradition

In a recently published study,
Modern Painting and The Northern Romantic Tradition, Robert Rosenblum isolates a predominantly North European tradition of nature-mysticism. Taking as his point of departure early Nineteenth Century works by Casper David Friedrich and Philipp Otto Runge, Rosenblum traces a line of development through such figures as Blake, Turner, Van Gogh, and Munch, to modernists such as Nolde, Marc, Kandinsky, Mondrian, and the Abstract Expressionists, notably Still, Pollock, Newman and Rothko.

Motivating this development are "dreams of mystical and spiritual realms" which, "in their transcendental ambitions,... perpetuated the Romantic search for an art that could penetrate beneath the material surfaces of things and extract a religious essence."

Occupying a key place in this scheme is the Dutchman, Piet Mondrian, who provided the clearest and most artistically compelling link between a nineteenth-century tradition based on the themes, the spaces, the emotions of Northern Romantic art and the transformation of these historical roots into a twentieth century art where all explicit references to the material world are banned.29

An obvious link between Mondrian and the earliest manifestations of the tradition invoked above is to be found in his "Tree" series. The special significance of trees for the Northern Romantic artist is discussed in some detail by Rosenblum, cites compelling examples by Friedrich, Constable, Dahl and Van Gogh. He speaks of "an empathy of the artist with the life of an individual tree" so intense that the tree can "become a sentient, almost human presence." Specifically comparing Mondrian's Red Tree with those of Friedrich and Van Gogh, he finds in this work and the Blue Tree reflections "of a radiant, organic vitality so potent that it can transform roots, trunk, and branches into a vibrant web, hovering in some transitional domain between matter and spirit, solid and void." Such works are really symbols evoking "elemental forces and mysteries." These themes are crystallized in his discussion of the "neo-Romantic botany" of Rudolph Steiner, founder of the immensly influential spiritual "science," Theosophy. To Steiner, heavily in debt to Goethe's notion of the "primordial plant," all plant species share a fundamental structural principle, reflecting the workings of the universe itself.30


In light of the fact that Steiner's Theosophy distills and elaborates on the tradition of nature mysticism invoked by Rosenblum, Mondrian's well known association with the Theosophical movement becomes especially significant. This association, documented in Robert P. Welsh's "Mondrian and Theosophy,"31 undoubtedly had a profound effect. Mondrian, who joined the Dutch Theosophical Society in 1909, was an avid reader of Steiner and his associate Madame Blavatsky, whose ideas, as Welsh demonstrates, are reflected in many aspects of his work and thought.

Particularly important to Mondrian were Theosophical notions regarding the role of certain geometrical figures as dematerialized essences, symbolizing fundamental forces of the universe. Especially significant are the triangle and the circle, but the figure of the cross is clearly basic. Madame Blavatsky has written of "the philosophical cross...which the geometrizing Deity divides at the intersecting point, and which forms the magical as well as the scientific quaternary..." This is "the master-key which opens the door of every science, physical as well as spiritual." This configuration is basic," for the circle of life circumscribes the four points of the cross...Everything in this world is a trinity completed by the quaternary..."32

Rosenblum points out how a motif like the tree "could suggest, in the natural structure of the trunk's vertical thrust against the horizontal expanse of the branches and of the earth a cruciform pattern..."33 Much in Mondrian's writings attests to the importance he attached to just this kind of distillation of abstract perpendicular forces from the observation of "natural appearance." This was far more to him than simply an element of design, however. For Mondrian, the intersecting lines of the cross are the "primordial relation."34 Rosenblum goes on to cite other early examples of the cross motif in Mondrian, concluding that he "could hardly have avoided the association of religious meaning with this elementary geometric pattern, a pattern that was in fact to become the structural basis of the remaining thirty years of his objectless, abstract art"35

The Archetype

Probably the most ambitious and, in many ways, convincing attempt, in modern times, to erect a theoretical framework for the nexus of ideas and associations invoked by belief systems such as nature-mysticism and Theosophy can be found in the writings of Freud's famous disciple, C. G. Jung. Basic to Jungs's theories is the notion of the
collective unconscious, a deep layer of the psyche, which is, in some sense, shared by all humans. The collective unconscious manifests itself by means of certain forms, found world-wide in myths, dreams, art and religious iconography, which according to Jung, carry a universally meaningful symbolism: the archetypes.

Mondrian's tree motif, especially as interpreted by Rosenblum, is an excellent example of an archetype. Jung has, in fact, devoted to this subject a lengthy essay, "The Philosophical Tree," which begins as follows:

An image which frequently appears among the archetypal configurations of the unconscious is that of the tree or the wonder-working plant. When these fantasy products are drawn or painted, they very often fall into symmetrical patterns that take the form of a mandala. If a mandala may be described as a symbol of the self seen in cross section, then the tree would represent a profile view of it: the self depicted as a process of growth.36

The above statement illustrates a somewhat confusing but extremely important aspect of Jung's thought: an archetype may be regarded both as a certain form-type (the tree) and the forces or principles underlying it (e.g., the mandala). Ultimately, the archetype itself may be regarded as the universal principle underlying all its manifestations.

A key to Jung's idea can be found in its source, the alchemical writings of Dionysius the Areopagite:

That the seal is not entire and the same in all its impressions... is not due to the seal itself... but the difference of the substances which share it makes the impressions of the one, entire, identical archetype to be different.37

This is less cryptic than it may seem. The archetype is here presented as a kind of mystical "seal" or stamp which in itself is completely uniform, thus free of any particular image. Any such image would derive only from "differences of substance" (lack of uniformity) in that which is stamped by it. This is the sense in which Jung ultimately distinguishes between the "archetype as such," a universal, imageless, essence, and the particular, though still highly generalized, "archetypal images" which represent it.38

Mandala and Cross

Blue Tree is one of a group of contemporary works which clearly exhibits, in the words of Jung, "symmetrical patterns that take the form of a mandala." The mandala, which means, literally, "circle" or "magic circle" is, of course, associated with that aspect of Oriental religious iconography which has had crucial significance for Theosophy. According to Jung, the mandala is among the most important of archetypes and is to be found almost universally as a symbol of the self. He has written that "most mandalas take the form of a flower, cross or wheel and show a distinct tendency toward quaternary structure. . ."39 The fourfold quaternary structure of the mandala is related to the alchemical notion of the "unification of opposites, "a very fundamental principle to which Jung devoted his last and most extensive work, Mysterium Coniunctionis."40 Here we are very close indeed to Theosophy. The conjunction of opposites is symbolized by the cross, to Jung the fundamental underlying structure of the mandala itself.

Bringing the above set of associations into line with Mondrian's theories, we might say that "neutralization" of the tree-image has more clearly revealed the abstract, circular, symmetrical mandala form that is veiled by "natural appearance." Since the mandala nevertheless remains a "limited form," it too must be broken up (in subsequent paintings) to reveal its underlying structural principle: the "unification of opposites" that is the cross. Interiorization of this powerful symbol would, finally, put one in touch with the mystic "archetype as such," existing prior to the formation of any image, equivalent to Mondrian's notion of space itself.


The above discussion, from Rosenblum's invocation of nature mysticism and Theosophy to the distillation of such notions in Jung's archetype, presents a totally convincing picture of Mondrian's development up to and including the period of the
Blue Tree (1910), adding a great deal, moreover, to our understanding of certain aspects of his work and thought throughout his career. Nevertheless, as should be clear from our initial analysis of the Tree series, it would be a serious error to assume that the impact of Cubism in 1911 did not profoundly alter Mondrian's relation to the whole set of ideas invoked by Rosenblum and Welsh. Failure to fully take this into account has, given the strong influence of their writings, had an unfortunate effect on the currently prevailing critical view of Mondrian's work as a whole.

For example, Dore Ashton, in a recent review, refers to "the occult symmetries through which Mondrian meant to depict his intimations of the essential world-essential as the ever-unchanged schema Plato admired in geometry. All radiates from the centre here as, eventually, all of Mondrian's circles would be squared."41 If we are to profit from the genuine insights of Rosenblum and Welsh, we must be careful to avoid this sort of misguided but completely typical generalization. Principle number 6 of Mondrian's "General Principles of Neo-Plasticism" is among his clearest and most unequivocal theoretical statements: "all symmetry shall be excluded "42

If the circle, the square, the mandala, the cross, the "four fold conjunction of opposites," can be anything at all, they must be symmetrical. Indeed, by 1910 Mondrian is turning his trees into mandalas where "all radiates from the centre." From 1911 onward, however, beginning with works such as the Gray Tree, he progressively decenters the image. The process of reduction and fragmentation begun in 1908 as a means of suppressing contingencies in favor of a dematerialized, symbolic essence is, in 1911, transformed into a means of subverting the symbolic process itself.

This involves not only the rejection of symmetry but also the rejection of any form of hierarchical, geometrically systematized proportioning. References to Plato, geometry, circles, squares are relevent only to those works completed before 1911. As has already been demonstrated, the proportions "which create the living rhythm" of dynamic equilibrium have their origin in the contingencies of observation, the active interaction of the eye and the object of its regard. Aside from the role of "geometric" elements such as straight lines and right angles in clarifying and stabilizing such interaction, geometry has no role whatever to play in Mondrian's later work.

If Mondrian had never been confronted with the discoveries of Cubism, he might have moved on from the Blue Tree to an ever clearer distillation of its underlying geometry, arriving finally at the ultimate Theosophic, archetypal and, of course, Christian, symbol: the cross. What in fact happened was much more complex. Fusing Cubism with the goals of Theosophy, he retained from the cross its basic principle -- the conjunction of opposites through the intersection of horizontal and vertical forces, the "primordial relation." But, "in each given case Neo-Plasticism must, so to speak, break up the represertation of the primordial relation ... To represent the horizontal position and the upright position as a unity, without anything else, would evidently not be art, but at most a symbol."

Thus, the cross itself, as a meaningful configuration, a "limiting form," a symbolizing unity, is thoroghly disrupted in virtually all the later works. One could, of course, produce a detail of almost any mature Mondrian in which a cross would be apparent -- these paintings usually contain at least one set of crossing lines. In the design as a whole, however, the configuration of the cross is not apparent as such -- each of the various elements balances the others in such a way that no particular gestalt presents itself to the eye.

Intensification as Reversal

Mondrian's relation to the Romantic project invoked by Rosenblum, the neo-Platonic search for a dematerialized, transcendent essence, is complex indeed. Beyond question, Mondrian's involvement with Theosophy had a lifelong effect on his thought, to the extent that there is little in his theories which could not be interpreted in purely Theosophical terms. Indeed, too many critics and scholars have overlooked the complete incompatiblility of such an interpretation with the actual structure of the mature paintings. If Mondrian's theories regarding the neutralization of natural appearance, the destruction of limited form, and the unification of opposites are to be read simply as invocations of some Theosophically inspired archetype, then his paintings would have to be mandalas!

On the other hand, Mondrian's relentless search for the fundamental principle behind Cubist negative syntax clearly has its source in his original, Theosophically orthodox, project -- the impetus of which was strong enough to carry him beyond the largely iconographic-iconoclastic preoccupations of Cubism. The necessary link with the Romantic tradition reveals much about the vital, subjective, "other side" of the evolution we have traced. Indeed it seems to have been the presence of a hyper-Romantic, expressionist intensity that distinguished the highly subjective, almost fanatical projects of Cézanne and the Cubists from the aloof scientism of the Impressionists. Cézanne's early canvasses are personal and impulsive in the extreme-his subsequent naturalism is no less intense. Picasso's painting, at the very threshold of Cubism, is remarkable for its slashing savagery. In characteristically expressionist fashion, Mondrian both projects his own feelings onto the motif and, at the same time, interiorizes it. The progressive fragmentations of the archetypal tree images may thus be considered equivalent in some sense to a process of internal disintegration and transformation, a process which intensifies after 1911.

In view of the history we have traced, it should not be difficult to understand the apparently paradoxical affinities between extreme realism and the expressionist impulse. The search for "objective" vision must ultimately involve consideration of "the way we see," which must, of course, have a subjective component. Only the artist with a strong subjectivity will in any case be aware of the extent to which the "real world" is a projection of the "world within." Only an artist with a passionate attachment to nature will so intensely internalize not only the motif but the naturalist project itself.
In this context we can much better grasp the deep inner need that motivates the struggle to see. It is a struggle which takes place "within," "without" and between the two, the expression of a profound desire for unification of the self through integration of self and world. At the core of this struggle, however, is the necessary reversal which takes us beyond the limits of the Romantic project. The self cannot be integrated with the visible world without first becoming disunified. The struggle to see involves the fragmentation of self, the opening out of self, spirit, meaning, to the contingencies of the visible (as opposed to the essences of the thinkable).

What to the Romantic sensibility would mean death, madness, or the opening to a vaguely pure "spirituality," becomes, simply, the liberation of the senses. Thus, for Mondrian the struggle to see is inseparable from what to him is the characteristically modern effort to overcome "the tragic."44 The ease with which Mondrian's theories may be read as orthodox Theosophy attests to the difficulty of grasping the reversal that carries him far beyond any form of Romantic idealism. Only a reading of Mondrian in terms of the framework we have presented can reconcile his ideas with the salient characteristics of his creative output. The archetype,as a centralized, mandala-like, symbolic conjunction of opposites, can be regarded as the essence of positive syntax, thus, in fact, the mirror image opposite of a painting by Mondrian, a "pure" instance of negative syntax. Such a painting is, in fact, an anti-mandala, decentralized by the disjunction of opposites, and thoroughly non-symbolic.

While the Jungian archetype achieves unification on an ideal, totally non-material plane, the realm of the "collective unconscious," a Mondrian painting achieves unification only on its own surface, a limited material entity which is the exact opposite of the archetype. On this surface as well, the limited, material realm of the senses achieves unification with "the world" in terms of the concrete perceptual field created therein by the artist (a field which in itself, however, is thoroughly disunified).

Mondrian, inspired by Theosophy, relentlessly pursues the archetype, but, during the course of this pursuit becomes charged with the iconoclastic energies of Cubism. Ultimately, therefore, he moves toward the archetype only to disassemble it as an ideal structure of the mind.

Chapter 9

Time: Webern, Serialism and Moment Form

We have reached a point where, to paraphrase Mondrian, concern for natural appearance gives way to concern for those relations veiled by natural appearance. Now that the issue of representation has been supplanted by that of perceptual determination, we need no longer limit ourselves to forms of expression which are primarily representational. Our discussion of space in terms of Mondrian has thus prepared the way for a discussion of time which must, very naturally, focus on the "abstract" art of music.

The Tonal-Metric System and "Perspective Time"

We may begin by stating outright that the system of "classical" tonality with which we are all familiar, strongly centered on a particular "key," dependent on an intricate hierarchy of harmonic and metric relations within which all elements take their place and fuse, is an excellent example of positive svntax, having much in common with spatial perspective and the cinematic denial of difference. Just as film involves the coordination of two "fields," screenspace and time, music is based in two closely analogous "fields," pitch and rhythm. It should not be difficult to understand how "pitch-space," as traditionally controlled by a complex system of tonalities (keys), can be related to the effects of pictorial (and photographic) perspective. Indeed, musicians routinely apply spatial analogies to pitch, referring to notes that are "high" or "low," keys that are "near" or "distant," motives that occupy the "foreground" or "background."

More explicitly, in the words of Robert Ericson,

A key gives unity to all the musical events which happen in it in much the same way that linear perspective organizes all the picture space in relation to a single point. In a key, the tonic, the home base, is analogous to the vanishing point. It provides the focal point to which every musical event is bound, the unifying point through which all the musical events are related to one another.1

Just as, in traditional pictorial representation, each visual detail is "polarized" in a particular direction by perspective, so, in traditional music, each note is similarly "polarized" by the contexts created by the tonal system. This profoundly affects our perception of pitch. As a given shape will look completely different when interpreted as receding to the left or to the right, a given pitch will have a completely different "sense" when heard in the context of different keys. An E played on an oboe in the key of A will be heard as a "dominant"; in G major, the same pitch played on the same instrument will have a completely different, far more unstable, quality ("submediant"). The unique sound of that particular oboe playing that particular pitch will be as subliminal to the average listener as the pictorial surface to the average viewer of a painting, photograph or film. Only if the oboe squeaks or plays out of tune will the audible "surface" become evident (as "noise").

The same process manifests itself on a multitude of architectonic levels. Each chord, phrase, motive, melody, section (roughly analogous to the paradigmatic levels of semiology) must take its place within the tonal hierarchy which, in turn, confers on it a specific (tonal) meaning; which, indeed, forces us to hear it in terms of such meaning, redeeming the sounds from their original status as "mere" noise.

The temporal structure of tonal music has a hierarchy all its own, designed to reinforce and, ultimately, coordinate with that of pitch. All individual rhythms are completely subordinated to a single periodic meter (or "measure"), based on an implied but often unexpressed, continuum of steady, equal beats. This meter, a module of potential time proportions or accent patterns, is in turn subordinate to larger periodic structures controlling the phrase, "sentence," etc. There is, in short, a hierarchy of controlling time proportions functioning as a temporal background or "container," analogous to the "container space" of perspective. As with perspective, the apparently neutral "background" is really the all determining syntax in disguise. Thus the metric system can be said to confer a syntagmatic dimension upon the "meanings" generated by tonality, uniting them within a single coherent temporal scheme.

The effects of musical "perspective-time" operate according to much the same ideology as that revealed in film by Baudry. Rapid melodic passages set strings of static individual notes into motion by virtue of essentially the same "denial of difference" that fuses static film-frames.2 The denial of difference is at work at slower tempos and higher levels of articulation as well, by virtue of a process of "musical implication" which parallels the principles of montage linkage discussed in Chapters 1 and 6.

As with the spatial organisation of traditional pictorial syntax, our perception of the temporal structure of tonal music is probably best understood in terms of gestalt psychology. The application of gestalt principles to the analysis of music is central to Leonard Meyer's Emotion and Meaning in Music, which has become a classic of its kind. Meyer cites the gestalt "law of good continuation," usually applied to spatial perception, as basic to our ability "to hear separate, discrete stimuli as continuous motions and shapes." Our perception of that "series of lifeless stimuli" which is "a line or motion initiates a mental process, and it is this mental process which ... tends to be perpetuated and continued."3

Meyer goes on to discuss musical "shape" and "texture," defining the latter in terms of the same figure-ground relationships we have cited in reference to pictorial and cinematic positive syntax.4 Ultimately, of course, every musical event, like every pictorial form, must be perceived as a configuration or "figure" against a "ground" in order to be understood within the overall scheme.
Perhaps no aspect of the metric system better illustrates the ideological effects of perspective time than that all important source of musical figuration, rhythm. In the context of classical tonality, all rhythmic figures manifest themselves as groupings of "attacks," points where a given note is first heard. The "release," the point at which the note stops sounding, is far less prominent and of little or no account in terms of musical meaning. This is what makes it possible for the piano, whose sounds begin to die away as soon as they are produced, to be as important as it is to the standard, classic repertoire. Few such works will fail to make perfect sense in piano transcription.

Attacks, as "points" in time, are easily perceived as abstract entities grounded within an equally abstract time field analogous to the container-space of perspective. They are really only the carriers of impulses, not true durations in the Bergsonian sense. With each note thus robbed of its temporal "weight," time is experienced rationalistically, i.e., in terms of an ideologically determined, purely conceptual, code.

Emancipation of the Dissonance

The tonal-metric system was undermined by a series of developments that parallel, both historically and functionally, the decline of pictorial positive syntax. Space permits only a rather sketchy review of a complex and gradual evolution.

A vital factor in the destruction of tonal pitch-space was the exact musical equivalent of passage, the process of shifting from one key to another that musicians call "modulation." It was mostly in the modulating "transition" sections of musical forms that the highly colored, tonally ambiguous, dissonant chords which gave Romantic music so much of its expressiveness could safely be accomodated. Because of their ambiguity, these chords could function easily as "pivots" from one key to another. Because they were so highly colored and expressive, however, they tended to assert themselves to the point that they could no longer be safely controlled as purely subordinate elements. Increasing emphasis on such chords coincided naturally with an increasing harmonic restlessness, which required more and more frequent changes of key and more emphasis on "exciting" adventures to more remote tonal areas.

Around the turn of the century, in the work of composers like Hugo Wolf, Debussy, Richard Strauss, Mahler and the young Schönberg, we find relatively long sections in what has come to be called "suspended" or "extended tonality." Here, temporary loss of any sense of tonal stability is produced by continual shifting from one key to another. Such sections can be considered a kind of pure passage, where modulation itself has moved into the foreground. Works featuring extended tonality may be compared to those paintings and films which reject positive syntax without the creation of negative syntax; such music is saturated with ambiguities.

It was in passages of extended tonality that the dissonant chords which had always held such fascination for the Romantics finally came into their own. So ambiguous was the context that the most extreme dissonances could be accomodated. The later music of Scriabin, for example, characterized by extreme tonal ambiguity, is a veritable hothouse of strange chords, the unusual properties of which are meant to symbolize all sorts of exotic, "spiritual" states of being.5

As it became increasingly apparent that the tonal system was exhausting itself, that there were limits beyond which it could only drift aimlessly (which is exactly what Scriabin did), the inevitable reaction followed. In an evolution paralleling the development of Cubism, certain composers eventually scrapped their ambitions to express "the ineffable" and concentrated their attention on the fascinating new chords that had been brought to light as "ineffabalic symbols." These chords were complex sounds, highly interesting simply as sounds, if they could be liberated from an apparently ever present implicational context. This "emancipation of the dissonance"6 could fully be achieved only if tonality were not simply suspended but actively destroyed and neutralized.

The dissolution of tonality was paralleled by disruption of the rationalized metric time-field. Tempo changes within a single movement became increasingly common in the mid to late Nineteenth Century, as did the use of rubato, a subtle flexibility of beat, in performance practice. Off beat accents (syncopations) and longer "cross-rhythmic" passages began to appear more and more often as composers felt the need to break up the rhythmic flow and stress particulars. In composers like Debussy and Scriabin, there are extended sections in which all sense of meter and sometimes even tempo is dissolved in rhythmically ambiguous passages which simply seem to "mark time" statically. Such passages often coincide with their tonal counterpart, periods of extended tonality.


The reaction against the tonal-metric system crystallized in the work of two major early Twentieth Century figures: Igor Stravinsky and Arnold Schönberg. Each had what seemed at the time to be a radically different approach from the other. Stravinsky attempted to neutralize the tonal hierarchy by combining harmonic and melodic elements from two mutually incompatible tonal centers. In such a context, tonal polarization toward a particular key is instantly balanced by the pull of another key. The resulting bi-tonality creates tensions resembling those between figure and ground in Cubism.

Stravinsky's most important contribution was in the area of rhythm. He broke up the closed configurations of the temporal gestalt by means of an original, completely intuitive, treatment of accent. Derived from syncopation, but much more continuously disruptive, his accents like the linear "accents" of analytic Cubism, always seem to come just at the right "wrong" place to abort configurative closure.

Schönberg's major early contribution was the creation of what is usually called "atonality," which, as the name suggests, can be translated simply as "negative tonality." Unlike Stravinsky, who retained many traditional chord formations and scales, Schönberg radically reworked the entire harmonic fabric. Atonality is the complete neutralization of tonal center, a context in which all pitches tend strongly to repel, rather than attract, one another. Tonal implication is disrupted in favor of a system of multiple polarities.

In both Stravinsky and Schönberg, the dissonant chords which were originally the problematic exceptions are now the rule. We must recall that such chords, like Cubist passage, had their origin in ambiguous transitions which carried the seeds of destruction. As soon as these chords began to call too much attention to themselves, their sheer sound as sound began to undermine the system. Modern music became the art of sound, not implication and meaning. In this context, dissonant chords need no longer "function," that is, lead anywhere -- they can tend simply to be heard as stable, complex sounds.

The Twelve-Tone Method

Between the years 1908 and 1920, Schönberg become increasingly dissatisfied with atonality. Basically a set of only partly understood ad hoc devices, lacking a fundamental principle, it was a poor substitute for the profound logic and flexibility of the rejected tonal-metric system. During the period 1914-1923, in response to this problem, he very painstakingly created what he called the method of composing with twelve tones related only to one another." Fundamental to this method is the "tone-row" or "series," a set in which each of the twelve pitches (more accurately, "pitch classes") traditionally available assumes a particular position in relation to all the others. Each piece is based on its own particular series, each series having unique properties and structural possibilities. The tone row has four basic forms: "original" form; inversion, in which all the intervals forming the original row are turned "upside down"; retrograde, the original pitches in reverse order; retrograde inversion, reverse order of the inversion. All of these forms can, moreover, like any musical idea, be transposed, so that twelve versions of each are available (in other words any form of any series may begin on any of the twelve pitches).

The series controls the structure of the piece in a manner which requires a good deal of preliminary systemization, yet permits the composer to create with at least as much freedom, control and expansiveness as in the tonal system. Unlike the tonal system, however, the series establishes no center -- each pitch bears an equal, mutually reciprocal relation to the others. These characteristics are particularly significant with reference to negative syntax, a matter to which we shall return shortly.


Despite his importance, which is undeniable, Schönberg's involvement with musical "negative syntax" was problematic. He, like Cézanne, was torn between revolutionary discoveries and deeply conservative instincts. As a result, his use of atonality and serialism reveals conflicts and inconsistencies. In his work, true negative musical syntax at the harmonic level is too often combined with characteristically tonal melody types and rhythms. Much of Schönberg's music. like Cézanne's painting, has a tortured quality due to the fact that neutralized tonal elements have been forced to fuse with one another as though they still carried tonal implications.

The conflicts that afflicted Schönberg were not shared by his pupil, Anton Webern, who became the first composer to fully embrace the most radical aspects of atonality (and, later, serialism). In Webern, even as early as 1909, all elements of the music share in the negative syntax. References to traditional musical gesture are practically eliminated. Melodies and themes in the usual sense are no longer present. Scale passages are all but eliminated. Melodic motion is disjunct in the extreme, with large intervals separating most of the notes. Harmonies are maximally dissonant and totally devoid of implication.

While Webern's treatment of pitch-space nevertheless owes much to Schönberg, his approach to time does not. In 1909, when Schönberg was writing rhythmic passages resembling those of Brahms or Wagner, Webern was anticipating the disjunctive accents of Stravinsky. Rejecting such restlessly shifting accents in his later, serial, works, he delves much farther into the mysteries of musical time, composing in terms of real durations, for which the release is as important as the attack. While a work such as his Symphony, Opus 21, has been described as "pointillist" because of its fragmentation into isolated notes, these notes are never merely points -- each is a separate presence, with a precise temporal "weight." Only in terms of a durational determination of this kind is a truly proportional division of the field of the "surface," in the spirit of Mondrian, possible. Only in such terms, moreover, could Webern hope to embody silence as a true "negative" of sound, with a weight of its own, as opposed to its usual function as a passive container or background into which sounds are placed.

The parallel with pictorial space has been explicitly drawn by theoretician Heinz-Klauss Metzger. Stating that Webern "was brought up on music composed of sounding events in silence, comparable to traditional painting, which placed figures against an empty background," he makes the point that, in such painting, "along with every elevated positive form there arose a negative one for the surrounding background." Noting that it is only in recent times that the emancipation of such negative forms has taken place, Metzger compares this emancipation with Webern's foregrounding of silence, concluding that "Webern's revolution may be compared only with that by which Mondrian created a new kind of painting."7

Perhaps the most thorough and thoughtful inquiry into Webern's approach to time has been made by composer-theorist, Henri Pousseur. Pousseur refers to the extreme symmetry and periodicity of the tonal-metric system as producing "an abstract spatial-temporal framework, a grid whose existence seemed to antedate the objects appearing in its interior and thus to create the illusion of an absolutely existing objective order." Such a system is an attempt to "appropriate things and their immediate appearance in a definitive manner...[denying] the reality of their (and our) ephemeral structure."

[Webern] refused to oppose the flow of time with attempts at consolidation... [Recognizing that] one can communicate with things only in the distance of their transivity, in their innate alternation between presence and absence...[he created a music of] pure instantaneousness, of undiluted acceptance ...of the appearance and disappearance of objects.

Pousseur notes how Webern uses asymmetry and discontinuity, fundamental principles of his musical language, to oppose the homogeneous symmetries of classical tonality. As a result, the possible existence of some archetypal "preestablished simply passed over in silence: until the appearance of events, time and space remain wholly indeterminate."8

We cannot help but be reminded of Cézanne's revolt against perspective, his insistence on an a posteriori space created by the idiosyncratic appearance of objects themselves. But the parallel with space should not confuse us. Webern's temporal "surface" is analogous with the pictorial surface of Cézanne or Mondrian, but it remains fully temporal, nevertheless. Only the abstract timepoints of the tonal-metric system, lacking true duration to begin with, may be accurately said to partake of the "timelessless" of painting. The weighted durations of Webern are, by virtue of their "weight," truly temporal, thus truly ephemeral.

Webern and the Series

It is no coincidence that the emergence of a new, more purely durational, approach to time accompanied Webern's adoption, in 1924, of the twelve-tone method. Schönberg's reorganisation of the pitch dimension of music, became, for Webern, the key to a profound rethinking of musical structure in general.

Let us recall that the twelve-tone method is grounded in the necessity that each tone be related only to every other tone (rather than a single tonal "center"). In order for each tone to retain its multi-polarity, all must be continually repelling one another. This mutual repulsion of the tones is the basis for the fundamental negativity of Schönbergian syntax. An orthodox tone row is already a highly organised structure, specifically designed to prevent any tone from coming under the sway of any other (beyond the purview of the most limited local encounters).9

In Schönberg's hands, his own method tends to waver between the negative destruction of tonality and the creation of a kind of substitute positivity in which the series, at times, seems to be striving to replace, rather than neutralize, the totalizing function of the tonal system. While his approach usually leads to mutual repulsion of the tones, this generally involves the neutralization of their tonal function only. The tones still come together to form melodies, "pregnant" motives and, in some cases, quasi-functional harmonies.

Rather than similarly seeking to accomodate serial repulsions within a framework of traditional musical gesture, Webern intensified the repulsions to the point that melody and functional harmony all but disappear. Motives are no longer "pregnant" with implication, but simply groupings of tones which can function as landmarks. As with Mondrian, everything is structured to maintain the kind of equilibrium which promotes clarity, freshness and, above all, openness to the overall field (for Mondrian space, for Webern time).

The importance of this development to our investigation of negative syntax cannot be overestimated. Cubism and the procedures of atonality involve ad hoc methods, largely intuitive reactions against positive syntax; Mondrian's neoplasticism reveals a much more solid theoretical grasp of fundamentals but, despite the systematic nature of its preliminary reductio, remains a fundamentally non-systematic, intuitive procedure. Webernian serialism, on the other hand, is unique in being a highly systematic structural principle designed specifically to maintain the independence of its elements and neutralize any possible implicational context that might arise on any but the most local, temporary level. It is in fact the first and really the only example we have of a basic generative principle for the free but controlled composition of negative syntax.

Symmetry-Asymmetry in Webern

Up to this point we have been defining negative syntax essentially as a reaction against any kind of systematic ordering, symmetry or regularity, aspects of structure which we have associated with positive syntax exclusively. Indeed, Webern's pre-serial work resembles that of Mondrian in fostering the kind of extreme reductionism which makes negative syntax a matter where intuition can function precisely and completely to defeat symmetry without the need for highly systematic pre-planning. Webern's strategy in these early works, exactly equivalent to that of Mondrian, has been admirably expressed by Pousseur: "the positioning of well-defined and clearly perceptible units, articulating themselves by means of reciprocal effect, each one limiting and defining the nature of its fellows."10 Theoretically this truly dialectical approach to structure ought to be self-sufficient, with each element defined by its partners, rather than some center, tonal or otherwise.

In practical terms, however, stringent limitations are involved, most obviously reflected in the extreme brevity of Webern's early atonal works (one complete movement from the pieces for cello and piano, Opus 11, is only 10 bars long). The longer the work, the greater the difficulty of balancing the elements, the greater the likelihood of lapsing into something that could suggest the traditional symmetries.

Schönberg's row showed Webern the way out of this dilemma. The "method of composing with twelve tones related only to one another" was, in fact, a system for generalizing into a basic principle that "reciprocal effect" which had only been an ad hoc strategy in the earlier works. The fundamental disruptions of negative syntax are "built-in" to the serial method itself, especially in the hands of Webern. The marvelously practical aspect of the Webernian series is its role as a central reference which de-centers, unifying only by spreading its disunifications systematically throughout the entire work. Thus only in his serial music is Webern able to develop the highly symmetrical germinal "cells" and hierarchic superstructures which permit the generation of complex and extended balanced asymmetries of the sort that defeat hierarchical domination without inhibiting variation and elaboration. In the words of Pousseur, "symmetry in the late work of Webern [is] not the remains of an obsolete classical system, but an attempt to regulate the proportion of regularity which must exist within any irregularity."11 In thus expanding the structural powers of negative syntax, Webern goes beyond Mondrian, not in perfection, but scope.

Symmetry-Asymmetry--An Example

The manner in which Webern produces highly organised asymmetries from symmetrical building blocks involves musical complexities going far beyond the purview of this book. A relatively simple example can, nevertheless, convey something of the general principle involved. Webern's
String Quartet, Opus 28, is based on a twelve-tone row, one form of which consists of the following pitches: Bb , A, C, B -- Eb , E, C# , D -- Gb , F, Ab , G. The pitches have been grouped into three sets of four notes each to clarify the fact that each four note set is a simple permutation of the others. The second is the inversion (also the retrograde) of the first. The third is a simple transposition of the first down a major third. The economy of this arrangement will be appreciated when we recall that a twelve tone row uses the complete set of twelve available pitches with none repeated.

The series as a whole is mirror symmetrical: the first six notes, in reverse order, produce the inversion of the last six notes. Each four note set is similarly mirror symmetrical. As a result of its peculiar structure, the inversion and retrograde of the series are identical-the same is true of each four note set.

Now let us transpose the entire series up by a major third. This produces the following permutation of the original twelve notes: D, C# , E, Eb -- G, Ab , F, Gb -- Bb , A, C, B. Note that the original four note sets remain intact. The second set is now the first, the third is the second and the first has become the third. Moreover, a fundamental transformation has taken place in their relationship: the pitches of sets two and three of the original row are now in reverse order, while set one (Bb , A, C, B) is exactly the same in both rows.12 This set is said to remain order-invariant with regard to this particular transposition of the row. As a result of this invariance, there is a marked and uniquely structural asymmetry between these two versions of the row, an asymmetry made possible by the high degree of symmetry within the row taken by itself. The principle of invariance is thus an important tool for the production of organised asymmetry from the highly symmetrical regularities of row structure and serial procedure.

The above example only touches on the complexities and subtleties called forth by Webern's (and Schönberg's) procedures. Indeed the difficulties surrounding Webern's techniques have created the false impression that the music itself is highly cerebral, requiring the listener to carefully follow and recognize each transformation of the row. This is true only to the extent that one insists on listening "positively," in terms of hierarchically ordered and unified gestalts. Listening thus, for what is not in fact there, can only reinforce the notion that some kind of mystique is at work.

The principle of invariance, for example, involves complex systemization, but ultimately works to bring certain elements (such as the Bb , A, C, B set) into sharp relief. This is only one example of the ways in which organisation in Webern functions to make each particular moment maximally "present," maximally clear and expressive in itself by putting us in closer touch with the audible, temporal, "surface." Unlike positive structures, in which all concrete materials are sublimated in favor of the realization of an abstract structural idea, negative structures sublimate themselves in favor of the vivid presentation of their concrete materials.

Cage and Webern

Among the first to respond to the most radical aspect of Webern's revolution was the American composer John Cage. Himself a student of Schönberg, Cage had quickly moved from the Schönbergian "emancipation of the dissonance" to what for him was the next logical step, the liberation of all "non-musical" sounds. In searching for a "structure hospitable to nonmusical sounds, noises, as it was to those of the conventional scales and instruments,"13 Cage found Webern's approach to time of great use.

Stating that, traditionally, musical structure has been defined harmonically, in terms of pitch relationships, Cage has credited Webern (along with Eric Satie) with introducing a completely new idea: the definition of structural parts "by means of time lengths."

If you consider that sound is characterized by its pitch, its loudness, its timbre, and its duration, and that silence, which is the opposite and, therefore, the necessary partner of sound, is characterized only by its duration, you will be drawn to the conclusion that of the four characteristics of the material of music, duration, that is, time length, is the most fundamental. Silence cannot be heard in terms of pitch or harmony: it is heard in terms of time length.14

Drawing on this new idea, Cage composed, in the forties, a series of works in which the proportional relationships between time lengths of sections were determined prior to decisions regarding the sounds which were to be placed within each section.


Webern's treatment of duration was only one part of his influence on Cage. More generally, the younger composer was to respond strongly to Webern's radical discontinuity. Speaking retrospectively of the attitude of himself and a small group of associates during the Forties, Cage has written as follows:

Where people had felt the necessity to stick sounds together to make a continuity, we four felt the opposite necessity to get rid of the glue so that sounds would be themselves.15

Cage, unlike Webern, had rejected the twelve-tone method precisely because it must have seemed like only another, newer form of musical "glue." Failing to see (as only Webern had seen) the disjunctive potential of the row, Cage sought elsewhere for a fundamental principle of disjunction. In the late Forties, he found it, and of course, much more, in his now notorious use of chance operations. The new, truly radical, method involved sounds, durational relationships, "actions," etc., established indeterminately, usually by a patently random procedure such as the tossing of dice. Works "composed" in this manner are "free of individual taste and memory (psychology) and also of the literture and `traditions' of the art. The sounds enter the time-space centered within themselves, unimpeded by service to any abstraction, their 360 degrees of circumference free for an infinite play of interpenetration."16 Such works affirm "the absence of the mind as a ruling agent."17

Although the parallel is far from obvious, Cage's project has much in common with that of Mondrian. Both artists engaged in a radically reductive process of what Richard Kostelanetz has called "ordered disorder,"18 culminating in the establishment of an "axiom" of disjunction. Cage's "axiom" is, of course, the principle of indeterminacy itself, a systematically unsystematic method for randomizing any and all aspects of a given work and/or performance.

Randomness and Negative Syntax

What, exactly, is the relation between Cage's randomizing "axiom" and negative syntax? This question raises complex and fascinating issues with which we cannot hope to fully deal in the present context. The following observations must suffice for now:
1. Insofar as indeterminacy can indeed promote perceptual differentiation and neutralize the mind "as a ruling agent" its function would certainly coincide with that of negative syntax.
2. Certain developments in "information theory" suggest a strong relationship between random functions and the perceptlon of discontinuity.
On the other hand,
3. Randomness, as we have learned, tends to call forth the context of implication, a purely mental phenomenon.
4. The findings of information theory with respect to perception seem contradictory. As randomness can be interpreted as resulting both in a maximum of "information" (differentiation) and entropy (non-differentiation), its ultimate function is something of a puzzle.19

It would, of course, be all too convenient if the most elusive and problematic goals of modernism could be attained through the employment of a simple mechanism. Nevertheless, there's an intriguing affinity between negative syntax and randomness which deserves exploration. Cage's practice may point to negative syntax in somewhat the same sense that numerology points to mathematics.

The Post-Webernians

At an opposite pole from Cage, but also profoundly affected by Webern, is a group of Europeans led by Pierre Boulez, Karlheinz Stockhausen and Henri Pousseur, often called the "post-Webern" school because of its intense involvement with Webernian serialism. This group shared with Cage a deep interest in those sound "surfaces" brought forcefully to light by the later Webern's emphasis on isolated, weighted notes and chords which could function as time "planes." All of the above named composers began to use complexes of sound in a manner analogous to Webern's treatment of pitches. These complexes, which could consist of dissonant chords, percussion "noises," electronic sounds, "real" sounds recorded by tape, or any combination thereof, were called by Boulez "sound objects." Sound objects may be defined as concrete clusters of sound heard simply as sound, with clearly defined intrinsic properties, including true duration.

Moment Form

In 1959-60, Stockhausen developed an approach to form which was an extension of the sound object principle. He called it moment form. The new approach, clearly indebted to Cage as well as to Webern, involved regarding a musical work as a series of isolated "moments." Like a sound object or an isolated Webernian note, "a given moment is not merely regarded as the consequence of the previous one and the prelude to the coming one, but as something individual, independent, and centered in itself, capable of existing on its own."20

In a remarkably clear and perceptive recent essay, "Moment Form in Twentieth Century Music," Jonathan Kramer has broadened Stockhausen's concept, demonstrating its profound relevence to much of the music of our time. Kramer begins by writing of the breakdown of musical continuity around the turn of the century: "the entire edifice of Western music had been built on the assumption that one event leads to another, that there is implication in music ..." With the dissolution of tonality, this "myth", which Kramer associates with "the metaphor of musical motion," was destroyed.

Kramer considers "moment-form pieces" as particularly characteristic of recent musical discontinuity. Such music "consists of a succession of self-contained sections that do not relate to each other in any functionally implicative manner." He credits Stockhausen with being the first to articulate this idea, but "the procedures ...derive ultimately from the practices of Debussy, Stravinsky, Webern (particularly in his variation movements), Varèse, and, above all, Messiaen."21

The sound-possibilities of moment-form are, theoretically, completely open. While, with the exception of Varèse, all the above-mentioned composers were content to restrict themselves, for the most part, to the traditional sound sources of music, more recent moment-form works incorporate a variety of non-"musical" sounds ranging from electronically produced "pure" sounds to vocal clicks and screams, recorded street sounds, radio broadcasts, etc.

Even completely conventional musical gestures can be incorporated into moment form. Kramer distinguishes between tonality as a "universe of discourse" and as a simple element which can co-exist with any other element. In certain works by Ives and, more recently, Rochberg, Berio, etc. (and, or course Cage) remnants of tonal-metric usage "are rendered static by contrast with the various nontonal surroundings,"22 Leftover fragments from positive syntax can be used "negatively" in a context in which their implicational powers have been defused. This is a basic principle of Cubist collage, where fragments of wallpaper, newspaper, lettering, etc. are incorporated along with "pure" elements such as lines and planes. Moment form "collage" similarly transforms familiar musical passages into neutral "sound objects."

Open Structure and Proportion

Needless to say, moment form involves totally different structural premises from those of the tonal-metric system. Since each "moment" is self-contained, the dynamic, developmental, goal-oriented procedures of classical form must be abandoned, as must even the basic notion of beginning-middle-end. To Stockhausen the distinction between beginning-ending and stopping-starting is particularly significant:

When saying "beginning," I imply a process, something that rises and merges; when saying "ending," I am thinking about something that ends, ceases to sound, extinguishes. The contrary is true with the words "start" and "stop," which delineate a duration, as a section, out of a continuum. Thus "beginning" and "ending" are appropriate to closed development forms which I have also referred to as dramatic forms, and "starting" and "stopping" are suitable for open moment forms.23

Traditional works, which evoke an idealist world of "transcendent" sound-meaning, cannot simply start as though they inhabited the same time-field as ordinary sounds. They must begin, that is, call forth, through conventionally established codes, the passage to their own time world. By the same token, such works cannot simply stop, but must, again through totally conventionalized procedures, set themselves off, as in a frame, by a process of ending. Moment form works, which would intensify, rather than transform, the time-field, may start and stop.

Stockhausen's distinction between "closed development forms" and "open moment forms" is particularly significant. Traditional forms "begin" and "end" as a function of the gestalt closure, which, as Leonard Meyer has demonstrated, they require. Moment form pieces, like the mature paintings of Mondrian, would disrupt gestalt perception, thus opening themselves to their surroundings (temporal or spatial). In this context, it is particularly important to understand that, theoretically, each moment of a moment form piece, while self contained, does not exhibit closure and should not be confused with a gestalt -- each moment also simply starts and stops, remaining open to the moments surrounding it.24

The notion of "open form" called forth in Stockhausen's essay is of great importance to the post-Webernians, gaining the status of a catch-phrase which, at times, seems to mean anything and everything distinguishing their structures from the traditional ones.25 The phrase itself, however, tells us little about the manner in which any given work is to be organized from "moment" to "moment." Indeed, the absence of beginning-middle-end organisation would seem to precipitate a structural crisis for moment form in this respect, as the very notion of temporal organization seems to demand such a progression. Having rejected any notion of teleological form, the composers cited by Kramer would seem to have accepted musical anarchy. As Kramer points out, however, one important organisational resource remains from the ruin of traditional form. It is the same resource claimed by Mondrian: proportion.

Global coherence cannot come from progression nor even, in most cases, from order of succession...But the nature of moment form suggests proportional lengths of moments as the one remaining principle of formal coherence...Whether or not a moment form is satisfying depends to a large degree on the proportional lengths of moments.

For Kramer, the crucial role of proportion goes hand in hand with the effects of musical staticism. Because of the many different levels of motion in traditional tonal music, our perception of its proportions "is too complex to be dealt with by objective measurement." Since moment form works tend to disrupt motion altogether, in such works,

the measurable length of one static section relates [perceptually] to that of another ...[Hence] it is safe to say that, when there is no large internal activity within sections, the objectively measurable durations correspond to the perceived proportions.26

In this passage, the fundamental difference between the roles of proportion in positive and negative syntax is brought into relief. In tonal music, perspective painting and positive montage, all relationships are internalized and experienced psychologically. The temporal proportions of traditional music and film are thus subliminal underpinnings of the various kinds of multi-level motion that come into the foreground of our awareness. In negative syntax, durations as static (i.e., non-moving) time lengths are thrust into the foreground of our awareness. This "flattens" our experience of time, permitting us to directly sense temporal proportions as simple relationships. Experienceed in this manner, such proportions can function to determine our perception of the temporal field in a manner analogous to that in which Mondrian's proportions determine perceptual space.

The heart of Kramer's essay is the proportional analysis of two works which he regards as keys to the development of moment form: Stravinsky's Symphonies of Wind Instruments and Messiaen's Chronochromie (literally, "time-color"). He assigns to each disjunct section (moment) of the Stravinsky piece an approximate time length in seconds (derived from the collation of rhythmic values and metronome markings). When the ratios between time lengths are rounded off, Kramer discovers some surprising proportional consistencies, particularly the predominance of the ratio 3:2.

I find the pervasiveness of this ratio impressive. It accounts for the formal balance of the first half of the piece. I do not of course claim that we listen and say, "Aha! A 3:2 piece." But we surely do hear something consistent and elegant in the way the proportions relate, and the persistence of 3:2 explains such an impression.27

Serialism and Temporal Determination

Nothing in the Stravinsky work suggests that the 3:2 ratio was arrived at by any but a purely intuitive process of give and take between motivic "content" and temporal "form." With Stockhausen, however, (as with Cage) we arrive at a situation where proportional relationships among moments are precisely calculated, prior to the determination of their sound-content. In order to understand the basis for Stockhausen's calculations, we must briefly review post-Webernian "total" serialism.
Webern himself never worked from any a priori serial ordering other than that determining pitch (the "twelve tone row"). Certain of his works do undoubtedly, however, point in the direction of serial (or at least highly rational) treatment of other parameters.

During the late Forties and early Fifties, when Messiaen and his students "discovered" Webern, there was a surge of interest in the project of generalizing Webernian serialism to the point that certain of its fundamental procedures could be applied "totally," that is to any and all musical parameters: rhythm, texture, timbre, register, loudness, etc. The process began with the realization that a tone-row was essentially a set of ratios between pitches; ratios which could be expressed numerically in various ways (e.g., on the basis of relative number of cycles per second, or interval size measured in half-steps). Since such ratios could also be applied to relative time lengths, it was possible to derive a "rhythmic series" from any twelve-tone row.

In early examples of "total" serialism by Messiaen (Mode de valeurs et d'intensités) and Boulez (Structures), the serialization of rhythm takes its place on more or less equal terms with the serialization of other parameters; "rhythm" is conceived traditionally, i.e., in terms of attacks, rather than durations; the rhythmic series controls local, note to note, relationships only. In a seminal essay, "How Time Passes," Stockhausen demonstrated that the determination of temporal relations goes far beyond questions of rhythm, having profound importance at all levels of musical organization, from pitch (cycles per second) to global form.28 In works associated with this essay, notably Gruppen (1958), Stockhausen developed procedures for extending the serial principle to the determination of the overall, large-scale duration proportions of an entire composition. It is this "promotion" of the temporal dimension, from simply one of many equally important "parameters" to a status equivalent to structure itself, which makes moment form possible. By the same token, the moment form concept, by permitting serial predetermination of each moment's duration, enables the series to extend its influence to structure on the largest scale.

The Triumph of Rationalism

Our search for the ultimate basis of negative syntax in time seems near an end. Kramer's analysis of moment form has demonstrated the fundamental role of large-scale temporal proportions. Our brief history of post-Webernian serialism has revealed the manner in which such proportions came to be calculated from a basic rhythmic series. We need apparently only carry the process one step further, inquiring as to the principle through which the rhythmic series itself comes to be determined.
At this point, however, difficult problems arise. While both Mondrian's intuitive determination of spatial proportions and Cage's principle of indeterminacy can be regarded as "axiomatic," thus primary (non-derivable), any given post-Webernian rhythmic series is indeed derived from something prior, usually a twelve-tone row.

A rhythmic series derived from the proportions of a tone row cannot inherit its "negative" disjunctions. The mutually repulsive dissonances of the row stem from an a priori system of tuning which applies to the pitch dimension alone. Simple time proportions derived from complex vibration ratios will have little more than a purely theoretical relation with their source.29 Post-Webernian serialism is indeed characterized by many arbitrary relationships of this sort, a failing which stems from a fundamental contradiction. On the one hand, the composers of this group seem fully aware of the importance of differentiation, discontinuity, decomposition; on the other hand, the series itself has generally been regarded as having a unifying function. Since the "unifications" of the serial method are hardly ever directly perceptible, a highly rationalistic faith in the unifying power of numbers grew with the development of total serialism. Through the workings of some mystical process, all the parameters of music were expected, somehow, to be unified through the continual use of permutations from a single number series.

A modernized idealism of this sort (recalling the Futurist "discovery" of geometry) reveals a serious underestimation of the dialectical properties of the row. In fact, of the major theories of total serialism, none reflects an awareness of the twelve-tone row as a perceptually disjunct construct which "unifies" the pitch field only insofar as this field becomes neutralized in the process. As with "dynamic equilibrium,"the tone-row is a destruction, not unification, of the "plastic means" (functioning, moreover, through the senses, not by means of abstract mathematical relationships).

In the effort to create a totally unifying, transcendent system within which all material elements might become transmuted toward some vaguely defined "higher" end, the total serialists created a monster of rationalism, a pseudo-science of artistic creation which, ultimately, they themselves were forced to reject. In the ensuing flight into the irrational which (perhaps inevitably) followed,30 fundamental questions regarding the determination of temporal proportion were left in abeyance.

If the post-Webernian's preoccupation with numbers (extending even beyond serialism to an involvement with aleatory and stochastic processes) led to a fetishization as problematic as that of the Futurists, their contributions to the organization of negative time remain considerable nevertheless. The extension of the serial idea to determination of the time-field makes powerful twelve-tone procedures (such as invariance, for example) at least potentially viable in the organization of temporal relations. Moment form, among the very few theories primarily concerned with the structuring of duration, clarifies much regarding the role of temporal disjunction in Twentieth Century music. The closely related notion of "open form" links the explorations of the post-Webernians with "opening of form" so crucial to negative syntax generally.


Chapter 8-- Space:Mondrian and the Archetypal Image

1. Michel Seuphor, Piet Mondrian:Life and Work (New York: Abrams, 1956) p. 198.
2. In order to avoid confusion, I will refer to Mondrian's artistic works according to the numbers and dates provided in Seuphor, ibid., "Classified Catalogue," pp. 355-395. The two studies referred to above are Seuphor 169 and 170.
3. Seuphor 171.
4. Seuphor 172, 173, 174. The last is also called (by Seuphor) "The Blue Tree."
5. Seuphor 175, 176, 177.
6. According to historian Hans Jaffé, Mondrian probably first viewed Cubist paintings at an Amsterdam exhibit held in the autumn of 1911, but had undoubtedly heard of the movement and seen reproductions before this time. Hans Jaffé, Piet Mondrian (New York:Abrams, undated) pp. 24, 25.
7. Seuphor 179.
8. Seuphor 190-200.
9. Seuphor 284.
10. Seuphor 294.
11. Alfred Jarry may have anticipated Mondrian with his only partially whimsical notion of "pataphysics," the "science of the laws governing exceptions."
12. Piet Mondrian, "Toward the True Vision of Reality" (1942), in Mondrian, Plastic Art and Pure Plastic Art (New York:Wittenborn, 1945) p. 10.
13. Ibid. p. 13.
14. "A New Realism," (1943) in Plastic Art ..., op. cit. p. 18.
15. "Toward the True Vision ...," op. cit. p. 13.
16. "Natural Reality and Abstract Reality" (1919-20), in Seuphor, op. cit. p. 304.
17. "A New Realism," op. cit. p. 20.
18. " Plastic Art and Pure Plastic Art" (1937), in Plastic Art... op. cit. p. 58.
19. "A New Realism," op. cit. p. 25.
20. Ibid. p. 25.
21. "Plastic Art and Pure ..." op. cit. p. 58.
22. "A New Realism," op. cit. p. 25.
23. "General Principles of Neo-Plasticism" (1926) in Seuphor, op. cit. p. 166.
24. "Pure Plastic Art" (1942), in Plastic Art ..., op. cit. p. 31.
25. Ibid. p. 31.
26. See discussion of Picasso's The Reservoir, pp. 77-79, above.
27. See, for example, Charles Bouleau, The Painter's Secret Geometry (New York:Hacker, 1963).
28. From the Journals of Charmion von Wiegand, as quoted in Seuphor, op. cit. p. 181.
29. Robert Rosenblum, Modern Painting and the Northern Romantic Tradition (New York:Harper and Row, 1975), p. 173.
30. Ibid. pp. 36, 184, 180.
31. Robert P. Welsh, "Mondrian and Theosophy," in Piet Mondrian 1872-1944, Centennial Exhibition Catalog (New York:Solomon R. Guggenheim Museum, 1971) pp. 35-51.
32. Helena Blavatsky, Isis Unveiled, vol. II, as quoted in Welch, ibid. p. 49.
33. Rosenblum, op. cit. p. 193
34. See "Natural Reality and Abstract Reality," op. cit., first three "scenes."
35. Rosenblum, op. cit. p. 193, 194.
36. C. G. Jung, "The Philosophical Tree," in Jung, Alchemical Studies (Princeton:Princeton University Press, 1967) p. 253.
37. Quoted as a source for Jung's notion of the archetype in Jolanda Jacobi, Complex/Archetype/Symbol in the Psychology of C. G. Jung (New York:Bollingen Foundation, 1959) p. 34.
38. See Jacobi, ibid. p. 35.
39. Alchemical Studies, op. cit. p. 22.
40. C. G. Jung, Mysterium Coniunctionis (New York:Bollingen Foundation, 1963).
41. Dore Ashton, "Mondrian:Notes on an Exhibition at the Guggenheim Museum," in Artscanada 226/227 (May, June 1979). The notion of a radiation from the center derives from a particularly misleading essay by the artist, Max Bill, who claims that "one may visualize [Mondrian's lines] extending beyond the rim of the image. The fixed center becomes a nucleus, surrounded by possibilities of unlimited extension." This idealized misreading of Mondrian's notion of open space is refuted by the canvasses themselves, where many of the lines are tucked in at the edge, and clearly stop. Bill's remarks would be better applied to the most ordinary landscape painting, where hills and dales ad infinitum are implied before, behind and to the sides. See Max Bill, "Composition 1 with Blue and Yellow, 1925 by Piet Mondrian," in Piet Mondrian 1872-1944, op. cit. p. 75
42. Op. cit. p. 166.
43. "Natural Reality and Abstract Reality," op. cit. p. 312.
44. See, for example, his comments in "Natural Reality and Abstract Reality," op. cit. p. 318.

Chapter 9--Time: Webern, Serialism and Moment Form

1. Robert Ericson. The Structure of Music (New York:Noonday Press, 1957) pp. 82, 83.
2. Here we part company with Bergson, for whom melody was the ideal realization of "pure duration," the exact opposite of "cinematographic time." The weakness of his position in this regard became evident to Bergson himself, who significantly qualified it in a late work. Durée et simultanéité (1922); see quotation in Victor Zuckerkandl, Sound and Symbol (New York:Pantheon, 1956) p . 244.
3. Leonard Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956) p. 92.
4. Ibid. pp. 157-196.
5. For a concise statement regarding the relation of extended tonality and its attendent ambiguities to the process of musical symbolization, see Arnold Schönberg, Structural Functions of Harmony (1954), revised and edited by L. Stein (New York:Norton, 1969) pp. 76-113.
6. Schönberg's phrase. See, e.g., ibid. p. 193.
7. Heinz-Klauss Metzger, "Webern and Schönberg," in Die Reihe 2 (Bryn Mawr, Pennsylvania:Presser, 1958) pp. 44, 45.
8. Henri Pousseur, "The Question of Order in New Music," in Perspectives of New Music vol. 5, no. 1 (Fall-Winter, 1966) pp. 99-101.
9. Space does not permit adequate discussion here of the currently widespread claim that many serial works contain tonal functions. In my view, this claim is misleading. While it is not at all unusual for a serial work to contain suggestions of tonality, consistent polarization of pitch space in a single "direction" is uncharacteristic. While certain invariant functions can give greater prominence to some pitch-classes, these are usually (in Webern, at least) disjunctive pairs (tritone) or tonally neutral chords (diminished 7th or augmented triad).
10. Pousseur, op. cit. pp. 104, 105.
11. Ibid. p. 104.
12. This is, of course, the famous BACH motive.
13. John Cage, "Composition As Process" (1958), in John Cage, Silence (Middletown, Connecticut:Wesleyan University Press, 1961) p. 19.
14. John Cage, "Defense of Satie"(1948) in John Cage, ed. Kostelanetz (New York:Praeger, 1970) p. 81.
15. John Cage, "History of Experimental Music in the United States" (1959) in Silence, op. cit. p. 71.
16. John Cage, "Composition" (1952) in Silence, op. cit. p. 59.
17. "Composition As Process," op. cit. p. 27.
18. Richard Kostelanetz, "John Cage: Some Random Remarks," in John Cage, op. cit. p. 196.
19. "Indeed, indeterminism is nothing other than a lack of determination, that is, of all characterization having the power to distinguish one thing from another and to determine it specifically. It is really nothing other than indifferentiation...." Henri Pousseur, op. cit. p. 103. See also Rudolf Arnheim, Entropy and Art (Berkeley:University of California Press,1971), especially pages 15-25, for a discussion of the same contradiction specifically applied to the claims of information theory.
20. Karlheinz Stockhausen, "Momentform" (1960) in Seppo Heikinheimo, The Electronic Music of Karlheinz Stockhausen (Helsinki, 1972) pp. 120, 121.
21. Jonathan Kramer, "Moment Form in Twentieth Century Music," in Musical Quarterly, vol. 64, no. 2 (April, 1978) pp. 177-179.
22. Ibid. p. 184.
23. Stockhausen, op. cit. pp. 121-122.
24. Unfortunately, both Stockhausen's original formulation and Kramer' s extrapolation from it are marred by idealizations which only serve to mystify. Thus Stockhausen speaks of "an eternity that is present in every moment" and the "explosion--yes--even more, the overcoming of the concept of duration." (Quoted in Kramer, op. cit. p. 179) Space does not permit analysis of the damage done by such wishful thinking. Possibly due, at least in part, to theoretical weaknesses of this sort, most moment form works lack the powerful negative temporality of Webern.
25. The term became associated with "variable form" and Cageian indeterminacy.
26. Kramer, op. cit. pp. 181-183.
27. Ibid. p. 187.
28. Karlheinz Stockhausen, "How Time Passes," in Die Reihe 3 (Bryn Mawr, Pennsylvania:Presser, 1959) pp. 10-40.
29. This failing is shared by the "time-point" system of Milton Babbitt, which in other respects improves on post-Webernian serial method.
30. During the Sixties, indeterminism of one sort or another became a pervasive characteristic of post-Webernian music.