The Tonal-Metric System and "Perspective Time"
We may begin by stating outright that the system of "classical" tonality with which we are all familiar, strongly centered on a particular "key," dependent on an intricate hierarchy of harmonic and metric relations within which all elements take their place and fuse, is an excellent example of positive svntax, having much in common with spatial perspective and the cinematic denial of difference. Just as film involves the coordination of two "fields," screenspace and time, music is based in two closely analogous "fields," pitch and rhythm. It should not be difficult to understand how "pitch-space," as traditionally controlled by a complex system of tonalities (keys), can be related to the effects of pictorial (and photographic) perspective. Indeed, musicians routinely apply spatial analogies to pitch, referring to notes that are "high" or "low," keys that are "near" or "distant," motives that occupy the "foreground" or "background."
More explicitly, in the words of Robert Ericson,
A key gives unity to all the musical events which happen in it in
much the same way that linear perspective organizes all the picture space in
relation to a single point. In a key, the tonic, the home base, is analogous to
the vanishing point. It provides the focal point to which every musical event
is bound, the unifying point through which all the musical events are related
to one another.1
The same process manifests itself on a multitude of architectonic levels. Each chord, phrase, motive, melody, section (roughly analogous to the paradigmatic levels of semiology) must take its place within the tonal hierarchy which, in turn, confers on it a specific (tonal) meaning; which, indeed, forces us to hear it in terms of such meaning, redeeming the sounds from their original status as "mere" noise.
The temporal structure of tonal music has a hierarchy all its own, designed to reinforce and, ultimately, coordinate with that of pitch. All individual rhythms are completely subordinated to a single periodic meter (or "measure"), based on an implied but often unexpressed, continuum of steady, equal beats. This meter, a module of potential time proportions or accent patterns, is in turn subordinate to larger periodic structures controlling the phrase, "sentence," etc. There is, in short, a hierarchy of controlling time proportions functioning as a temporal background or "container," analogous to the "container space" of perspective. As with perspective, the apparently neutral "background" is really the all determining syntax in disguise. Thus the metric system can be said to confer a syntagmatic dimension upon the "meanings" generated by tonality, uniting them within a single coherent temporal scheme.
The effects of musical "perspective-time" operate according to much the same ideology as that revealed in film by Jean Louis Baudry. Rapid melodic passages set strings of static individual notes into motion by virtue of essentially the same "denial of difference" that fuses static film-frames.2 The denial of difference is at work at slower tempos and higher levels of articulation as well, by virtue of a process of "musical implication" which parallels the principles of montage linkage.
As with the spatial organisation of traditional pictorial syntax, our perception of the temporal structure of tonal music is probably best understood in terms of gestalt psychology. The application of gestalt principles to the analysis of music is central to Leonard Meyer's Emotion and Meaning in Music, which has become a classic of its kind. Meyer cites the gestalt "law of good continuation," usually applied to spatial perception, as basic to our ability "to hear separate, discrete stimuli as continuous motions and shapes." Our perception of that "series of lifeless stimuli" which is "a line or motion initiates a mental process, and it is this mental process which ... tends to be perpetuated and continued."3
Meyer goes on to discuss musical "shape" and "texture," defining the latter in terms of the same figure-ground relationships we have cited in reference to pictorial and cinematic positive syntax.4 Ultimately, of course, every musical event, like every pictorial form, must be perceived as a configuration or "figure" against a "ground" in order to be understood within the overall scheme.
Perhaps no aspect of the metric system better illustrates the ideological effects of perspective time than that all important source of musical figuration, rhythm. In the context of classical tonality, all rhythmic figures manifest themselves as groupings of "attacks," points where a given note is first heard. The "release," the point at which the note stops sounding, is far less prominent and of little or no account in terms of musical meaning. This is what makes it possible for the piano, whose sounds begin to die away as soon as they are produced, to be as important as it is to the standard, classic repertoire. Few such works will fail to make perfect sense in piano transcription.
Attacks, as "points" in time, are easily perceived as abstract entities grounded within an equally abstract time field analogous to the container-space of perspective. They are really only the carriers of impulses, not true durations in the Bergsonian sense. With each note thus robbed of its temporal "weight," time is experienced rationalistically, i.e., in terms of an ideologically determined, purely conceptual, code.
Emancipation of the Dissonance
The tonal-metric system was undermined by a series of developments that parallel, both historically and functionally, the decline of pictorial positive syntax. Space permits only a rather sketchy review of a complex and gradual evolution.
A vital factor in the destruction of tonal pitch-space was the exact musical equivalent of passage, the process of shifting from one key to another that musicians call "modulation." It was mostly in the modulating "transition" sections of musical forms that the highly colored, tonally ambiguous, dissonant chords which gave Romantic music so much of its expressiveness could safely be accommodated. Because of their ambiguity, these chords could function easily as "pivots" from one key to another. Because they were so highly colored and expressive, however, they tended to assert themselves to the point that they could no longer be safely controlled as purely subordinate elements. Increasing emphasis on such chords coincided naturally with an increasing harmonic restlessness, which required more and more frequent changes of key and more emphasis on "exciting" adventures to more remote tonal areas.
Around the turn of the century, in the work of composers like Hugo Wolf, Debussy, Richard Strauss, Mahler and the young Schönberg, we find relatively long sections in what has come to be called "suspended" or "extended tonality." Here, temporary loss of any sense of tonal stability is produced by continual shifting from one key to another. Such sections can be considered a kind of pure passage, where modulation itself has moved into the foreground. Works featuring extended tonality may be compared to those paintings and films which reject positive syntax without the creation of negative syntax; such music is saturated with ambiguities.
It was in passages of extended tonality that the dissonant chords which had always held such fascination for the Romantics finally came into their own. So ambiguous was the context that the most extreme dissonances could be accomodated. The later music of Scriabin, for example, characterized by extreme tonal ambiguity, is a veritable hothouse of strange chords, the unusual properties of which are meant to symbolize all sorts of exotic, "spiritual" states of being.5
As it became increasingly apparent that the tonal system was exhausting itself, that there were limits beyond which it could only drift aimlessly (which is exactly what Scriabin did), the inevitable reaction followed. In an evolution paralleling the development of Cubism, certain composers eventually scrapped their ambitions to express "the ineffable" and concentrated their attention on the fascinating new chords that had been brought to light as "ineffabalic symbols." These chords were complex sounds, highly interesting simply as sounds, if they could be liberated from an apparently ever present implicational context. This "emancipation of the dissonance"6 could fully be achieved only if tonality were not simply suspended but actively destroyed and neutralized.
The dissolution of tonality was paralleled by disruption of the rationalized metric time-field. Tempo changes within a single movement became increasingly common in the mid to late Nineteenth Century, as did the use of rubato, a subtle flexibility of beat, in performance practice. Off-beat accents (syncopations) and longer "cross-rhythmic" passages began to appear more and more often as composers felt the need to break up the rhythmic flow and stress particulars. In composers like Debussy and Scriabin, there are extended sections in which all sense of meter and sometimes even tempo is dissolved in rhythmically ambiguous passages which simply seem to "mark time" statically. Such passages often coincide with their tonal counterpart, periods of extended tonality.
Bitonality-Atonality
The reaction against the tonal-metric system crystallized in the work of two major early Twentieth Century figures: Igor Stravinsky and Arnold Schönberg. Each had what seemed at the time to be a radically different approach from the other. Stravinsky attempted to neutralize the tonal hierarchy by combining harmonic and melodic elements from mutually incompatible tonal centers. In such a context, tonal polarization toward a particular key is instantly balanced by the pull of another key. The resulting bi-tonality creates tensions resembling those between figure and ground in Cubism.
Stravinsky's most important contribution was in the area of rhythm. He broke up the closed configurations of the temporal gestalt by means of an original, completely intuitive, treatment of accent. Derived from syncopation, but much more continuously disruptive, his accents like the linear "accents" of analytic Cubism, always seem to come just at the right "wrong" place to abort configurative closure.
Schönberg's major early contribution was the creation of what is usually called "atonality," which, as the name suggests, can be translated simply as "negative tonality." Unlike Stravinsky, who retained many traditional chord formations and scales, Schönberg radically reworked the entire harmonic fabric. Atonality is the complete neutralization of tonal center, a context in which all pitches tend strongly to repel, rather than attract, one another. Tonal implication is disrupted in favor of a system of multiple polarities.
In both Stravinsky and Schönberg, the dissonant chords which were originally the problematic exceptions are now the rule. We must recall that such chords, like Cubist passage, had their origin in ambiguous transitions which carried the seeds of destruction. As soon as these chords began to call too much attention to themselves, their sheer sound as sound began to undermine the system. Modern music became the art of sound, not implication and meaning. In this context, dissonant chords need no longer "function," that is, lead anywhere -- they can tend simply to be heard as stable, complex sounds.
The Twelve-Tone Method
Between the years 1908 and 1920, Schönberg become increasingly dissatisfied with atonality. Basically a set of only partly understood ad hoc devices, lacking a fundamental principle, it was a poor substitute for the profound logic and flexibility of the rejected tonal-metric system. During the period 1914-1923, in response to this problem, he very painstakingly created what he called the method of composing with twelve tones related only to one another." Fundamental to this method is the "tone-row" or "series," a set in which each of the twelve pitches (more accurately, "pitch classes") traditionally available assumes a particular position in relation to all the others. Each piece is based on its own particular series, each series having unique properties and structural possibilities. The tone row has four basic forms: "original" form; inversion, in which all the intervals forming the original row are turned "upside down"; retrograde, the original pitches in reverse order; retrograde inversion, reverse order of the inversion. All of these forms can, moreover, like any musical idea, be transposed, so that twelve versions of each are available (in other words any form of any series may begin on any of the twelve pitches).
The series controls the structure of the piece in a manner which requires a good deal of preliminary systemization, yet permits the composer to create with at least as much freedom, control and expansiveness as in the tonal system. Unlike the tonal system, however, the series establishes no center -- each pitch bears an equal, mutually reciprocal relation to the others. These characteristics are particularly significant with reference to negative syntax, a matter to which we shall return shortly.
Webern
Despite his importance, which is undeniable, Schönberg's involvement with musical "negative syntax" was problematic. He, like Cézanne, was torn between revolutionary discoveries and deeply conservative instincts. As a result, his use of atonality and serialism reveals conflicts and inconsistencies. In his work, true negative musical syntax at the harmonic level is too often combined with characteristically tonal melody types and rhythms. Much of Schönberg's music. like Cézanne's painting, has a tortured quality due to the fact that neutralized tonal elements have been forced to fuse with one another as though they still carried tonal implications.
The conflicts that afflicted Schönberg were not shared by his pupil, Anton Webern, who became the first composer to fully embrace the most radical aspects of atonality (and, later, serialism). In Webern, even as early as 1909, all elements of the music share in the negative syntax. References to traditional musical gesture are practically eliminated. Melodies and themes in the usual sense are no longer present. Scale passages are all but eliminated. Melodic motion is disjunct in the extreme, with large intervals separating most of the notes. Harmonies are maximally dissonant and totally devoid of implication.
While Webern's treatment of pitch-space nevertheless owes much to Schönberg, his approach to time does not. In 1909, when Schönberg was writing rhythmic passages resembling those of Brahms or Wagner, Webern was anticipating the disjunctive accents of Stravinsky. Rejecting such restlessly shifting accents in his later, serial, works, he delves much farther into the mysteries of musical time, composing in terms of real durations, for which the release is as important as the attack. While a work such as his Symphony, Opus 21, has been described as "pointillist" because of its fragmentation into isolated notes, these notes are never merely points -- each is a separate presence, with a precise temporal "weight." Only in terms of a durational determination of this kind is a truly proportional division of the field of the "surface," in the spirit of Mondrian, possible. Only in such terms, moreover, could Webern hope to embody silence as a true "negative" of sound, with a weight of its own, as opposed to its usual function as a passive container or background into which sounds are placed.
The parallel with pictorial space has been explicitly drawn by theoretician Heinz-Klauss Metzger. Stating that Webern "was brought up on music composed of sounding events in silence, comparable to traditional painting, which placed figures against an empty background," he makes the point that, in such painting, "along with every elevated positive form there arose a negative one for the surrounding background." Noting that it is only in recent times that the emancipation of such negative forms has taken place, Metzger compares this emancipation with Webern's foregrounding of silence, concluding that "Webern's revolution may be compared only with that by which Mondrian created a new kind of painting."7
Perhaps the most thorough and thoughtful inquiry into Webern's approach to time has been made by composer-theorist, Henri Pousseur. Pousseur refers to the extreme symmetry and periodicity of the tonal-metric system as producing "an abstract spatial-temporal framework, a grid whose existence seemed to antedate the objects appearing in its interior and thus to create the illusion of an absolutely existing objective order." Such a system is an attempt to "appropriate things and their immediate appearance in a definitive manner...[denying] the reality of their (and our) ephemeral structure."
[Webern] refused to oppose the flow of time with attempts at
consolidation... [Recognizing that] one can communicate with things only in the
distance of their transivity, in their innate alternation between presence and
absence...[he created a music of] pure instantaneousness, of undiluted
acceptance ...of the appearance and disappearance of objects.
We cannot help but be reminded of Cézanne's revolt against perspective, his insistence on an a posteriori space created by the idiosyncratic appearance of objects themselves. But the parallel with space should not confuse us. Webern's temporal "surface" is analogous with the pictorial surface of Cézanne or Mondrian, but it remains fully temporal, nevertheless. Only the abstract timepoints of the tonal-metric system, lacking true duration to begin with, may be accurately said to partake of the "timelessless" of painting. The weighted durations of Webern are, by virtue of their "weight," truly temporal, thus truly ephemeral.
Webern and the Series
It is no coincidence that the emergence of a new, more purely durational, approach to time accompanied Webern's adoption, in 1924, of the twelve-tone method. Schönberg's reorganisation of the pitch dimension of music, became, for Webern, the key to a profound rethinking of musical structure in general.
Let us recall that the twelve-tone method is grounded in the necessity that each tone be related only to every other tone (rather than a single tonal "center"). In order for each tone to retain its multi-polarity, all must be continually repelling one another. This mutual repulsion of the tones is the basis for the fundamental negativity of Schönbergian syntax. An orthodox tone row is already a highly organised structure, specifically designed to prevent any tone from coming under the sway of any other (beyond the purview of the most limited local encounters).9
In Schönberg's hands, his own method tends to waver between the negative destruction of tonality and the creation of a kind of substitute positivity in which the series, at times, seems to be striving to replace, rather than neutralize, the totalizing function of the tonal system. While his approach usually leads to mutual repulsion of the tones, this generally involves the neutralization of their tonal function only. The tones still come together to form melodies, "pregnant" motives and, in some cases, quasi-functional harmonies.
Rather than similarly seeking to accomodate serial repulsions within a framework of traditional musical gesture, Webern intensified the repulsions to the point that melody and functional harmony all but disappear. Motives are no longer "pregnant" with implication, but simply groupings of tones which can function as landmarks. As with Mondrian, everything is structured to maintain the kind of equilibrium which promotes clarity, freshness and, above all, openness to the overall field (for Mondrian space, for Webern time).
The importance of this development to our investigation of negative syntax cannot be overestimated. Cubism and the procedures of atonality involve ad hoc methods, largely intuitive reactions against positive syntax; Mondrian's neoplasticism reveals a much more solid theoretical grasp of fundamentals but, despite the systematic nature of its preliminary reductio, remains a fundamentally non-systematic, intuitive procedure. Webernian serialism, on the other hand, is unique in being a highly systematic structural principle designed specifically to maintain the independence of its elements and neutralize any possible implicational context that might arise on any but the most local, temporary level. It is in fact the first and really the only example we have of a basic generative principle for the free but controlled composition of negative syntax.
Symmetry-Asymmetry in Webern
Up to this point we have been defining negative syntax essentially as a reaction against any kind of systematic ordering, symmetry or regularity, aspects of structure which we have associated with positive syntax exclusively. Indeed, Webern's pre-serial work resembles that of Mondrian in fostering the kind of extreme reductionism which makes negative syntax a matter where intuition can function precisely and completely to defeat symmetry without the need for highly systematic pre-planning. Webern's strategy in these early works, exactly equivalent to that of Mondrian, has been admirably expressed by Pousseur: "the positioning of well-defined and clearly perceptible units, articulating themselves by means of reciprocal effect, each one limiting and defining the nature of its fellows."10 Theoretically this truly dialectical approach to structure ought to be self-sufficient, with each element defined by its partners, rather than some center, tonal or otherwise.
In practical terms, however, stringent limitations are involved, most obviously reflected in the extreme brevity of Webern's early atonal works (one complete movement from the pieces for cello and piano, Opus 11, is only 10 bars long). The longer the work, the greater the difficulty of balancing the elements, the greater the likelihood of lapsing into something that could suggest the traditional symmetries.
Schönberg's row showed Webern the way out of this dilemma. The "method of composing with twelve tones related only to one another" was, in fact, a system for generalizing into a basic principle that "reciprocal effect" which had only been an ad hoc strategy in the earlier works. The fundamental disruptions of negative syntax are "built-in" to the serial method itself, especially in the hands of Webern. The marvelously practical aspect of the Webernian series is its role as a central reference which de-centers, unifying only by spreading its disunifications systematically throughout the entire work. Thus only in his serial music is Webern able to develop the highly symmetrical germinal "cells" and hierarchic superstructures which permit the generation of complex and extended balanced asymmetries of the sort that defeat hierarchical domination without inhibiting variation and elaboration. In the words of Pousseur, "symmetry in the late work of Webern [is] not the remains of an obsolete classical system, but an attempt to regulate the proportion of regularity which must exist within any irregularity."11 In thus expanding the structural powers of negative syntax, Webern goes beyond Mondrian, not in perfection, but scope.
Symmetry-Asymmetry--An Example
The manner in which Webern produces highly organised asymmetries from symmetrical building blocks involves musical complexities going far beyond the purview of this book. A relatively simple example can, nevertheless, convey something of the general principle involved. Webern's String Quartet,Opus 28, is based on a twelve-tone row, one form of which consists of the following pitches: Bb , A, C, B -- Eb , E, C# , D -- Gb , F, Ab , G. The pitches have been grouped into three sets of four notes each to clarify the fact that each four note set is a simple permutation of the others. The second is the inversion (also the retrograde) of the first. The third is a simple transposition of the first down a major third. The economy of this arrangement will be appreciated when we recall that a twelve tone row uses the complete set of twelve available pitches with none repeated.
The series as a whole is mirror symmetrical: the first six notes, in reverse order, produce the inversion of the last six notes. Each four note set is similarly mirror symmetrical. As a result of its peculiar structure, the inversion and retrograde of the series are identical-the same is true of each four note set.
Now let us transpose the entire series up by a major third. This produces the following permutation of the original twelve notes: D, C# , E, Eb -- G, Ab , F, Gb -- Bb , A, C, B. Note that the original four note sets remain intact. The second set is now the first, the third is the second and the first has become the third. Moreover, a fundamental transformation has taken place in their relationship: the pitches of sets two and three of the original row are now in reverse order, while set one (Bb , A, C, B) is exactly the same in both rows.12 This set is said to remain order-invariant with regard to this particular transposition of the row. As a result of this invariance, there is a marked and uniquely structural asymmetry between these two versions of the row, an asymmetry made possible by the high degree of symmetry within the row taken by itself. The principle of invariance is thus an important tool for the production of organised asymmetry from the highly symmetrical regularities of row structure and serial procedure.
The above example only touches on the complexities and subtleties called forth by Webern's (and Schönberg's) procedures. Indeed the difficulties surrounding Webern's techniques have created the false impression that the music itself is highly cerebral, requiring the listener to carefully follow and recognize each transformation of the row. This is true only to the extent that one insists on listening "positively," in terms of hierarchically ordered and unified gestalts. Listening thus, for what is not in fact there, can only reinforce the notion that some kind of mystique is at work.
The principle of invariance, for example, involves complex systemization, but ultimately works to bring certain elements (such as the Bb , A, C, B set) into sharp relief. This is only one example of the ways in which organisation in Webern functions to make each particular moment maximally "present," maximally clear and expressive in itself by putting us in closer touch with the audible, temporal, "surface." Unlike positive structures, in which all concrete materials are sublimated in favor of the realization of an abstract structural idea, negative structures sublimate themselves in favor of the vivid presentation of their concrete materials.
Cage and Webern
Among the first to respond to the most radical aspect of Webern's revolution was the American composer John Cage. Himself a student of Schönberg, Cage had quickly moved from the Schönbergian "emancipation of the dissonance" to what for him was the next logical step, the liberation of all "non-musical" sounds. In searching for a "structure ...as hospitable to nonmusical sounds, noises, as it was to those of the conventional scales and instruments,"13 Cage found Webern's approach to time of great use.
Stating that, traditionally, musical structure has been defined harmonically, in terms of pitch relationships, Cage has credited Webern (along with Eric Satie) with introducing a completely new idea: the definition of structural parts "by means of time lengths."
If you consider that sound is characterized by its pitch, its
loudness, its timbre, and its duration, and that silence, which is the opposite
and, therefore, the necessary partner of sound, is characterized only by its
duration, you will be drawn to the conclusion that of the four characteristics
of the material of music, duration, that is, time length, is the most
fundamental. Silence cannot be heard in terms of pitch or harmony: it is heard
in terms of time length.14
Indeterminacy
Webern's treatment of duration was only one part of his influence on Cage. More generally, the younger composer was to respond strongly to Webern's radical discontinuity. Speaking retrospectively of the attitude of himself and a small group of associates during the Forties, Cage has written as follows: "Where people had felt the necessity to stick sounds together to make a continuity, we four felt the opposite necessity to get rid of the glue so that sounds would be themselves."15
Cage, unlike Webern, had rejected the twelve-tone method precisely because it must have seemed like only another, newer form of musical "glue." Failing to see (as only Webern had seen) the disjunctive potential of the row, Cage sought elsewhere for a fundamental principle of disjunction. In the late Forties, he found it, and of course, much more, in his now notorious use of chanceoperations. The new, truly radical, method involved sounds, durational relationships, "actions," etc., established indeterminately, usually by a patently random procedure such as the tossing of dice. Works "composed" in this manner are "free of individual taste and memory (psychology) and also of the literature and `traditions' of the art. The sounds enter the time-space centered within themselves, unimpeded by service to any abstraction, their 360 degrees of circumference free for an infinite play of interpenetration."16 Such works affirm "the absence of the mind as a ruling agent."17
Although the parallel is far from obvious, Cage's project has much in common with that of Mondrian. Both artists engaged in a radically reductive process of what Richard Kostelanetz has called "ordered disorder,"18 culminating in the establishment of an "axiom" of disjunction. Cage's "axiom" is, of course, the principle of indeterminacy itself, a systematically unsystematic method for randomizing any and all aspects of a given work and/or performance.
Randomness and Negative Syntax
What, exactly, is the relation between Cage's randomizing "axiom" and negative syntax? This question raises complex and fascinating issues with which we cannot hope to fully deal in the present context. The following observations must suffice for now:
1. Insofar as indeterminacy can indeed promote perceptual differentiation and neutralize the mind "as a ruling agent" its function would certainly coincide with that of negative syntax.
2. Certain developments in "information theory" suggest a strong relationship between random functions and the perceptlon of discontinuity.
On the other hand,
3. Randomness, as we have learned, tends to call forth the context of implication, a purely mental phenomenon.
4. The findings of information theory with respect to perception seem contradictory. As randomness can be interpreted as resulting both in a maximum of "information" (differentiation) and entropy (non-differentiation), its ultimate function is something of a puzzle.19
It would, of course, be all too convenient if the most elusive and problematic goals of modernism could be attained through the employment of a simple mechanism. Nevertheless, there's an intriguing affinity between negative syntax and randomness which deserves exploration. Cage's practice may point to negative syntax in somewhat the same sense that numerology points to mathematics.
The Post-Webernians
At an opposite pole from Cage, but also profoundly affected by Webern, is a group of Europeans led by Pierre Boulez, Karlheinz Stockhausen and Henri Pousseur, often called the "post-Webern" school because of its intense involvement with Webernian serialism. This group shared with Cage a deep interest in those sound "surfaces" brought forcefully to light by the later Webern's emphasis on isolated, weighted notes and chords which could function as time "planes." All of the above named composers began to use complexes of sound in a manner analogous to Webern's treatment of pitches. These complexes, which could consist of dissonant chords, percussion "noises," electronic sounds, "real" sounds recorded by tape, or any combination thereof, were called by Boulez "sound objects." Sound objects may be defined as concrete clusters of sound heard simply as sound, with clearly defined intrinsic properties, including true duration.
Moment Form
In 1959-60, Stockhausen developed an approach to form which was an extension of the sound object principle. He called it moment form. The new approach, clearly indebted to Cage as well as to Webern, involved regarding a musical work as a series of isolated "moments." Like a sound object or an isolated Webernian note, "a given moment is not merely regarded as the consequence of the previous one and the prelude to the coming one, but as something individual, independent, and centered in itself, capable of existing on its own."20
In a remarkably clear and perceptive recent essay, "Moment Form in Twentieth Century Music," Jonathan Kramer has broadened Stockhausen's concept, demonstrating its profound relevence to much of the music of our time. Kramer begins by writing of the breakdown of musical continuity around the turn of the century: "the entire edifice of Western music had been built on the assumption that one event leads to another, that there is implication in music ..." With the dissolution of tonality, this "myth", which Kramer associates with "the metaphor of musical motion," was destroyed.
Kramer considers "moment-form pieces" as particularly characteristic of recent musical discontinuity. Such music "consists of a succession of self-contained sections that do not relate to each other in any functionally implicative manner." He credits Stockhausen with being the first to articulate this idea, but "the procedures ...derive ultimately from the practices of Debussy, Stravinsky, Webern (particularly in his variation movements), Varèse, and, above all, Messiaen."21
The sound-possibilities of moment-form are, theoretically, completely open. While, with the exception of Varèse, all the above-mentioned composers were content to restrict themselves, for the most part, to the traditional sound sources of music, more recent moment-form works incorporate a variety of non-"musical" sounds ranging from electronically produced "pure" sounds to vocal clicks and screams, recorded street sounds, radio broadcasts, etc.
Even completely conventional musical gestures can be incorporated into moment form. Kramer distinguishes between tonality as a "universe of discourse" and as a simple element which can co-exist with any other element. In certain works by Ives and, more recently, Rochberg, Berio, etc. (and, or course Cage) remnants of tonal-metric usage "are rendered static by contrast with the various nontonal surroundings,"22 Leftover fragments from positive syntax can be used "negatively" in a context in which their implicational powers have been defused. This is a basic principle of Cubist collage, where fragments of wallpaper, newspaper, lettering, etc. are incorporated along with "pure" elements such as lines and planes. Moment form "collage" similarly transforms familiar musical passages into neutral "sound objects."
Open Structure and Proportion
Needless to say, moment form involves totally different structural premises from those of the tonal-metric system. Since each "moment" is self-contained, the dynamic, developmental, goal-oriented procedures of classical form must be abandoned, as must even the basic notion of beginning-middle-end. To Stockhausen the distinction between beginning-ending and stopping-starting is particularly significant:
When saying "beginning," I imply a process, something that rises and merges; when saying "ending," I am thinking about something that ends, ceases to sound, extinguishes. The contrary is true with the words "start" and "stop," which delineate a duration, as a section, out of a continuum. Thus "beginning" and "ending" are appropriate to closed development forms which I have also referred to as dramatic forms, and "starting" and "stopping" are suitable for open moment forms.23Traditional works, which evoke an idealist world of "transcendent" sound-meaning, cannot simply start as though they inhabited the same time-field as ordinary sounds. They must begin, that is, call forth, through conventionally established codes, the passage to their own time world. By the same token, such works cannot simply stop, but must, again through totally conventionalized procedures, set themselves off, as in a frame, by a process of ending. Moment form works, which would intensify, rather than transform, the time-field, may start and stop.
Stockhausen's distinction between "closed development forms" and "open moment forms" is particularly significant. Traditional forms "begin" and "end" as a function of the gestalt closure, which, as Leonard Meyer has demonstrated, they require. Moment form pieces, like the mature paintings of Mondrian, would disrupt gestalt perception, thus opening themselves to their surroundings (temporal or spatial). In this context, it is particularly important to understand that, theoretically, each moment of a moment form piece, while self contained, does not exhibit closure and should not be confused with a gestalt -- each moment also simply starts and stops, remaining open to the moments surrounding it.24
The notion of "open form" called forth in Stockhausen's essay is of great importance to the post-Webernians, gaining the status of a catch-phrase which, at times, seems to mean anything and everything distinguishing their structures from the traditional ones.25 The phrase itself, however, tells us little about the manner in which any given work is to be organized from "moment" to "moment." Indeed, the absence of beginning-middle-end organisation would seem to precipitate a structural crisis for moment form in this respect, as the very notion of temporal organization seems to demand such a progression. Having rejected any notion of teleological form, the composers cited by Kramer would seem to have accepted musical anarchy. As Kramer points out, however, one important organisational resource remains from the ruin of traditional form. It is the same resource claimed by Mondrian: proportion.
Global coherence cannot come from progression nor even, in most cases, from order of succession...But the nature of moment form suggests proportional lengths of moments as the one remaining principle of formal coherence...Whether or not a moment form is satisfying depends to a large degree on the proportional lengths of moments.
For Kramer, the crucial role of proportion goes hand in hand with the effects of musical staticism. Because of the many different levels of motion in traditional tonal music, our perception of its proportions "is too complex to be dealt with by objective measurement." Since moment form works tend to disrupt motion altogether, in such works,
the measurable length of one static section relates [perceptually]
to that of another ...[Hence] it is safe to say that, when there is no large
internal activity within sections, the objectively measurable durations
correspond to the perceived proportions.26
The heart of Kramer's essay is the proportional analysis of two works which he regards as keys to the development of moment form: Stravinsky's Symphonies of WindInstruments and Messiaen's Chronochromie (literally, "time-color"). He assigns to each disjunct section (moment) of the Stravinsky piece an approximate time length in seconds (derived from the collation of rhythmic values and metronome markings). When the ratios between time lengths are rounded off, Kramer discovers some surprising proportional consistencies, particularly the predominance of the ratio 3:2.
I find the pervasiveness of this ratio impressive. It accounts for
the formal balance of the first half of the piece. I do not of course claim
that we listen and say, "Aha! A 3:2 piece." But we surely do hear
something consistent and elegant in the way the proportions relate, and the
persistence of 3:2 explains such an impression.27
Serialism and Temporal Determination
Nothing in the Stravinsky work suggests that the 3:2 ratio was arrived at by any but a purely intuitive process of give and take between motivic "content" and temporal "form." With Stockhausen, however, (as with Cage) we arrive at a situation where proportional relationships among moments are precisely calculated, prior to the determination of their sound-content. In order to understand the basis for Stockhausen's calculations, we must briefly review post-Webernian "total" serialism.
Webern himself never worked from any a priori serial ordering other than that determining pitch (the "twelve tone row"). Certain of his works do undoubtedly, however, point in the direction of serial (or at least highly rational) treatment of other parameters.
During the late Forties and early Fifties, when Messiaen and his students "discovered" Webern, there was a surge of interest in the project of generalizing Webernian serialism to the point that certain of its fundamental procedures could be applied "totally," that is to any and all musical parameters: rhythm, texture, timbre, register, loudness, etc. The process began with the realization that a tone-row was essentially a set of ratios between pitches; ratios which could be expressed numerically in various ways (e.g., on the basis of relative number of cycles per second, or interval size measured in half-steps). Since such ratios could also be applied to relative time lengths, it was possible to derive a "rhythmic series" from any twelve-tone row.
In early examples of "total" serialism by Messiaen (Mode de valeurs et d'intensités) and Boulez (Structures), the serialization of rhythm takes its place on more or less equal terms with the serialization of other parameters; "rhythm" is conceived traditionally, i.e., in terms of attacks, rather than durations; the rhythmic series controls local, note to note, relationships only. In a seminal essay, "How Time Passes," Stockhausen demonstrated that the determination of temporal relations goes far beyond questions of rhythm, having profound importance at all levels of musical organization, from pitch (cycles per second) to global form.28 In works associated with this essay, notably Gruppen (1958), Stockhausen developed procedures for extending the serial principle to the determination of the overall, large-scale duration proportions of an entire composition. It is this "promotion" of the temporal dimension, from simply one of many equally important "parameters" to a status equivalent to structure itself, which makes moment form possible. By the same token, the moment form concept, by permitting serial predetermination of each moment's duration, enables the series to extend its influence to structure on the largest scale.
The Triumph of Rationalism
Our search for the ultimate basis of negative syntax in time seems near an end. Kramer's analysis of moment form has demonstrated the fundamental role of large-scale temporal proportions. Our brief history of post-Webernian serialism has revealed the manner in which such proportions came to be calculated from a basic rhythmic series. We need apparently only carry the process one step further, inquiring as to the principle through which the rhythmic series itself comes to be determined.
At this point, however, difficult problems arise. While both Mondrian's intuitive determination of spatial proportions and Cage's principle of indeterminacy can be regarded as "axiomatic," thus primary (non-derivable), any given post-Webernian rhythmic series is indeed derived from something prior, usually a twelve-tone row.
A rhythmic series derived from the proportions of a tone row cannot inherit its "negative" disjunctions. The mutually repulsive dissonances of the row stem from an a priori system of tuning which applies to the pitch dimension alone. Simple time proportions derived from complex vibration ratios will have little more than a purely theoretical relation with their source.29 Post-Webernian serialism is indeed characterized by many arbitrary relationships of this sort, a failing which stems from a fundamental contradiction. On the one hand, the composers of this group seem fully aware of the importance of differentiation, discontinuity, decomposition; on the other hand, the series itself has generally been regarded as having a unifying function. Since the "unifications" of the serial method are hardly ever directly perceptible, a highly rationalistic faith in the unifying power of numbers grew with the development of total serialism. Through the workings of some mystical process, all the parameters of music were expected, somehow, to be unified through the continual use of permutations from a single number series.
A modernized idealism of this sort (recalling the Futurist "discovery" of geometry) reveals a serious underestimation of the dialectical properties of the row. In fact, of the major theories of total serialism, none reflects an awareness of the twelve-tone row as a perceptually disjunct construct which "unifies" the pitch field only insofar as this field becomes neutralized in the process. As with Mondrian’s "dynamic equilibrium, "the tone-row is a destruction, not unification, of the "plastic means" (functioning, moreover, through the senses, not by means of abstract mathematical relationships).
In the effort to create a totally unifying, transcendent system within which all material elements might become transmuted toward some vaguely defined "higher" end, the total serialists created a monster of rationalism, a pseudo-science of artistic creation which, ultimately, they themselves were forced to reject. In the ensuing flight into the irrational which (perhaps inevitably) followed,30 fundamental questions regarding the determination of temporal proportion were left in abeyance.
If the post-Webernian's preoccupation with numbers (extending even beyond serialism to an involvement with aleatory and stochastic processes) led to a fetishization as problematic as that of the Futurists, their contributions to the organization of negative time remain considerable nevertheless. The extension of the serial idea to determination of the time-field makes powerful twelve-tone procedures (such as invariance, for example) at least potentially viable in the organization of temporal relations. Moment form, among the very few theories primarily concerned with the structuring of duration, clarifies much regarding the role of temporal disjunction in Twentieth Century music. The closely related notion of "open form" links the explorations of the post-Webernians with "opening of form" so crucial to negative syntax generally.
Notes
1. Robert Ericson. The Structure of Music (New York:Noonday Press, 1957) pp. 82, 83.
2. Here we part company with Bergson, for whom melody was the ideal realization of "pure duration," the exact opposite of "cinematographic time." The weakness of his position in this regard became evident to Bergson himself, who significantly qualified it in a late work. Durée et simultanéité (1922); see quotation in Victor Zuckerkandl, Sound and Symbol (New York:Pantheon, 1956) p . 244.
3. Leonard Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956) p. 92.
4. Ibid. pp. 157-196.
5. For a concise statement regarding the relation of extended tonality and its attendent ambiguities to the process of musical symbolization, see Arnold Schönberg, Structural Functions of Harmony (1954), revised and edited by L. Stein (New York:Norton, 1969) pp. 76-113.
6. Schönberg's phrase. See, e.g., ibid. p. 193.
7. Heinz-Klauss Metzger, "Webern and Schönberg," in Die Reihe 2 (Bryn Mawr, Pennsylvania:Presser, 1958) pp. 44, 45.
8. Henri Pousseur, "The Question of Order in New Music," in Perspectives of New Music vol. 5, no. 1 (Fall-Winter, 1966) pp. 99-101.
9. Space does not permit adequate discussion here of the currently widespread claim that many serial works contain tonal functions. In my view, this claim is misleading. While it is not at all unusual for a serial work to contain suggestions of tonality, consistent polarization of pitch space in a single "direction" is uncharacteristic. While certain invariant functions can give greater prominence to some pitch-classes, these are usually (in Webern, at least) disjunctive pairs (tritone) or tonally neutral chords (diminished 7th or augmented triad).
10. Pousseur, op. cit. pp. 104, 105.
11. Ibid. p. 104.
12. This is, of course, the famous BACH motive.
13. John Cage, "Composition As Process" (1958), in John Cage, Silence (Middletown, Connecticut:Wesleyan University Press, 1961) p. 19.
14. John Cage, "Defense of Satie"(1948) in John Cage, ed. Kostelanetz (New York:Praeger, 1970) p. 81.
15. John Cage, "History of Experimental Music in the United States" (1959) in Silence, op. cit. p. 71.
16. John Cage, "Composition" (1952) in Silence, op. cit. p. 59.
17. "Composition As Process," op. cit. p. 27.
18. Richard Kostelanetz, "John Cage: Some Random Remarks," in John Cage, op. cit. p. 196.
19. "Indeed, indeterminism is nothing other than a lack of determination, that is, of all characterization having the power to distinguish one thing from another and to determine it specifically. It is really nothing other than indifferentiation...." Henri Pousseur, op. cit. p. 103. See also Rudolf Arnheim, Entropy and Art (Berkeley:University of California Press,1971), especially pages 15-25, for a discussion of the same contradiction specifically applied to the claims of information theory.
20. Karlheinz Stockhausen, "Momentform" (1960) in Seppo Heikinheimo, The Electronic Music of Karlheinz Stockhausen (Helsinki, 1972) pp. 120, 121.
21. Jonathan Kramer, "Moment Form in Twentieth Century Music," in Musical Quarterly, vol. 64, no. 2 (April, 1978) pp. 177-179.
22. Ibid. p. 184.
23. Stockhausen, op. cit. pp. 121-122.
24. Unfortunately, both Stockhausen's original formulation and Kramer' s extrapolation from it are marred by idealizations which only serve to mystify. Thus Stockhausen speaks of "an eternity that is present in every moment" and the "explosion--yes--even more, the overcoming of the concept of duration." (Quoted in Kramer, op. cit. p. 179) Space does not permit analysis of the damage done by such wishful thinking. Possibly due, at least in part, to theoretical weaknesses of this sort, most moment form works lack the powerful negative temporality of Webern.
25. The term became associated with "variable form" and Cageian indeterminacy.
26. Kramer, op. cit. pp. 181-183.
27. Ibid. p. 187.
28. Karlheinz Stockhausen, "How Time Passes," in Die Reihe 3 (Bryn Mawr, Pennsylvania:Presser, 1959) pp. 10-40.
29. This failing is shared by the "time-point" system of Milton Babbitt, which in other respects improves on post-Webernian serial method.
30. During the Sixties, indeterminism of one sort or another became a pervasive characteristic of post-Webernian music.
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