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Volume 2.6:

Victor A. Grauer*

Toward a Unified Theory of the Arts

KEYWORDS: aesthetic, semiotics, negative syntax, positive syntax, antax, gestalt, negative field, positive field, tonality, atonality, disjunction, multireferentiality, poststructuralism, modernism, Cubism, Mondrian, Schoenberg, Webern, Baumgarten

ABSTRACT: My essay, "Toward a Unified Theory of the Arts," originally published in the journal Semiotica (see details below), outlines the essential ingredients of a theory intended ultimately to encompass all art forms, traditional and modern, western and non-western, within the purview of an approach to semiotics which also does justice to aesthetic (not "aesthetics") as a fully independent "logic" of sensory experience. For practical purposes, I have confined myself to two areas only: the pictorial arts and music. The theory is divided into two opposed but complementary sets of principles, the first concerned with the unifying syntactic or "positive" field of traditionally conceived semiosis, the second with the disjunctive "antactic" or "negative" field established in certain works of modernist art and music which disrupt semiosis. In order to clarify, for the readers of this journal, the relation of my ideas to certain issues in the theory of music, I have added a Preface and Postscript.

0. Preface

1. Toward a Unified Theory of the Arts

2. Postscript


0. Preface

[0.1] From 1979 through 1981 I labored on a book-length monograph dealing with modernism, semiotics and poststructuralism as they pertain to cinema, painting, music and (prior to the final revision, which required drastic cuts) poetry. My volume, recommended for publication by Thomas Sebeok in his Advances in Semiotics series, was ultimately turned down by the publisher as not sufficiently marketable. For many years I contemplated a more readily publishable essay that would convey the essentials of the new approach to a theory of the arts which lay at the heart of this work. As its treatment of already difficult material was quite complex, I believed for some time that such a condensation was not possible. Finally, after having put the matter out of my mind for some years, I decided that such an essay could work if I were content to limit myself to painting and music only, and simply outline my ideas with only minimal explanations, arguments and references, so a reasonably knowledgeable reader could at least get the gist of what I had in mind.

[0.2] The resulting paper, "Toward a Unified Theory of the Arts," published in the journal Semiotica,{1} turned out better than I thought it might, as it forced me to concentrate on basics, thinking through certain issues more deeply than before. As Semiotica is not the sort of journal regularly studied by music theorists, I am most grateful to Music Theory Online for making my essay available here, to a group of scholars already experienced in dealing with theoretical issues pertaining to the arts. I do not, however, expect easy sailing over the already famously stormy seas of music-theoretic argument. Even for highly informed readers, the paper's necessary condensations can be puzzling and even irritating. A prime concern has been that my quick run-throughs of certain complex historical developments and theoretical issues might appear superficial, dogmatic or both. I am especially grateful, therefore, for the opportunity to prepare my readers in this Preface and flesh out some especially difficult aspects of my theory in a concluding postscript.

[0.3] Theories attempting the "unification" of two or more art forms are hardly a novelty.{2} What sets mine apart and makes it, if I may say so, particularly timely, is the fact that it "unifies" only in so far as it is able to establish a radical break, an "abyss" at the heart of that-which-is-to-be-unified. Paradoxically it is this break which enables me to posit "unification" in the very teeth of the currently fashionable "postmodern" view that "grand unified theories" are now and forever after passe.{3} Had I wished to cater to this view, I could well have titled my work "Against A Unified Theory of the Arts," or "Toward A Disunified Theory of the Arts." (It could certainly, in a sense, be described as a "grand disunified theory.") But, as you shall see, I am no postmodernist. In fact, my theory challenges certain basic tenets of one of the driving forces of postmodernism: poststructuralism.

[0.4] Fundamental to the poststructuralist view is the notion, derived from structural linguistics and semiotics, that "everything" consists of systems of "empty" codes, referring only to one another; that there is nothing "outside" such signifying systems, no "metaphysical presence" that could conceivably transcend language, no prior perceptual or even sensory "givens" that could serve as its building blocks; that there is, in "fact," no "reality" "out there" for all the many "signifiers" to be either made from or "signify." For musical scholars, the notion that music, like language, is made up of "empty" codes, that there is no "reality" for music to signify, will for obvious reasons, not be a matter of serious concern. But hand in hand with this goes the notion that there are no musical "givens," no "neutral level" (to invoke Nattiez{4}), no ultimate reality either "out there," for the notes to "mean," or "in here," for the notes to "be," as purely auditory objects.

[0.5] Simple as they are, the musical examples presented at the outset of my paper illustrate an important aspect of what is at stake: that we cannot normally hear musical passages outside a kind of tonal "force-field" not unlike that which produces, for language, what linguist Ferdinand Saussure called "value." Music, like language, must thus be regarded as "a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others..."{5} Thus, from the poststructuralist viewpoint, heavily indebted to Saussure, what we "perceive" when we "listen musically," is not really given as "audible" sounds, but is the result, as with verbal language, of a system of differences articulating an "etic" (physically measurable) soundstream into "emic" (culturally determined) classes.{6} Thus, we hear music virtually, in terms of essentially mental semiotic fields (gestalts produced by systems of differences), not in terms of the material, purely sensory experience of something we might want to call the "sounds themselves." The sensory is repressed by such fields, to be experienced, if at all, in terms of something like what Derrida has called "the trace."{7}

[0.6] A basic premise of my paper is that the poststructuralist view 1. must be taken very seriously, as it has been rigorously argued; 2. precipitates a crisis for theory of the arts, as it demands that any such theory be totally subservient to an (already shaky) theory of the sign function. In other words, to accept such a position would be to regard music, painting, sculpture, cinema, architecture, dance, etc. as languages which can be "read" and fully analyzed, "deconstructed," what have you, in essentially literary terms.

[0.7] The first part of my paper presents a framework within which both music and pictorial art can be understood more or less in such terms. (Extending the approach to cinema, drama, dance, sculpture, architecture, the literary arts, etc. would certainly have been possible, but would clearly have taken me beyond the limits of the essay format.) Central is the notion of the syntactic field, a conflation of the most general semiotic and gestalt principles, understood as a fundamental ground of all traditional discourse. The second half is an attempt to go beyond the poststructuralist position by demonstrating how certain modernist artists and composers have subverted the syntactic field to promote a negative field essentially beyond the reach of verbal discourse, poststructural or otherwise. Such a field can serve as a ground of the trace or, equivalently, promote it to the status of ground. Serious consideration of either possibility would certainly be the postmodernist equivalent of heresy.

[0.8] My discussion of the relation between the traditionally conceived syntactic field and the completely untraditional antactic field of the modernists, is, to use a much abused term, heavily "dialectical." What makes any such argument difficult is that certain terms can never really be "defined," as their meaning can change and indeed often reverse itself during the course of the argument. Thus the meaning of certain oppositions, such as foreground/background, continuous/discontinuous, unified/ disunified, perceptual/ logical, must be continually reconsidered according to the changing context of the presentation. Unless one follows the thread quite carefully in this manner it is easy to misinterpret what I am saying.

[0.9] Another possible sticking point is what may appear a cavalier tendency on my part to draw analogies between visual art and music. It is, indeed, all too easy to come up with loosely defined analogies of all sorts between and among any number of fields. I must, therefore, underline the fact that almost all my analogies are firmly grounded in one fundamental analogy, which can be considered well established: traditional music, like traditional visual art (and, indeed, semiosis itself), is subject to principles of gestalt perception.{8} Once the fundamentally gestalt/anti-gestalt basis of my position is understood, most of the other analogies can be seen as derivations, or necessary extensions, of it. Thus, once we understand that negative space is a necessary consequence of figure/ground relations, the necessity for notions such as negative tonal space (negative tonality) and negative time becomes apparent.

[0.10] A relation between my theory and certain aspects of the writings of Derrida has been noted and deserves some comment here. When the theory was first conceived I had never heard of him. At the urging of an editor, who felt that my book required some consideration of recent developments, I undertook an examination of certain works of, among others, Jacques Lacan, Julia Kristeva and Jacques Derrida. To my amazement, much of what I read seemed quite relevant to (though hardly in complete agreement with) my own ideas and, as a result, I added a chapter to the book. Kristeva's approach to the "poetic language" of modernist poets such as Mallarme and Artaud has much in common with aspects of my theory, as acknowledged in an all too brief reference in my paper. Derrida's differance and trace always seemed tantalizingly close to some of my own ideas, but these "non-concepts" are shielded by such an array of paradoxes and circumspections that I was unsure what to think. At this time, while still unsure, I feel I have at least some understanding of trace (see above). As for differance, I am now willing to speculate in public that it might bear some relation to my notion of passage. For those intrigued by such parallels, I might add that one could claim a strong relation between my "syntactic field" and what Derrida calls "metaphysical presence." Finally, the negative syntax I find in the work of certain modernist masters seems to have something in common with, and might some day even be shown to have been in some sense a model for, deconstruction. Now that I have stuck my neck out very far indeed, I will pull it all the way back in again by insisting that none of the central points of my essay is in any way dependent on an "understanding" (mine or yours) of Derrida. This is fortunate, for, by its very nature, his "position" is also a "non-position" and can neither be easily understood nor in any sense "equated" with anything else.

[0.11] I hope the above has served as a reasonably helpful preparation for what follows. I have added a concluding Postscript, addressed to those who, having read the essay, may well feel the need for more detailed explanation. For every point that has been clarified, of course, many others, which themselves might require further clarification, have been introduced. This cannot be helped, as the matter is, indeed, complex.

[1] Toward a Unified Theory of the Arts

[First published in Semiotica 94-3/4(1993), pp. 233-252. Reprinted with permission of Mouton de Gruyter, a division of Walter de Gruyter & Co, Berlin, Germany.]

[1.1.1] With the great successes of structuralism, semiotics and poststructuralism during the past three decades, the theory of the sign-function and the ideological issues associated with it threaten to dominate the entire realm of aesthetic discourse. This paper presents the essential ingredients of a unified theory of the arts which, while reflecting the very real insights of structuralism and its offspring, seeks to move beyond them to a realm where the aesthetic can find a meaningful place. The theory is "unified" in the sense that it is intended ultimately to encompass: 1. any and all art forms; 2. the full historical and ethnological range of artistic expression, non-Western as well as Western, modernist and postmodernist as well as "traditional"; and 3. semiotic as well as aesthetic principles.

[1.1.2] A complete elucidation of such a theory would be beyond the scope of this paper. For now I would like simply to define and discuss certain fundamental principles and possibilities with respect to two important areas: the pictorial arts (painting, drawing, etc.) and music. The reader should bear in mind that my intention, in this context, is simply to convey a clear idea of the general outlines of the theory, not present a carefully reasoned set of arguments in its defense.{9}

[1.2] An Analogy

[1.2.1] Consider Figure 1. From an iconographic point of view, the most we can say is that it is rhomboid, essentially geometrical and flat.

Figure 1

[1.2.2] Adding some lines (Figure 2) we can immediately recognize the sign, however crude, for "house." Our rhombus has become one side of the house. It is, moreover, no longer perceived as flat, but polarized in a particular direction with respect to three dimensional space: rearward to the right.

Figure 2

[1.2.3] Consider the variation in Figure 3. The same rhombus is now perceived as polarized in a completely different direction: rearward to the left.

Figure 3

[1.2.4] Now let us attempt to combine the two (Figure 4). Something is clearly wrong. The Figure contains all the elements of the sign for house, but does not make sense. The difficulty centers on the original rhombus, which can no longer be perceived as having an unambiguous spatial orientation of any kind. The result can be described as "ungrammatical."

Figure 4

[1.2.5] Withholding, for the moment, any attempt at analysis, let us move to what seems an entirely different realm. Imagine listening to the unaccompanied musical line of Figure 5.

Figure 5

[1.2.6] Harmonized in the key of G Major (Figure 6), the line is clearly polarized in a particular tonal direction. Note how the final "A" sounds "up in the air." Figure 7 presents the same notes polarized toward a completely different tonal center (A Major), giving them a musical meaning very different from that found in Figure 6. In this context, the line ends with a sense of finality and repose.

Figure 6

Figure 7

[1.2.7] Finally, in Figure 8, which superimposes the two previous settings, we have something that sounds, from the "common practice" point of view, wrong, "ungrammatical." Unrelated to any key, the line cannot be oriented in tonal space. Its musical meaning is therefore unclear and, from a traditional standpoint, it sounds out of place.

Figure 8

[1.3] The Syntactic Field

[1.3.1] While the above visual and musical situations may not strictly parallel one another, there is a close analogy nonetheless. In the pictorial examples, a particular figure took on a different meaning and a different appearance depending on its apparent orientation within pictorial space. In the musical examples something very similar happened, but this time in the context of what we must call "tonal space." In both cases, instances which could not be understood within any given "spatial" context seemed in some sense to violate a "grammatical" rule and were understood as meaningless.{10}

[1.3.2] Similar examples could doubtless be drawn from, say, "color space," the "space" of musical time ("metric space"), sculptural space, architectural space, cinematic space, cinematic time, etc. What they would all have in common can be summarized in the following, which I call the "first semio-aesthetic principle": any object of perception can signify (take on meaning) only in relation to a controlling syntactic field.

[1.3.3] The notion of syntax is appropriate for more than one reason: it is associated with the rules of "grammar" to which we have already referred -- in this sense pictorial or musical "space," by analogy with linguistic syntax, can be regarded as the source of a set of rules determining pictorial or musical signification; the term implies a purely formal, structural entity, functioning independently of any possible content; the derivation of the word suggests the useful notion of a structure (tax) which brings-together (syn) -- in this sense a syntactic field must be understood as having a unifying function.

[1.3.4] The notion of a syntactic field should not present serious problems. A field is a kind of invisible controlling spacelike region or extent within which certain types of activity have the potential to take place. In the physical sciences, prior to the field idea, bits of matter and the forces between them were considered fundamental. For Faraday, followed by Maxwell and Einstein, what is fundamental are the fields (e.g. electromagnetic, gravitational) through which forces and matter can be understood to operate. Similarly we can consider a syntactic field as a controlling, determining fundamental entity or function by means of which syntax and signs can be understood to operate.

[1.3.5] Principle one does not, of course, follow inevitably from our analysis of Figures 1-8. However, these examples do provide simple, readily apprehensible illustrations of the workings of syntactic fields in the pictorial arts and music. In Figure 2, a spatial syntactic field is produced from a few carefully placed lines just as an electromagnetic field would be produced by a small burst of electrical current. A differently oriented field is produced in Figure 3. Figure 4 is "ungrammatical" simply because it cannot be unambiguously oriented within a field. Since the differences between Figures 2 and 3 relate to orientation in depth, we know that these fields are equivalent to three dimensional spaces. Since the Figures have been drawn on a two dimensional surface, the fields in question can only be understood as virtual, that is essentially mental, imaginary. The most highly evolved example of this sort of thing can be found, of course, in perspective space, where invisible "lines of force" control the syntactic field of an entire picture.

[1.3.6] Figures 6 and 7 produce analogous syntactic fields in tonal space. Since the difference between the fields produced by the two keys cannot be accounted for with reference to one dimensional (high to low) pitch "space," the tonal field must also be regarded as virtual. In its most highly evolved form, the "common practice" tonal system of Western culture during the Eighteenth and Nineteenth centuries, virtual "lines of force" deriving from the Circle of Fifths control the syntactic tonal field of an entire musical composition.

[1.3.7] The same tradition has produced an equally systematic method of controlling musical time. Virtual "lines of force" in the form of measures orient each note within a metric field. Thus, for example, a note occurring on the first beat of a measure will sound different and carry a different musical meaning from the same note occurring on the second beat, even if both are played in exactly the same way.

[1.3.8] A second principle arises naturally from the first: before any perceptible can function as a sign, it must be apprehended as a gestalt, i.e. a form or figure perceived against a ground.

[1.3.9] In other words, insofar as a syntactic field is also a perceptual field syntax must be first and foremost organized according to the laws of gestalt psychology, where figures are perceived against grounds and wholes are greater than the sum of their parts. The field itself functions as the ground within which sign-gestalts are placed. It would, indeed, be difficult to imagine how one would attempt to describe or deal logically in any way with a sign that was not also perceptible as a gestalt.

[1.3.10] In the rush to establish semiotics as a theory of everything this rather obvious point seems to have been lost. (There is no reason, however, to deny to semiotics the complementary notion: every gestalt must signify.)

[1.3.11] Gestalt principles are, of course, the basis for the traditional pictorial art of the West and many other cultures as well, as reflected, for example, in relations between shapes and backgrounds or, in more modern terms, positive and negative space. While not so obvious, analogous relations are found in traditional Western music, where, for example, various kinds of figurations and motives generate gestalts, as do points of closure such as cadences.{11}

[1.3.12] A third principle is the result of poststructuralist insights: every syntactic field is a construct with an ideologically determined basis.

[1.3.13] In other words, there is no such thing as a passive or even neutral ground. The fields associated with all signifying processes are the products of culture and reflect ideologically determined value systems enforced by explicit or implicit rules.

[1.3.14] Principle four: in the absence of a clearly defined syntactic field, there arises a context of free floating, ambiguous implication which functions as though a syntactic field were present. Thus one cannot defeat the ideological effect of the syntactic field simply by breaking the rules, invoking rhetoric or bricolage as a substitute for logic, making random marks or random sounds, etc. While such devices may not unambiguously signify, they will always imply the existence of some transcendent field within which their ambiguities can be resolved and a kind of mystical sign function can arise. This is undoubtedly the source of the special appeal of Surrealism.

[1.4] Signification vs. Aesthesia

[1.4.1] Let us pause for a moment to ponder some issues raised by the above. The examples with which we began illustrate how pictorial and musical meaning is related to a process of signification within a syntactic field. What is most remarkable and disturbing about this process is the fact that the shifts in meaning produced shifts in the way our figure and our notes were actually perceived. When understood as "side of a house," our rhombus is seen as a rectangle oriented in a certain direction. When understood as "in the key of G," our melodic line is heard as ending "up in the air." Indeed, in such a context meaning and perception can hardly be distinguished.

[1.4.2] For traditional semiotics this sort of thing reveals a surprisingly intimate connection between signification and perception. For the more radical poststructuralists it leads to a profoundly disturbing metaphysical gap. From this point of view all perception is completely dependent upon codes of signification -- we literally cannot see or hear anything that is outside a signifying process.

[1.4.3] In terms of the principles outlined above, we could say that all perception is dependent upon syntactic fields and, since such fields are controlled by ideologically determined thought processes, we are inherently incapable of perception per se. In more radical terms, not only perception, but reality itself falls away in favor of a purely mental process devoted exclusively to the decoding and encoding of "empty" signs.

[1.4.4] In the present context we can leave aside the difficult metaphysical issues raised by this position. We cannot, however, avoid an obvious question: in view of the total absorption of perception into signification, what is the status of the work of art or, more specifically, how does the art work differ in kind from any other coded entity?

[1.4.5] Let us recall that the word aesthetic, derived from the Greek aesthesia, originally meant "of or pertainable to things perceptible by the senses, things material as opposed to things thinkable or immaterial."{12} Indeed, the Eighteenth Century philosopher Alexander Baumgarten, in establishing aesthetic for the first time as an autonomous field of study, specifically relates the term to "things perceived" as opposed to "things known"{13} (Baumgarten 1954:78). We will be using the word in this original sense throughout the remainder of this essay. Though the provenance of this term has broadened considerably since Baumgarten, it would be difficult to imagine an aesthetic theory in any sense of the word which excluded the sensory world.

[1.5] Signification and its Other

[1.5.1] Semiotics, poststructuralism, "deconstruction" etc., in denying the ultimate validity of sensory experience, remove thereby any basis for an autonomous theory of the arts. If perception is reduced to a mode of signification, aesthetic must simply take its place within a system of essentially linguistic codes, hardly distinguishable from an intensified rhetoric.{14}

[1.5.2] While it is not our intention, here, to "deconstruct" poststructuralism, it is necessary to put this issue in historical perspective. The conflict between perception and signification is an old one and, consciously or unconsciously, has always posed a problem for the artist. The issue came to a head with the development of naturalist painting in late Nineteenth Century Europe, which entertained the naive hope of a perfectly straightforward, unmediated representation of the material world.

[1.5.3] Naturalism came to grief during a remarkable period when artists such as the Impressionists, Cezanne, Braque and Picasso delved progressively farther into the most fundamental problems of observation and representation. Finally, in the crucible, or should we say "cyclotron," of Cubist art, aesthetic and semiotic collided, the atom of cognition was split, and a new sensibility was born. Structuralism and modern semiotics can trace much of their ancestry to the Russian Formalist school of linguistics, born as a response to this sensibility as expressed in Futurism and Constructivism, direct outgrowths from Cubism.{15}

[1.5.4] In our view, the remarkable group of paintings and constructions produced by Picasso and Braque in the years 1908 to 1914 already encompass the central issues not only of semiotics but also deconstructionism. As a result, these works, which became the foundation stones of modernism (and postmodernism), also provide a key to the functioning of "traditional" pictorially based sign-systems.

[1.6] Disruption of the Sign

[1.6.1] Space does not permit an adequate analysis of the Cubist achievement in these pages. I will make do, instead, with a few comments which, if they are so brief as to appear dogmatic, will at least, hopefully, clarify my point of view.

[1.6.2] Cubism begins as an extension of the project of Cezanne, i.e., the use of painting as part of a relentless struggle to observe the material world directly, free of any representational scheme (such as perspective). Like Cezanne, the Cubists proceed by breaking up pictorial space to do justice to the unique space generated by each object. The various contending spaces are linked by areas of "passage," a time-honored device in which painters have traditionally linked foreground and background elements in order to create vague areas of transition that could, among other things, mask spatial discrepancies. As Cezanne learned, extreme use of passage leads to distortion. Seeking to resolve this problem, the Cubists radically fragment space into ever smaller "facets," so that each can absorb some of the distortion.

[1.6.3] Extreme fragmentation and passage, coupled with devices such as reverse perspective, cause forms to disintegrate, details to be emphasized at the expense of the whole. As a result, the syntactic field breaks into its constituent signs and sign-parts. No longer visible as gestalts, however, these fragments cannot fully signify. At this point Cubism becomes a self-referential meditation on the relation between perception and signification, playing a thousand different games with the now defused signs for spaces and things.

[1.6.4] With the disruption of the three dimensional syntactic field, areas such as the rhombus of Figure 1 can no longer be "read" as polarized in any direction and begin to reveal themselves simply as patches of color on an intensified surface. A new kind of space begins to emerge from such areas and the areas of passage surrounding and infiltrating them: "negative space," the space between forms.

[1.6.5] As Cubism moves into its so-called "synthetic" phase, fragments of negative space resolve into large, flattened areas of solid color or collage, punctuated by forlorn, thoroughly deconstructed sign fragments. As Cubist energies wane, the project is taken up by Mondrian, who methodically eliminates all reference to signification in an effort to equilibrate the newly acquired space through control of proportion. With Mondrian, the realist ambition ultimately becomes transformed into the project of determining perception itself.

[1.7] The Musical Analogue

[1.7.1] Parallels with the development of music over a somewhat broader time span are striking. Musical "modulation," a transitional device linking more or less distant keys is, of course, analogous to pictorial passage, which links more or less distant spaces. Modulation is usually characterized by the use of "pivot chords," ambiguous harmonies which have a function in both the old and the new key.

[1.7.2] During the Nineteenth Century, as composers seek to incorporate farther ranging tonal relationships, increasing emphasis is placed on a group of dissonant, inherently ambiguous pivot chords which can afford ready "passage" to distant keys via enharmonic relationships: the chord of the diminished seventh, the "French," "Italian" and "German" Sixths and the so-called "Tristan" chord. By the late Nineteenth Century, these and other transitional harmonies are enabling composers to fragment tonal space through frequent, almost routine, modulation. In the process, as with painting, forms begin to disintegrate and details, in the form of a host of new, highly colored dissonant harmonies, increasingly appreciated in and for themselves as sounds, begin to assert themselves at the expense of the whole.

[1.7.3] Finally, in the work of Arnold Schoenberg, the tonal system itself breaks down. With Schoenberg's "emancipation of the dissonance," the ambiguous chords which originally functioned as musical "passage" take on a new role as stable, unambiguous landmarks of a new "negative" tonality: atonality.

[1.7.4] The new musical space, designed to prevent any one note from becoming a stable tonal center, defeats the tendency, illustrated in Figures 6 and 7, for every note to be polarized in a particular tonal "direction." Notes and chords begin to be heard, not in terms of musical "meaning," but as sounds with unique and interesting properties of their own.

[1.7.5] Atonality, in which the notes repel one another, initially functions as a fundamentally disruptive strategy, comparable with analytic Cubism. The systemization of atonality by Schoenberg's twelve tone method, by analogy with synthetic Cubism and the later work of Mondrian, builds a completely new, multipolar "space" in which all elements (notes of the series) are in equilibrium.{16}

[1.7.6] Despite his radical break with the tonal system, Schoenberg is reluctant to completely do away with rhythmic and motivic gestalts. The final break comes in the work of his disciple Anton Webern, whose opening out of the motive-gestalt, liberation of timbre and rhythm, and acceptance of the ephemeral, eventually inspire the most influential compositional movement of the Twentieth Century: total serialism.

[1.7.7] The serialists, led by Pierre Boulez and Karlheinz Stockhausen, continue the process of radical fragmentation, increasingly emphasizing (as in "moment form") the ephemeral part at the expense of the transcendent whole, the audible "surface" (the "sound object") at the expense of tonal "depth" and (as with Mondrian's treatment of space) attending carefully to the proportional division of musical time.{17}

[1.8] Negative Syntax

[1.8.1] The striking parallels between the pictorial and musical developments outlined above encourage us to draw up a set of principles which might clarify this new situation:

[1.8.2] Principle five: a syntactic field is always associated with an opposing, usually hidden field, which, by analogy with negative space, we will call the negative field.

[1.8.3] As demonstrated by Cubism, negative space is more than simply the space between forms. The latter is only a fragment of a larger entity, repressed by the syntactic field which it threatens. As Cubism develops, this new space, first perceived as a distortion of three dimensional "positive space," emerges as a "negative field" of the surface, functioning in direct opposition to the gestalt structure of the more familiar "positive" syntactic field.

[1.8.4] Principle six: while the syntactic field is virtual, i.e., fundamentally conceptual, the negative field is material, i.e., fundamentally sensory, defined in terms of what Kant has called "Transcendental Aesthetic," the "two pure forms of sensuous intuition": space and time.{18}

[1.8.5] In painting, the negative field is the two dimensional space of the canvas itself, which must be suppressed to permit representation in depth. In this context, negative space, if noticed at all, is always perceived as part of the material (sensual) two dimensional surface, never as part of the virtual (mental) three dimensional space-in-depth.

[1.8.6] In music, the negative field is the simple, one-dimensional pitch "space" of the sound-spectrum (as opposed to the multidimensional syntactic "space" of the tonal system, with its functions and class identities) coordinated with the time of simple duration (as opposed to the multi-leveled time of the metric system, with its hierarchically structured periodicities).{19} The "negative times" of music (analogous to the "negative spaces" of painting) are the actual durations of sounds or the silences between them as opposed to the "figures" created by attack-points.{20}

[1.8.7] We must be careful to distinguish (as Kant did not) between the virtual, abstract space and time of the syntactic field, and the space and time of the negative field, perhaps best described as experiential or even existential.

[1.8.8] Principle seven: the negative field disrupts signification -- to the extent that sign elements are present in a predominantly negative field they will be multireferential.

[1.8.9] While its value to purely aesthetic experience should never be minimized, the negative field also has an important role to play in the opening out of the ideological forces behind the signifying process. Unlike simple ambiguity, which only tends to mystify the sign, the negative field, in defeating gestalt perception, totally disrupts the sign, revealing the rich, multiple play of interconnected, often contradictory, channels of reference hidden within the apparently straightforward message of any "text." It should thus be of interest to the poststructuralists, whose attack on semiotics is based largely on the latter's neglect of the "polysemic" implications of the sign-function.

[1.8.10] Principle eight: the negative field, normally suppressed by the process of signification, can only be liberated by a structural principle in direct opposition to syntax -- we can refer to this principle as negative syntax (or antax).

[1.8.11] Though we have left it for last, negative syntax is especially important, the key to the liberation of the negative field. Its operation has, to some extent, already been described in our earlier discussions of the development of Cubism and serial music. Initially, negative syntax is a repellent force, working against the tendency of positive syntax to promote gestalt perception and unify the syntactic (positive) field. Negative syntax opens the gestalt, promotes the part at the expense of the whole, perception at the expense of signification, disunifying the (positive) syntactic field while, at the same time, unifying the (negative) aesthetic field. Ultimately, after its analytic moment has been supplanted by a synthetic moment, negative syntax is equivalent to what can be called the "aesthetic determination" of the negative field, a pure sensory play of rhythm, proportion and surface.

[1.8.12] The above description of this extremely complex and revolutionary structural principle is only partially adequate. To pursue the matter further, we must take a detour into the past.

[1.9] Ars Analogi Rationis

[1.9.1] Strangely enough, the position we have arrived at via the practice of some of the most advanced minds of our century betrays a remarkable affinity with the thought of an obscure Eighteenth Century metaphysician, the aforementioned Alexander Baumgarten. Usually considered the founder of aesthetics as an independent discipline, Baumgarten is nevertheless so rarely read his major work has apparently never been translated from the original Latin.

[1.9.2] For Baumgarten, aesthetica, the knowledge of the "lower" faculties of cognition (i.e., the senses), cannot be reduced to the categories of logical thought, but must be treated independently, as an ars analogi rationis ("art of the analogy of reason"). Reversing the priorities of his rationalistic forbears, he concentrates not on the clarities of the mind, with its distinct, "intensive" categories, but the clarities of the senses, with their potential for apprehension of conceptually confused but vividly observed "extensive" particulars. It is in the "lower" faculty that we can find the "perfect sensate discourse" of "the poetic," analogous but opposed to the "perfect conceptual discourse" of "the rational."{21}

[1.9.3] While the greater part of Baumgarten's argument is all too heavily indebted to the rationalism (and artistic taste) of his day, its core remains remarkably fresh, providing us with a valuable insight into the meaning of the very similar analogies we have drawn. Indeed, negative syntax can be understood as in some sense equivalent to Baumgarten's aesthetica. Both seek to balance the cognitive equation.

[1.10] The Aesthetic Function

[1.10.1] Baumgarten, in treating aesthetic as an artifice or construct, not, as did his contemporaries, an inborn faculty for direct, unmediated knowledge a priori, places the object of his concern beyond the reach of the perennial debate over the status of the "real." Instead of attempting, as have so many others, to use sensory experience as both an empirical given of thought and that which can only be redeemed by thought, he opens for sensory processes a balanced, symmetrical relation to mental processes in which neither is given, neither exists as anything more (or less) than a function.

[1.10.2] Taking our cue from Baumgarten, we must define negative syntax as a function analogous to (though also in opposition to) logic. As logic can be said to determine thought, so negative syntax (aesthetic) can be said to determine perception. Thus negative syntax promotes perception by determining it, not valorizing its supposedly privileged position with respect to "reality" or "presence."

[1.11] Axioms of Perception

[1.11.1] Moving deeper into our analogy with an analogy, we are faced with some difficult questions. If negative syntax is, indeed, ars analogi rationis, then: 1. what aspects of negative syntax resemble what aspects of logic? 2. how does a "logic" operating in opposition to logic work? 3. how can such a "logic" determine sensory experience? While an attempt to provide more or less complete answers to such questions would take us far beyond the limitations of this essay, let us suggest some paths of research which might prove fruitful.

[1.11.2] Of all the visual artists whose work we have thus far discussed, the only one to make a serious theoretical contribution was Mondrian. An important clue to the workings of negative syntax can be found in his notion of dynamic equilibrium, "a dynamic rhythm of determinate mutual relations which excludes the formation of any particular form."{22} While Mondrian's meanings are often far from clear, it is possible to distill from his writings, as a key to dynamic equilibrium (and negative syntax), the following sequence: neutralization of representation through abstraction; opening of forms (i.e., gestalts, which, even when abstract, can still signify) to space; determination of equilibrated proportions in space (equivalent to the determination of perceptual space itself).

[1.11.3] In "logical" terms, this could be equivalent to: abstraction (e.g., dealing with logical symbols or numbers rather than, say, apples); analysis (the basic tool of logical thought); ratio (the traditional term for reason itself, apparently conceived as a proportioning of logical "space").

[1.11.4] Studying Mondrian's artistic development, from the earliest influence of Cubism in 1911 to the period just before his emigration to America in the early Forties, we see his principles at work in a process of reduction and distillation leading to a group of paintings that can, in fact, be characterized as axiomatic with respect to perceptual experience. The result is a dynamic, balanced interplay of line, plane and color which cannot be perceived in terms of figure-ground and contains no gestalt.

[1.11.5] As a logical axiom is a single thought, self-evident to the mind, an aesthetic axiom must be a single (non-hierarchical) image, "self-evident" to the senses. Aided by his theoretical principles, Mondrian simplifies to the point that he can determine proportions (and, of course, colors) exclusively by eye, with no recourse to logic, representation, geometry or system of any kind. We can compare this to the process with which Euclid arrived at his axioms by a similarly reductive, purely mental process, with no need for empirical (perceptually confirmable) input.

[1.11.6] The musical equivalent of Mondrian's axiomatic paintings would undoubtedly be the highly reductive, extremely brief works of Webern's early, pre-serial period (e.g. the Five Pieces for Orchestra, Six Bagatelles for String Quartet, Four Pieces for Cello, etc.).

[1.11.7] The tone row itself can, in a different sense, also be regarded as a kind of musical axiom. A twelve tone series is an essentially disjunctive, equilibrated arrangement (proportioning) of the twelve pitch classes which, as the basis for an extended composition, functions as an axiom. As with a logical proof, the entire construct inherits the properties of the axiom(s). Thus in a well made twelve tone work, the entire piece inherits the disjunctive tonal space of the row, in addition to any special motivic/harmonic characteristics a particular row may have. While in the hands of many composers the row can function conjunctively as a substitute for positive tonal syntax, this is not the case for Webern, whose treatment of the row always remains a fundamentally disjunctive system-for-the-disruption-of-system.

[1.12] Negative Syntax, Art and Signification

[1.12.1] From the point of view presented here, contrary to the conventional wisdom of the "postmodern" era, the modernism of the Cubists, Mondrian, Schoenberg, Webern, etc. is more than a style period to be followed by the next style period.{23} It represents the founding of a new sensibility, a new mode of awareness and, like all fundamental paradigm shifts, alters our view of past and future alike.

[1.12.2] The modernist attack on the sign-function reveals the presence, in the words of Mondrian, of "liberated and universal rhythm distorted and hidden in the individual rhythm of the limiting form".{24} Thus negative syntax does not produce something completely new, but liberates that which has always been present but repressed.{25}

[1.12.3] We must think, therefore, of negative syntax (aesthetic) and positive syntax (logic, representation, signification, semiosis) as two poles of a dialectic which must pervade any but the most thoroughly sublimated sign system. In substituting a dialectical, semio-aesthetic process for a monistic, rule-based semiotics, we may even be able to win back for systematic theory a portion of the territory now claimed by deconstructionist bricolage.{26}

[1.12.4] A complete elaboration of a semio-aesthetic theory of expression/communication would, of course, be a major undertaking. At the present time, we must be satisfied with the following somewhat disconnected thoughts:

[1.12.5] 1. In most cases of more or less traditional expression, negative and positive syntax may be seen as opposing (or, in another sense, complementing) one another on many levels. On the lowest level, negative syntax produces the disruptions that articulate (analogous to, say, the "phonetic" stream). Positive syntax pulls these articulations together to produce the next ("phonemic") level. On higher levels, the same process is repeated, negative syntax opposing the positive field just enough to make perceptible the differences which positive syntax will bring together to produce thinkable (meaningful) gestalts on the next level.

[1.12.6] 2. The above dialectic resembles the workings of the Japanese game of go, where each side tries to incorporate space previously carved out by the other. In all but modernist discourse, positive syntax always wins. Thus, in traditional works of art, all the space, even that once occupied by the negative field, ends by belonging to the positive field. The negative is usually present only in repressed, all but subliminal form.

[1.12.7] 3. Whenever negative syntax is incorporated into the process of signification by the unification of its disruptions through positive syntax, the portion of the negative field that has been (provisionally) revealed is then "understood" as having some sort of expressive value or adding to the impact, vividness or drama of the result. The stronger the pull of negative syntax, the more dramatic the effect will be. (Of course, negative syntax that has not been incorporated by positive syntax will not be understood at all and will convey only the notion that either "something is wrong" or "this is modern art.")

[1.12.8] For example, many Futurist paintings incorporate the extreme spatial fragmentations of Cubism, but use geometric structure (positive syntax) to pull the fragments together into an ultimately positive totality. Such paintings, essentially far more conventional than those of the Cubists, have a very exciting, hyperdramatic quality, gained through appropriation of a powerful negative field.

[1.12.9] More traditional works are replete with less extreme, but very similar effects, where distortions, spatial disruptions, coloristic anomalies, etc. are understood as "expressive" where and when they are comprehended positively on a higher structural level. Negative syntax also contributes to the degree to which local relationships or particular details hold their own with respect to the whole.

[1.12.10] 4. Negative syntax must be distinguished from weaker ad hoc devices that can have a disruptive function. Negative syntax is a structure, albeit a structure which disrupts structure. The key to differentiating a structure from a simple device is that the former is always associated with a field.

[1.12.11] 5. Of all expressive means, language alone is not fully grounded in either space or time, hence lacks a true negative field. This is not to say that the sounds of spoken or the marks of written language do not exist in time and space, but that they are not precisely defined therein. As soon as one attempts to be precise with the time of spoken language one begins to turn it into music (e.g., chant). As soon as one attempts to be precise with the space of written language it becomes visual art (e.g., concrete poetry). The precisions of language exist exclusively within the realm of signification and the logic (positive syntax) which grounds it.

[1.12.12] Thus, while a truncated form of negative syntax is certainly present in language and can even manifest itself strongly (e.g. Mallarme, Artaud, Joyce, Stein), language based art forms can never completely resolve onto a negative ground, thus can never move beyond essentially rhetorical devices such as overcoding or code shifting.{27} This may be the reason why structuralists, semioticians and poststructuralists, primarily linguists or literary scholars, have tended to either explicitly or implicitly place all artistic expression within the realm of rhetoric.

[1.12.13] The limitation of language with respect to the negative field has consequences for the deconstructionist enterprise, which uses language in an attempt to negativize the signifying process from within (rather than outside itself, from the realm of the senses, as is the case with, say, Cubism). This essentially ungrounded, self-reflexive strategy can result in a fascinating, if unending, play of paradoxes and witty "openings" of the sign, but can never resolve, as, lacking a negative field, it lacks any ground but that of the logic it seeks to demystify.{28} Consequently, what begins as a bid for expressive freedom ends with reincorporation within the bonds of the positive. Postmodernist art operates according to essentially the same model, choosing to ignore or minimize potential negative fields in favor of a play of mutually negativising positivities.

[1.12.14] There is a certain advantage to be gained from such play, which, by traveling in circles, need never fear reaching a "dead end." But it is unfair and, indeed, repressive of the deconstructionists, on the basis of the limitations of language, to insist that all expressive forms share the same limitations and that, as a result, logic (ideology) can be attacked only from within itself. Such a policy leads to mystifications as disturbing as any deconstructionism seeks to overcome.

[1.12.15] 6. While positive syntax always reflects culturally accepted and controlled procedures and values (ideology), negative syntax seems to work against them, toward a universal experience which is not culture bound. Initially, of course, negative syntax opposes positive syntax and, in so doing, becomes a kind of image (albeit a negative image) of that which it has engaged. Ultimately, however, negative syntax disrupts the ideologically controlled signifying process in favor of a liberated sensory play. The extent to which this play will reflect socially determined value systems can, of course, only be decided by examination of its function in a variety of cultural settings.

[1.12.16] If, as it would seem, negative syntax is resistant to such local variation, it would be extremely valuable as a tool for isolating universals in cross-cultural studies of the arts and communication. Negative syntax may, indeed, have something to do with the fact that all art forms with the exception of those that are language-based may be appreciated, if not understood, trans-culturally. In fact, the crucial difference between the appreciation and understanding of a work of art may derive from the distinction between negative and positive syntax.

[1.12.17] (7) The discourse of the traditional Western arts, with their elaborate hierarchical structures, would seem to be far more heavily positivized than that of non-Western or "folk" cultures. Would careful study of the arts of these "simpler" societies reveal a compensatory development of the negative?

[1.13] Summary

[1.13.1] Semiotic and poststructuralist theory argues that all aesthetic experience must take its place within the essentially language-based, ideologically controlled codes of the signifying process. While acknowledging the validity of much of this argument, we have taken exception to the notion that the world of the senses cannot be independently grounded. Determining that any signifying process must be based on what we have called a "syntactic field," we found, in certain modernist paintings and musical compositions, a structural principle which disrupts this field to promote sensory experience and multireferentiality: negative syntax.

[1.13.2] Following the lead of Alexander Baumgarten, for whom aesthetic is the basis of perception, we have attempted to understand negative syntax as, in his words describing aesthetic, "ars analogi rationis." Indeed, certain paintings of Mondrian seem to function as "axioms of perception," and certain examples of twelve tone music operate, like (anti)logical proofs.

[1.13.3] While negative syntax was first revealed in, and can help us to analyze, modernist art, it also clearly plays an important role in traditional art, if not all forms of expression and/or communication. In this regard, we have attempted to speculate on the manner in which negative and positive syntax operate dialectically within "normal" communication and the meaning such a dialectic might have cross-culturally.

[1.13.4] These speculations are intended to stimulate further thought and should, of course, be regarded as provisional. Sorting out the role of aesthesis vis a vis semiosis in traditional Western art and discourse, not to speak of the traditional arts of non-Western cultures, is bound to be a technically difficult, intellectually challenging and time consuming task. Perhaps this paper will convince some readers that such a task would be worthwhile.

[2] Postscript

[2.1] I'd like to take the opportunity here to clarify and, to a limited extent, amplify, certain points which may remain unclear to readers of the above. As is appropriate in the present context, I will confine myself, for the most part, to topics of interest to musical scholars.

[2.2] My "first semio-aesthetic principle" is indeed a "first principle," or even in some sense an "axiom." Thus the notion of a syntactic field must be regarded as, for all practical purposes, "given." Any attempt to derive it from anything more fundamental would force me to sound far too much like Hegel or Heidegger for my own or anyone else's good. The most I can say is that, as I indicated in the Preface, it is intimately related to the notion of the gestalt field. All the following principles, in one way or another, follow from this.

[2.3] The definition of "meaning" as solely a function of a syntactic field, with no regard for semantics, may seem odd.{29} Such a definition is necessitated primarily by musical considerations. If semiotics can ever hope to establish itself as a truly general discipline it must come to terms with the problem of music's apparent lack of a clearly determined semantic dimension. Since even totally non-referential music can clearly be meaningful, meaning must have its source in something prior to semantics.{30}

[2.4] The notion of "tonal space" functioning as a "field" deserves further comment. Among the simplest examples would be the pitch classes of any scale, each of which could be understood as uniquely "colored" by its orientation within the "field of difference" produced by the scale itself. More generally, the term "field" relates to both the gestalt principle, in which vision and hearing are conceived as taking place within "perceptual fields," and the "vector fields" of physics, in which the direction and strength of "forces" at any given point can be symbolized by an arrow and a number. The tonal system can be understood as a conflation of the two, a perceptual "force field," with implied "vector arrows" associated with the harmonic "orientation" of each pitch class, the size of the arrow indicating the strength with which, at a given moment, one hears it as attracted to any other pitch class. For example, we could, in the penultimate chord of a perfect cadence, attach to the "leading tone" an especially large vector arrow pointing toward the tonic. If the tonic note, at that point, were not the same as the key note of the movement, it too would have a vector arrow pointing toward this more fundamental tonic. (Such a system of analysis exists, at the present moment, only in principle, and would certainly not be easy to construct. The vector arrows could by no means be determined empirically, but would, as in Schenkerian analysis, reflect the tonal intuition of the individual analyst.)

[2.5] My field approach is not inconsistent with accepted theories, especially that of Schenkerian analysis, which already has certain field characteristics. However, the notion of a tonal vector field has the potential to take us beyond traditional paradigms, toward an examination of questions such as, for example, why it is that composers such as Wagner and Debussy, who so often share the same harmonic vocabulary, have such a different sound. For, if the first chord of the Tristan Prelude sounds utterly different from essentially the same chord at the opening of Debussy's Faun, this difference could well be ascribed to the totally different vector fields within which each chord appears.{31}

[2.6] Milton Babbitt's notion of "time-point class," conceived as a very untraditional tool for the serialization of rhythm, can help us understand the workings of the syntactic field of traditional common practice musical time. Just as each pitch class within a given scale or key has a unique tonal "coloration," determined by its place in the vector space of the tonal field, so any such sound will take on a certain metric "coloration" depending on its time-point class, which determines its place in the metric field (similarly conceivable as a vector space).{32} As time-point class membership depends solely on point of attack, not duration, impulse, not substance, the rhythmic figurations of common practice music, like the notes themselves, can be regarded as virtual.

[2.7] As theorists such as Cooper, Meyer and Cone have suggested,{33} the theory of metric relations can, in some sense, be expanded to encompass entire musical forms. Thus musical structure itself could be considered a function of a large scale "metric" field. Among the many advantages of this paradigm would be the way in which structural landmarks, temporal proportions, etc. could be understood as simply taking their place as part of the determination of a field, rather than as a series of interrelated moments which must be subject to psychological processes of memory and recognition.

[2.8] Ultimately we would want to combine the tonal and temporal fields into what could only be called a "field of musical motion," a "master" field in which the various aspects of the tonal/metric system would be considered in toto.

[2.9] Principle three, "every syntactic field is a construct with an ideologically determined basis" encapsulates a great deal. Such fields are not simply entities embedded in a "text," but complexes produced by interaction between the text and each individual involved with it. The manner in which what I have called "syntactic fields" manifest themselves and the effects they can have will vary enormously in terms of culture, society, history, class, gender, ethnicity, individual psychology, etc. Since such matters have already been treated extensively in the poststructuralist literature, from Lacan, Barthes and Althusser to Kristeva, Derrida, Lyotard, Baudrillard, etc. I felt no need to elaborate.

[2.10] Some have assumed that the references to randomness in my discussion of principle four are aimed specifically at John Cage. Nothing could be farther from the truth. While randomness is, in itself, not capable of fully resisting the pull of the positive field, Cage's work is not simply "random," but would be more accurately described as a highly systematized treatment of randomly derived elements. Cage's great sensitivity to the requirements of the negative field is revealed in a great many decisions which have nothing to do with randomness: 1. emphasis on duration as opposed to attack; 2. foregrounding of silence as an expression of negative time; 3. negation of motivic and melodic formations; 4. refusal to distinguish foreground from background (negation of the musical gestalt); etc.

[2.11] I'm afraid my encapsulations of late nineteenth and early twentieth century art and music "history" may be misconstrued as more dogmatic than I intended. I have no argument whatever with the postmodern view that there can be no such thing as a "definitive" history, a single, unbiased standpoint from which the past may be transparently observed. When I discuss the manner in which Cezanne's project is taken up and developed by the Cubists, or describe how the enharmonic pivot chords of the late nineteenth century "gave way" to the "emancipated" dissonances of the twentieth, I am simply attempting to demonstrate that certain aspects of my theory can be understood historically. I make no claim that this is simply what "really happened," that there are no other meaningful ways of describing such an extraordinarily complex set of musical and historical relationships. Nor, in fact, do I make such a claim for the theory itself, which will stand or fall by virtue of its consistency and explanatory power, not its validity as some sort of "deeper" truth about the way things "really are."

[2.12] My encapsulated "music history" has been taken to task for claiming that 1. modulations are analogous to pictorial passage; 2. in atonality the notes "repel one another"; 3. total serialism is "the most influential compositional movement of the twentieth century." The last, relatively trivial, point has seriously annoyed some readers. I'll take it first, to get it out of the way.

[2.13] Please notice that I refer to a "movement," not a composer or even a style. Of other such movements that could be named, such as impressionism, nationalism, verismo, Gebrauchsmusik, neo-primitivism, the "music hall" esthetic of les Six, the "Tudor revival," dodecaphony, folclorismo, indeterminism, electronic music, musique concrete, minimalism, the first two were indeed highly influential, but essentially of the previous century, while the others (some of which may not really be movements in any case) seem to have been strictly limited in provenance. In my view neoclassicism is too loosely defined to count as a movement (as is the current trend toward neoromanticism), but if it were, it would be the only one I can think of that had nearly so wide an influence during the twentieth century. Total serialism was a truly international movement, with important branches in both Europe (Boulez, etc.) and the USA (Babbitt, etc.). It flowered at a moment when increased interest in musical composition in the academic world was leading to unprecedented bumper crops of composition majors, MA's and Ph.D's, so that a list of the "serious" composers of today, the great majority of whom have been (how could they not have been?) influenced in one way or another by total serialism, would undoubtedly be far longer than at any other time. The movement began in the late Forties and persists, in some circles, to this day, a span of close to fifty years (yes, we are getting older!). Even among composers who rejected it, such as Xenakis, Ligeti, Penderecki, Riley, Young, Reich, Glass, etc., etc., its influence (or counter-influence) has been considerable. And its influence on the way music is taught has been, I should think, even greater. So, yes, I think my statement is defensible.

[2.14] The question of whether modulation is analogous to pictorial passage can be treated adequately only by the kind of careful analysis of historical developments which I presented fully in my book, but had to drastically encapsulate in my paper. This analogy is the product of a dialectic in which procedures such as passage and modulation, designed to promote continuity by covering over structural breaks, ultimately become promoters of the discontinuity they originally were intended to obscure. Once one sees how this can happen in painting, the parallels with music should not be difficult to accept. We are talking, as with so much else in my paper, not so much about painting and music, as about gestalt principles and the ways in which such principles (and their subversion) can be manifested in different media.

[2.15] The notion of atonal notes "repelling" one another can also best be understood dialectically. If we can say that the "force-field" of tonality promotes mutual attractions among the notes, we ought to be able to say that the subversion of this field (atonality) causes them to repel one another. To put it in somewhat milder terms, the notes could be said to "stand out" from one another in an atonal context, as opposed to the "harmonious" blending promoted by the tonal system. In any case, "repulsion" is characteristic only of earlier phases of the dialectic, when the negative field is defined in terms of its opposition to the positive. At a later phase, beginning, I suppose, with Webern's dodecaphony, we can speak of the notes being in a state of "dynamic equilibrium" (to borrow Mondrian's phrase).

[2.16] Principles five through eight are concerned with the negative field. This, the heart of my theory, is admittedly a difficult and certainly controversial topic. Painfully aware that any efforts at clarification may well raise more questions than they settle, I will nevertheless venture the following.

[2.17] As far as common practice music is concerned, there is little if anything in principles one through four that is incompatible with traditionally accepted theories and modes of analysis, from Rameau through Riemann and Schenker to the latest forays into the arcana of musical semiotics. But it would be a serious mistake to assume that a theory of the syntactic field, or any other "unifying" approach, can account for everything of importance. Even in the common practice realm, not to speak of "early," "ethnic," "modernist" and "postmodernist" music, the notion that all elements necessary to a successful work of art can be smoothly integrated within the operations of a single, unifying "field," "concept," "semiosis," "Ursatz," what have you, is not only inadequate, but repressive. In terms that will be familiar to students of Derrida, the contradictions smoothed over within all such doctrines make them ripe for "deconstruction."

[2.18] At this point in my paper, one might indeed expect the deployment of some form of poststructuralist "strategy" along deconstructionist lines. For me, such an attempt, while certainly valid and potentially quite valuable, would not be sufficient. Space does not permit me to treat with any degree of adequacy the manner in which poststructuralism, like the positive field of which, willy nilly, it is a part, functions in an ultimately repressive manner with respect to artistic experience. Associating perception with either "metaphysical presence," or the ephemeral, ungrounded, "trace," this critical practice effectively places all art "under erasure" (to (mis)use Derrida's phrase), treating it as "readable," not perceptible, analyzable only as a form of rhetoric. In my view, the poststructuralists, virtually all absorbed in literary pursuits of one form or other, have simply failed to notice that certain painters, sculptors, composers, filmmakers, choreographers, etc. of our century have already engaged in highly successful "deconstructions" of their own, without benefit of a theory of the "text."{34} The negative field and negative syntax are the product of my attempts to come to terms with the true (no quotes necessary thank you) achievement of these remarkable artists.

[2.19] The question of the nature of the negative field, what it actually is, can take us easily into the sort of metaphysical/antimetaphysical issues that would quickly return us to all too familiar poststructuralist controversies. To say, for example, in the spirit of modernist art critic Clement Greenberg, that this field can ultimately be equated with the physically tangible, flat, surface of the painted canvas, would be to risk the reinstatement of "metaphysical presence." To totally deny it would be to imply that the negative field is not material but, like the positive field, virtual. And how, in such terms, could we deal with music, which is certainly not presented on a tangible flat material surface? Principle six therefore defines the "material" in terms of sensory experience which, in turn, must be understood as grounded in the precise determination of space and time. Ultimately, therefore, in the "purest" of negative structures, it is the special nature of the proportions (of a Mondrian, say, or a late Webern) which establish such works as fundamentally material. (Such proportions must not, however, be confused with the geometrical, harmonic or metrical proportions common in traditional art and music. Negative proportions disrupt such structures to determine an experiential space and/or time which is uniquely sensory.)

[2.20] One might suppose that I regard the negative field as representing a "hidden truth" or the "reality behind" the positive field. This would be a mistake. The negative field does not transcend or in any way deny the validity of the positive field, but simply subverts its hegemony within the realm of the sensory. Since neither field is more fundamental than the other, the two can be regarded as complementary.{35}

[2.21] Principle seven raises the issue of "multireferentiality," which might be confusing. The negative field disrupts signification but often there will be a residue of what could be called "liberated" reference. For example, consider a Cubist collage in which bits of wallpaper or newspaper appear. They can no longer signify in the traditional sense, but they still contain what might be called "empty" reference, which, as part of the negative field, can be interpreted in a variety of different ways. Such interpretation is "multireferential" in that, since there is no longer any unifying structure there to "tell" the viewer what to think about what is being seen, he or she can pick and choose freely among various interpretations. Something similar occurs in, for example, works as different (and not so different!) as Stravinsky's L'Histoire and Schoenberg's Septet-Suite Opus 29 (other works by either composer could also be cited), both of which abound in explicit references to various types of music -- we are free to hear them as such references, or simply as part of an abstract musical structure, or both. Multireferentiality is part and parcel of the process which enables Stravinsky's neoclassic works to simultaneously invoke the past and keep their distance from it.

[2.22] Negative syntax, the structural principle which promotes the negative field, can be understood as possessing two dialectical "moments," which we can call (in terms of the well known and quite apt Cubist terminology) "analytic" and "synthetic." Initially negative syntax, in opposing the positive field, pulling it apart "analytically," is radically disjunctive. Ultimately, as the analytic gives way to the synthetic, disjunction with respect to the positive field gives way to unification of the negative field. (Note that this is an absolutely unique form of "synthesis," not at all comparable to that of traditional dialectic, in which the original oppositions are resolved on a higher level. The unification of the negative field does not resolve the positive-negative opposition but in fact maximizes it.)

[2.23] Musical negative syntax is most clearly exemplified by certain works of Stravinsky, Schoenberg and Webern. Due to lack of space I will have to be very general, glossing over all sorts of exceptions and subtleties. Stravinsky's approach to tonal structure in his pre-serial works (and to an extent the serial ones as well), can be regarded as "dialectical," as it so often involves the opposition of two disjunctive tonal areas.{36} While this "bipolarity" permits traditional formations, such as triads, seventh chords, diatonic scales, etc., any tonal field they might tend to produce is usually nullified or at least severely weakened by juxtaposition with similar formations from the opposing area.{37} While many of his works may favor a particular pitch class or chord, such entities are heard as important structural landmarks, not really tonics or even tone "centers." Stravinsky's famously disjunctive rhythms and accents clearly disrupt the metric field by continually redefining, thus negating, time-point class, thereby encouraging us to listen in terms of experiential time, i.e., durationally. In the absence of an overall controlling tonal or metric field, and despite a veneer, in the neoclassical works, of conventionalized form, his pieces tend to break down into static, self contained sections.

[2.24] Concerning Schoenberg and Webern, I must also be far too general. Schoenberg's journey toward negative syntax was much longer and more gradual than that of Stravinsky. Especially meaningful with respect to the early phase is the following statement from "Composition With Twelve Notes:" "In the works of Strauss, Mahler, and, even more, Debussy... it is already doubtful... whether there is a tonic in power which has control over all these centrifugal tendencies of the harmonies... I do not have to be ashamed of producing something of this sort myself."{38} The tension between this "centrifugal" force and the "centripetal" pull of tonality dominates virtually all of Schoenberg's mature pre-atonal work. The theoretical issue is encapsulated in the following words (based on her reading of the Harmonielehre) from a recent study by Silvina Milstein: "At the centre of Schoenberg's harmonic theory lies the notion that tonally interesting progressions often exploit the fact that chords can be reinterpreted as simultaneously belonging to several tonal areas. The functional ambiguity afforded by the reinterpretation of tonal triads and their interaction with tonally evasive chords and non-tonal formations led Schoenberg to conceive an all-embracing monotonal system based on the twelve tones of the chromatic scale."{39} Milstein applies this insight to aspects of the first three movements of the Second Quartet, where "we can observe that the reinterpretation of function through common tones applies not only to chords but to motifs. At the large-scale level this is manifested in the reappearances in different harmonic contexts of the untransposed opening motif."{40} In terms of the analogy developed in my paper, "the reinterpretation of function through common tones" can be understood as passage from one harmonic area to another,{41} not only locally but "at the large scale level," not only in terms of notes and chords, but motifs as well. The notion of notes, chords and motifs sharing the same function leads directly to Schoenberg's collapsing of the two tonal "dimensions" (melodic and harmonic) and from there to the notion of a harmonic "field." Thus, we can speak not only of "pivot chords," but "pivot motifs" and "pivot fields," which can function "centrifugally," in a manner analogous to Cubist passage, to disrupt tonality. It is, moreover, not too difficult to see in the "reappearances in different harmonic contexts of the untransposed opening motif" a precursor of both the row itself (the same motif in different contexts) and the serial device known as "invariance" (the untransposed motif in different contexts). We can see, in other words, how musical "passage" can take us from modulation and "reinterpretation of function," to the row itself and, moreover, an important device for organizing serial relationships: invariance.

[2.25] With the appearance of the tone row, we arrive at the famous "method of composing with twelve tones related only with one another" - one another, that is, as opposed to being related to a tonic. Despite the currently widespread view that Schoenberg's serial works are "really" in some sense tonal, the definition quoted above must, in my opinion, stand. Certainly Schoenberg very often emphasizes certain notes at crucial structural junctures or favors certain row transpositions which appear to mimic tonal practice. Nevertheless, in terms of the theoretical context presented here, for tonality to be unambiguously present a tonal field must be established. The favoring of certain note complexes or the deployment of certain row transpositions is not enough. To produce a syntactic field all these things and many others as well must relate to and reinforce one another. Moreover, if one looks carefully at the type of note complexes which receive emphasis one will see, time and again, that they are disjunctive (the tritone) or tonally neutral (augmented triad, whole tone complex, diminished seventh chord). Often in fact we find in Schoenberg's supposed "tonality" something more closely resembling Stravinsky's "bipolarity," with the opposing foregrounded elements functioning more like structural landmarks than tonics. There are indeed many types of bipolar disjunction to be found in Schoenberg, including, of course, hexachordal combinatoriality.

[2.26] As far as Webern is concerned, I'd like to begin by quoting a 1955 statement by Pierre Boulez, whose words might still, to many, be as surprising as when first published: "Webern -- via Debussy, one might say -- reacts violently against all inherited rhetoric, in order to rehabilitate the powers of sound... He has even been found cerebral to the exclusion of all sensibility -- so it is well to realize that his sensibility is so radically new that it indeed runs the risk of appearing cerebral at first."{42} Webern, in my view, is not necessarily so "radically new" as Schoenberg. However, in carrying certain of the latter's innovations to their logical conclusion, thus moving from "analysis" to (negative) "synthesis," his work reaches a point where the relation of negative syntax to "the powers of sound" is more readily apparent. To understand this connection we must, first, consider his treatment of pitch and pitch-class. His frequent disjunctive leaps of a major seventh, minor ninth or greater are particularly difficult to hear in terms of interval class, calling attention to the pitches as such, rather than their pitch class identity. To Henri Pousseur the structural weakening of pitch class is already apparent as early as Opus 9, where certain pitches an octave apart function "no longer as possible octave transpositions of the same note but as absolutely different notes."{43} In Webern's serial compositions, the fixing of pitches at certain absolute points for sections at a time becomes quite common. This, combined with his use of invariance, much more common and clearly delineated than in Schoenberg, can give such pitches enormous structural weight in and for themselves rather than merely as pitch class tokens. Since the series is based on pitch class identity, the notion that such identity could be disrupted in and through the strict application of serial principles is indeed a paradox. Since pitch class identity as a source of musical semiosis (see paragraph 0.5 of the Preface) is intimately bound up with the workings of the positive field, the disruption of the "vector arrows" of pitch class is a significant measure of the degree to which Webern has succeeded in establishing a negative field.{44}

[2.27] Next, we must turn our attention to Webern's treatment of musical time. Analytic Cubist paintings and early Mondrians contain many disjunctive linear "accents" which, while in some sense still "figures" against a ground, nevertheless tend to disrupt the figure-ground gestalt. The similarly disjunctive accents of Stravinsky and early Webern have an analogous effect. The later, "classic" Mondrians equilibrate figure-ground without such accents, as do certain later Webern works, notably the Symphony first movement, where each note has a "planar" rather than a figurative quality and release can be as important as attack. A work such as this can serve as an excellent demonstration of the profound difference between a music based on time-point classes, where release is far less important than attack and time is experienced virtually, and a music based on durations, where attack and release are of equal importance and time is experienced materially. Such duration based music anticipates what Karlheinz Stockhausen has called "moment form." For Stockhausen, "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..."{45} In disrupting the continuities, the "flow," of positive time, Webern's negative time similarly places maximal structural weight on local relationships and ultimately, individual notes.

[2.28] From the viewpoint of my theory, the field of positive musical syntax (tonality) can be regarded as a structural background which, in a manner roughly equivalent to that described by Schenker, controls what we hear "from behind the scenes," unobtrusively unifying musical space and time. Negative syntax, in its analytic "moment," disrupts this field and, in so doing, brings structure "up" from the background onto the "surface" of our awareness. Thus it can be said that certain atonal works, especially certain very brief works of Webern, lack any sort of structural background at all, with everything of importance directly present to the listener. I have described such works, along with the equally reductive classic canvasses of Mondrian, as "axiomatic," in the sense that structure has been reduced to bare essentials, to the point of "self evidence."

[2.29] Once one accepts the opposition between positive syntax as a systematic, unifying background and negative syntax as an anti-systematic, disruptive foreground, Webern's serialism can come as something of a shock. For once again we have a unifying system which has retired into the background. Thus Webern's completion of the dialectical movement from the analytic to the (negative) synthetic goes beyond that of Mondrian in a truly remarkable way, establishing, as I characterized it in paragraph 1.11.7 of my essay, a "system-for-the-disruption-of-system," in which Webern's serial procedures systematically unify the negative field as thoroughly as they disrupt the system of the positive. When Webern claims, therefore, as he so often does, that "unification" is the primary goal of his patently disjunctive structures, I can wholeheartedly agree. Only he is, perhaps without fully comprehending it, speaking from the other side of the "looking glass," from the viewpoint of Baumgarten's Ars Analogi Rationis.

[2.30] The final section of my paper is concerned with an especially intriguing but difficult question: what, if any, is the relation between negative syntax and positive syntax in the operation of "traditional" discourse? It is possible that there is none at all, that the disjunctions we find in the normal course of things have nothing to do with the disjunctions of modernism, that the latter's evolution from the former does not necessarily reflect back upon it. This seems unlikely, but in terms of the "abyss" opened in my essay, it can certainly remain an "open" question. If such a relation does exist, and I strongly suspect it does, we can already find many important clues to the nature of its operation in the existing literature on linguistics, semiotics, psychology and, most of all, psychoanalysis and rhetoric, both of which have been explored with some zeal in poststructuralist circles. And, as I have already speculated, the work of Kristeva and Derrida seems especially relevant here. As far as music is concerned, I find much of interest along these lines in Lawrence Kramer's work, particularly Music and Poetry, where, in the chapter "Generative Form"{46} he examines the relation between disruptive and integrative forces in both Beethoven and Wordsworth in truly dialectical terms. Some recent works published in Music Theory Online, notably Richard Cochrane's "The Phases of Fire"{47} and John Covach's "Destructuring Cartesian Dualism in Musical Analysis"{48} also seem relevant.

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1. See Semiotica (vol. 94-3/4), 1993, pp. 233-252.
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2. Among the better known works, out of a great many which could be brought together in this rather vaguely defined category: Richard Wagner's Art Work of the Future; Wassily Kandinsky's "On the Spiritual in Art," and "Point and Line to Plane," in Kandinsky, Complete Writings on Art, (New York: DaCapo Press, 1994), pp. 114-220 and 532-699 respectively; Joseph Schillinger's incomplete and somewhat simplistic, but nonetheless remarkable The Mathematical Basis of the Arts, (New York: Philosophical Library, 1948); and Marshall McLuhan's Understanding Media, (New York: McGraw-Hill, 1964). Almost any work on general semiotics would also be relevant, a good example being Umberto Eco's comprehensive A Theory of Semiotics, (Bloomington: Indiana University Press, 1976). The field of Comparative Literature has, over the last twenty years or so, extended its reach to various other arts, an interest reflected in the 1983 edition of the Yearbook of Comparative and General Literature, no. 32, devoted to "Interdisciplinary Aspects of Comparative Literature." Included in this volume is Steven P. Scher's "Theory in Literature, Analysis in Music: What Next?," a useful survey of some cross-disciplinary research of that time. More recently, Scher has edited Music and Text: Critical Inquiries, (Cambridge: Cambridge University Press, 1992), which includes, among other thought provoking essays, Marshall Brown's "Origins of Modernism: Musical Structures and Narrative Forms," pp. 75-92, a study which, like my own, relates semiotics, dialectics, modernism and music. An especially important work in this genre is Lawrence Kramer's Music and Poetry (Berkeley: University of California Press, 1984). Interdisciplinary studies involving literature and visual art and/or cinema abound, especially among poststructuralists such as Roland Barthes, Deleuze and Guattari, Julia Kristeva, Jean Baudrillard and Jacques Derrida, but studies involving music are, with some trivial exceptions, rare in this milieu.
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3. See Jean-Francois Lyotard, The Postmodern Condition, trans. Bennington and Massumi (Minneapolis: University of Minnesota Press, 1984).
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4. For the music-semiotics of Jean-Jacques Nattiez, the neutral level, a vital one-third of the "semiological tripartition," is the level of the "text," stripped of the intentions of its creator (poietic level) and the culturally determined perceptions/interpretations of the listener (esthesic level). Nattiez, without explanation, refers to the neutral level as a "trace," possibly reflecting the influence of Derrida. See Nattiez, Music and Discourse: Toward a Semiology of Music, trans. Carolyn Abbate (Princeton: Princeton Univ. Press, 1990), pp. 10-16.
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5. See Ferdinand de Saussure, Course in General Linguistics, trans. Wade Baskin (London: Peter Owen Limited, 1959) p. 114.
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6. The "etic"/ "emic" opposition, drawn from the linguistic terms "phonetic" and "phonemic," is an important part of the music-semiotics of Nattiez, though he does not draw the distinction along quite the same lines as I. See Music and Discourse, op. cit., especially p. 61.
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7. Derrida's "trace" turns up in many places in his extensive writings. Among the earliest and most important is Of Grammatology, trans. Gayatri Spivak (Baltimore: Johns Hopkins University Press, 1974). To give something of the flavor of Derrida's problematization of this term, I quote the following: "The trace is nothing, it is not an entity, it exceeds the question What is? and contingently makes it possible" (p. 75).
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8. Leonard Meyer's Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956) is the classic treatment of the gestalt foundations of musical perception.
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9. An extensive, carefully argued treatment and defense of crucial aspects of the theory can be found in Victor Grauer, Montage, Realism and the Act of Vision (Unpublished monograph, 1982).
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10. The so-called "abstract" nature of music should not confuse the reader into thinking that because musical notes or passages cannot be translated into words they cannot have meaning. We need not look for lexical meanings in music any more than we would look for musical meanings in language. To say, for example, that a certain passage functions as a "cadential figure" is already a perfectly sufficient statement about its signification within musical discourse.
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11. For a thorough treatment of the role of the gestalt in music, see Leonard Meyer, Emotion and Meaning in Music, Op. Cit.
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12. The Oxford English Dictionary second edition, volume one (Oxford: Clarendon Press, 1989), p. 206.
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13. Baumgarten, Alexander, Meditationis philosophicae de nonnullis ad poema pertinintibus, trans. by K. Aschenbrenner and W. B. Holther (Berkeley: University of California Press, 1954) p. 78.
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14. Such is the impression given by the discussion of art in Umberto Eco's A Theory of Semiotics (= Advances in Semiotics) (Bloomington: Indiana University Press, 1979) pp. 261-276. Eco treats the "aesthetic text" as a means of "overcoding" and/or "code-changing," categories that appear as part of the more extensive discussion of rhetoric which follows [see pp. 276-298]. Julia Kristeva, in an attempt to carve an independent place for the "poetic language" of modernism in a spirit very close to our own, nevertheless concludes that it must posit "its own process as an undecidable process between sense and nonsense, between language and rhythm . . ., between the symbolic and" that which is prior to symbolization. Essentially, her notion of poetic language involves a process of continual mutation within signification, a function hardly distinguishable from that of rhetoric. [See "From One Identity to Another" in Julia Kristeva, Desire in Language (New York: Columbia University Press, 1980) pp. 124-147.] Further arguments for rhetoric as the basis of aesthetic experience can be found in Paul De Man, "Semiology and Rhetoric" in Textual Strategies, ed. Josua Harari (Ithaca: Cornell University Press, 1979) pp. 121-140..
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15. For documentation of the links between the artists and poets of the Futurist/Constructivist school and the linguists of the Russian Formalist group, as well as the latter's influence on the development of structuralism and semiotics, see Steiner (1984).
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16. Additional, equally relevant developments should also be mentioned: Stravinsky's tonal bipolarities and rhythmic fragmentations disrupt the tonal/metric gestalt as effectively as atonality; Schoenberg's ironic, self-referential treatments of traditional musical materials in, for example, Pierrot Lunaire or the Serenade , mirror the "semiotic" playfulness of Cubism; likewise Stravinsky's Le Histoire du Soldat and, of course, all his subsequent neoclassical work.
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17. Interest in sound for its own sake drew Boulez to the concept of the "sound object" [see Andre Hodier, Since Debussy (New York: Grove Press, 1961) pp. 136-142]. For a discussion of moment form and its role in the proportional determination of time in the work of Stravinsky, Messiaen and Stockhausen, see Jonathan Kramer, "Moment Form in Twentieth Century Music," in Musical Quarterly 64(2), 1978, pp. 177-187.
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18. Emmanual Kant Critique of Pure Reason, trans. Max Muller (New York: Doubleday, 1966) pp. 22,23.
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19. See Jonathan Kramer op. cit., pp. 181-183, for a convincing analysis of temporal "flattening" in certain modernist compositions.
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20. Note how effectively a piano arrangement of any traditional Western art music conveys its essential "logic" or "meaning" despite the instrument's very limited ability to sustain. The greater part of Twentieth Century music, which places more emphasis on "negative time," where the release is as important as the attack, would not be well served by piano arrangements, and in fact they are rare.
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21. See Baumgarten, op. cit., especially propositions 3, 9, 14, 15, 17, 19, 22, 112, 113. My summary of Baumgarten owes a good deal to Leonard P. Wessel's "Alexander Baumgarten's Contribution to the Development of Aesthetics," in Journal of Aesthetics and Art Criticism 30(3), 1972, pp. 333-342.
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22. Piet Mondrian "Plastic Art and Pure Plastic Art" In Mondrian Plastic Art and Pure Plastic Art (New York: Wittenborn, 1945) p. 58.
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23. For an extended discussion of the meaning of postmodernism with respect to some of the issues raised in this paper see my essay "Modernism/Postmodernism/Neomodernism" in Downtown Review 3 (1 & 2), 1982, 3-7.
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24. Piet Mondrian, "Pure Plastic Art," in Plastic Art and Pure Plastic Art, op. cit., p. 31.
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25. A remarkably similar point of view is revealed in Julia Kristeva's notion of the chora. See, for example, Kristeva op. cit., pp. 133-137.
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26. The paradoxes of a purely semiotic (i.e. logic-based) attack on the ideology of the signifying process are discussed in Jacques Derrida, "Structure, Sign and Play in the Discourse of the Human Sciences," in Derrida, Writing and Difference, trans. A. Bass (Chicago: Chicago University Press, 1978) pp. 278-293. Derrida argues that ideology can only be "deconstructed" by an informal, anti-systematic process of disruption-from-within which he calls bricolage.
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27. Umberto Eco, A Theory of Semiotics, op. cit., pp. 261-275.
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28. See Derrida op. cit., pp. 278-281, for the classic statement on this founding paradox of deconstructionism.
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29. My principle one is certainly no more cryptic than Nattiez' quite similar "meaning exists when an object is situated in relation to a horizon." See Music and Discourse, op. cit., p. 9. Also similar, in spirit, is John Covach's "Musical understanding arises when we are able to situate a particular piece within a musical world, and musical meaning arises as we appreciate the particular way in which the work is situated." See Covach, "Destructuring Cartesian Dualism in Musical Analysis," in Music Theory Online 0.11 (1994): 19.
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30. The fact that music can and very often does carry explicit reference testifies to what I would call the semantic "valence" of musical syntagms, the readiness with which they can attach themselves to semantic entities. Since musical signifiers can thus be said to imply the existence of possible signifieds, even when none can be explicitly invoked, music appears to have at least a potential sign function. Some of the more penetrating treatments of the issue of musical meaning in the literature are Meyer, Emotion and Meaning in Music, op. cit., especially pp. 33-40; Victor Zuckerkandel, Sound and Symbol, (New York: Pantheon, 1956), pp. 67-71; Nattiez, Music and Discourse, op. cit.; Eero Tarasti, A Theory of Musical Semiotics, (Bloomington: Indiana University Press, 1994); Rosario Mirigliano, "The Sign and Music: A Reflection on the Theoretical Bases of Musical Semiotics" and Raymond Monelle, "Music and Semantics," both in Musical Signification: Essays in the Semiotic Theory and Analysis of Music, edited by Eero Tarasti (Berlin/NY: Mouton de Gruyter, 1995). Many others could be added to this list, yet the issue is far from being fully resolved.
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31. The similarity of Debussy's harmonic vocabulary with that of Wagner, particulary the Wagner of Parsifal, is exhaustively demonstrated in Robin Holloway, Debussy and Wagner (London: Eulenburgh Books, 1979). What Holloway fails to notice is the totally different sound identical chords can have in the work of each composer.
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32. The principles of time-point class theory are set forth in Milton Babbitt, "Twelve-Tone Rhythmic Structure and the Electronic Medium," in Perspectives on Contemporary Music Theory (New York: Norton, 1972), pp. 148-179. My references to time-point class reflect a very different usage from that of Babbitt and, though based on his theory, should not in any way be taken as representative of his thought.
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33. See Grosvenor Cooper and Leonard Meyer, The Rhythmic Structure of Music (Chicago: University of Chicago Press, 1969) pp. 144-167 and Edward T. Cone, Musical Form and Musical Performance (Norton, NY, 1968) pp. 25-26.
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34. The only well known poststructuralist figure who, to my knowledge, has produced a major study of modernist aesthetics is Julia Kristeva, whose viewpoint, as expressed in Revolution in Poetic Language, trans. Leon Roudiez (New York: Columbia University Press, 1984) and other works, has, I feel, much in common with my own.
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35. In a fascinating study, Complementarity: Anti-epistemology after Bohr and Derrida (Durham: Duke University Press, 1994), comparing the ideas of Derrida and noted physicist Niels Bohr, Arkady Plotnitsky identifies Bohr's notion of complementarity as a key to understanding both. I feel that this term, possibly the only one which can effectively relate the profoundly disjunct terms of a "negative dialectic," is applicable to my theory as well.
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36. The prototype for Stravinsky's "dialectical" approach to harmonic structure can be found, of course, in the second movement of Petroushka, equilibrated harmonically by the polarization of two tonal fields, dominated respectively by C and F#. It should go without saying that I completely disagree with the non-dialectical view of Arthur Berger and Pieter van den Toorn, which rejects "bitonality" and finds in the octatonic scale some sort of occult unifying force for this, as well as most of Stravinsky's other work [See Arthur Berger, "Problems of Pitch Organization in Stravinsky," in Perspectives on Schoenberg and Stravinsky, ed. Boretz and Cone (Princeton: Princeon University Press, 1968) and Pieter van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press, 1983)]. In this matter I side wholeheartedly with Richard Taruskin, who, in the very process of demonstrating Stravinsky's indebtedness to Rimsky's octatonicism, nevertheless insists, in response to Berger and van den Toorn: "We are meant [in Petroushka] to hear C and F# in terms of an active, not static, polarity -- as competing centers, not merely as docile components of a single, static octatonically referable 'hyper-harmony' . . . " [Richard Taruskin, "Chez Petroushka: Harmony and Tonality chez Stravinsky," in Music at the Turn of Century, ed. Joseph Kerman (Berkeley: University of California Press, 1990)]. In a paper more broadly aimed at certain underlying principles in Stravinsky's work as a whole, "Cross-Collectional Techniques of Structure in Stravinsky's Centric Music" [in Stravinsky Retrospectives, ed. Haimo and Johnson (Lincoln: University of Nebraska Press, 1987)], Paul Johnson affirms the importance of the octatonic collection yet at the same time emphasizes the role of disjunctive intervals in the establishment of tonal polarizations in Stravinsky's work as a whole.
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37. We must be careful not to confuse Stravinsky's bipolarity with the dialectic of traditional music, where conflicting tonal areas (e.g., tonic and dominant) are ultimately resolved in a unifying "synthesis." The musical dialectic of the composers we are considering here never really resolves, thus is closer, perhaps, to the "negative dialectics" of T. W. Adorno (who was, not surprisingly, inspired by Schoenberg). [See Adorno, Negative Dialectics (1966), trans. E. B. Ashton (New York: Continuum, 1994).]
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38. "Composition With Twelve Tones," in Style and Idea, rev. ed., ed. Leonard Stein (London, 1975), p. 245.
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39. Silvina Milstein, Arnold Schoenberg: Notes, Sets, Forms (Cambridge: Cambridge University Press, 1992) pp. 44, 45.
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40. Ibid., p. 45.
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41. See Ibid., pp. 45-47, where Milstein's illustrations of "the stabilization of a dissonant event in terms of overall structure" can be equally understood in terms of musical passage. Her entire analysis of portions of the Second Quartet in this section is highly relevant.
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42. "The Threshold," in Die Reihe, Anton Webern issue (Bryn Mawr: Theodore Presser, 1955) p. 40.
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43. "Webern's Organic Chromaticism," in Die Reihe, op. cit., p. 54. Especially relevant from my point of view is Pousseur's "The Question of Order in New Music," in Perspectives of New Music, Vol. 5, No. 1, Fall-Winter 1966. I want to take this opportunity to acknowledge Pousseur's influence, as theoretician and teacher, on my own thinking regarding the structure and aesthetics of modernist music.
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44. Stravinsky's tendency to emphasize certain musical events which return always at the same pitch level and with the same instrumentation has a similarly disruptive effect with respect to pitch-class. Examples abound, the most notorious being the remarkable opening chord of the Symphony of Psalms.
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45. "Momentform" (1960) in Seppo Heikinheimo, The Electronic Music of Karlheinz Stockhausen (Helsinki, 1972) pp. 120, 121. Jonathan Kramer's excellent essay on moment form also contains much that is relevant to my theory. See his "Moment Form in Twentieth Century Music," in Musical Quarterly, vol. 64, no. 2 (April, 1978), p. 177.
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46. in Lawrence Kramer, Music and Poetry, op. cit., pp. 57-90.
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47. Music Theory Online 1.1 (1995): 1-11.
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48. John Covach, op. cit.
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