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IN HIS BOOK The Origins of Knowledge and Imagination (1978) Jacob Brownowski has written:

I believe that we need to review the whole of our natural philosophy in the light of scientific knowledge that has arisen in the last fifty years. It really is pointless to go on talking about what the world is like (as much of philosophy does) when the modes of perception of the world which are accessible to us have so changed in character. And we become more and more aware that what we think about the world is not what the world is but what the human animal sees of the world. (1) Those who are deeply involved with the arts of our time will understand immediately the significance of Bronowski's deceptively simple observation. If recent art, music and literature teaches us anything it is that our understanding of the world is a reflection of the way in which we appropriate the things around us; that, in the end, what we understand is not what we perceive of the world, but rather, how we perceive it.

Composition, of course, is an act of exploration. What this exploration reveals (as it is undertaken time and time again by innumerable composers) is just how complex and seemingly contradictory our perceptions can be. Each new discovery reveals previously hidden dimensions. Each new work reveals the world from a different perspective, and represents one of many ways to give it meaning.

With the death of Iannis Xenakis on February 4, 2001, the music world lost one of its greatest explorers. Truly, for Xenakis, the process of composing was a process of investigation and discovery, an ongoing search for new sonic materials as yet untested as musical matter, and for new tools with which to engage those new materials within the artistic enterprise. I can think of few composers of the twentieth century who have so radically changed our way of thinking about music. In every one of his works we sense a passion for discovery, the discovery of previously hidden or even completely unimagined facets of our aural experience. When we allow his music into our lives, it rewards us in rich and unexpected ways.

Of all the changes that have swept across our musical landscape, it seems to me that none has been more significant than the simple fact that what we now accept as material for making music includes virtually anything that we hear in our daily lives. The joy of bringing new sounds into the world of music is truly one of discovery; the discovery of new and previously unimagined connections between things always believed unconnected. As we embrace the full diversity of sonic matter in the world and seek to integrate this diversity into our creative lives, we reconfigure our culture itself. For almost fifty years Xenakis's music has vivified this fact.

In order to work with wholly new types of sounds (new to music, at least) a composer must find new tools with which he can engage those sounds. Hence the famous (infamous, to some) mathematical tools that Xenakis uses to work with the materials of his sonic universe. Of course, his music is no more "mathematical" than Mozart's (or Babbitt's for that matter). After all, a sound wave is a sound wave. But new sounds engender new compositional tools. In turn, the creation of new tools leads to original musical designs and ultimately to a fresh evaluation of the ways that the world appears to cohere, even if only momentarily. As poet and literary critic Charles Bernstein has put it, form is "how any one of us interprets what's swirling so often incomprehensively about us . . . ." (2) Our culture provides a framework through which we experience and interpret the world. It is this framework that shapes our understanding of the world. As our materials and tools change, this framework changes and our entire worldview takes on new dimensions. I find it impossible to hear one of Xenakis's works and then not attend to the sounds of every day life in new ways; not just the sounds themselves, but the ways that I perceive those sounds. The world, at least the part that we hear, becomes malleable after Xenakis; we feel that we can shape it as we wish. In this sense his music is truly empowering.

Xenakis's work has been immensely important to me as a composer, teacher and scholar. Indeed, my own music has been deeply influenced by that of Xenakis. Certainly, as with many others, I can cite the influence of his techniques, his early explorations with computer technology, and his philosophical outlook. But there are also more specific influences. Whenever I use pitches in a piece (a truly rare occurrence these days) I instinctively feel the need to add noise of some kind to that piece. If I don't, I feel that I have cheated nature--the listener included. (I am far from alone in feeling this impulse.) Of course, we know that what we loosely label "noise" is really just another manifestation of what we call "pitch." At one point in music history the boundary for Western music consisted of a set of twelve pitch classes. Thanks to composers like Xenakis, such boundaries seem to have disappeared; we hear every sound of a musical work in the context of the entire world of sounds. In addition, when designing a composition I also find it essential to embrace fully the seemingly opposite worlds of determinism and indeterminism. (Again, I am far from alone in feeling this impulse.) Thanks to composers such as Xenakis we are today fully cognizant of the fact that there is no single, optimal conceptualization of musical design. Materials have multiple implications and invite a wide range of creative responses. Each new composition arises from some integration of these multiple responses and, hence, becomes an expression of the very existence of such multiplicity. No single perspective will suffice for the creation of music today. For me, as a composer, this has been one of the great lessons of Xenakis's work.

As I have written on a number of occasions, one of the endlessly fascinating aspects of the music of our time is its diversity. Our world consists of a vast collection of seemingly incompatible musics. With respect to what we commonly refer to as art music alone we find composers as different as John Cage, Gyorgy Ligeti, Elliott Carter, Luigi Nono, Alvin Lucier, Morton Feldman and, of course, Xenakis sharing time and space (literally and creatively, as we will see); each providing one panel of the mosaic which has become our musical landscape. Xenakis's own body of work itself reflects this remarkable diversity to an extraordinary degree. Indeed, if we follow carefully his remarkably varied career we can begin to comprehend the meaning of this diversity, and we can begin to understand that the multiplicity of ideas, sounds and tools that make up the music world today are all part of a larger framework of understanding, one whose very guiding principle itself is multiplicity. From Xenakis's music we learn to d istrust any false sense of unity that may result from simplistic reductive thinking; we learn, instead, to favor the kind of unity that comes from an acceptance of the world's inherent contradictions. As the poet William Carlos Williams once wrote: "by multiplication a reduction to one." (3) In this regard Xenakis's own career reflects the state of music itself in the twentieth century, the hallmark of which is its staggering diversity. Composers today have come to understand that there are no barriers separating serialism from indeterminacy, acoustic music from electronic sound, Western music from Eastern music, pitch from noise. Their music world is not the product of any one, overriding teleology. It consists rather of a multitude of evolutionary paths. No composer has contributed to so many of these different paths than has Xenakis.

As a teacher I have often taken great delight in presenting analyses of Xenakis's Achoripsis (1956-57) and Cage's Music of Changes (1951) alongside one another. Their mutual impulses to create statistical designs ("stochastic" in Xenakis's terminology) as evidenced by these (and many other works) are remarkably similar; the results truly complementary. From the beginning of his career Xenakis seems to have been eager to embrace chance and chaos and to try to understand what role these concepts play in our world, and hence, what role they could play in the creation of music. As the composer himself once wrote:

Since antiquity concepts of chance (tyche), disorder (ataxia) and disorganization were considered the opposite and negation of reason (logos), order (taxis), and organization (systasis). It is only recently that knowledge has been able to penetrate chance and has discovered how to separate its degrees--in other words to rationalize it progressively, without, however, succeeding in a definitive and total explanation of the problem of "pure chance." (4)

In a revealing set of interviews with Cage, Daniel Charles touched upon the interconnection between these two composers' statistically based compositions:

Daniel Charles: If I compare your position to Xenakis, for example, I see that you begin much the same as he. Xenakis uses probability formulae to describe, and to make his music describe, in the graphic sense of the term, the movement of a crowd, or the tapping of hail on a window pane. But he controls these movements by collecting them into a rule which controls the direction of the general, statistical tendency. You, yourself; do not attempt to control or orient these movements.

John Cage: What I hope for is the ability of seeing anything whatsoever arise. No matter what; that is, everything, and not such and such a thing in particular. The problem is that something occurs. But the law governing that something is not yet there...

Daniel Charles:... Your music is not opposed to Xenakis's music. It is situated before it; it describes its condition of possibility.

John Cage: Yes... (5)

Cage and Xenakis encounter chance at different points at which this concept becomes part of our experience. Each perceives chance and chaos through a different teleological framework. Hence, their compositions reveal remarkable similarities as well as striking differences vis-a-vis their individual ways of engaging the world. The question of whether either composer was fully cognizant of the other's work in this area is irrelevant. Each composer's work sheds light upon that of the other, which is all that matters for those of us who benefit from their explorations.

Similar revelations abound when comparing the more deterministic designs Xenakis creates in such works as Nomos alpha (1966) and Nomos gamma (1967-8), with the serial structures of any number of Milton Babbitt's compositions. Again, we find both remarkable similarities and striking differences. Nomos alpha and Nomos gamma were both composed with the aid of mathematical group theory which influences the design of both their micro- and macro-structures. The various mappings, permutations and transformations by which he organizes his sonic materials are drawn from the structural properties of groups. Babbitt's structures too reflect many of these design properties. The differences, however, are significant. Most significantly, Babbitt's procedures are an outgrowth of the specific properties of specific collections of sonic materials. His structures arise organically from certain properties inherent in these materials, a fact which is, of course, essential to understanding the function of more local, group-derive d properties of his compositions. Xenakis, in contrast, uses mathematical groups as higher-order abstractions, to be imposed upon materials regardless of their specific physical properties, as if from above. Xenakis gravitates toward permutation groups precisely because these allow him to create more abstract, generalized structures. Indeed, his works vividly demonstrate how the abstract nature of the mathematical groups can be imposed upon a vast array of radically different materials. Thus, the works of Xenakis and Babbitt are also deeply complementary.

On other occasions I have directed my students' attention to the curious relationships that exist between such seemingly different compositions as Xenakis's Duel (1958) and Christian Wolff's For 1, 2, or 3 People (1964). The structure of Xenakis's work constitutes a type of interactive contest fashioned with the help of mathematical game theory (a branch of probability theory). Specifically, a mathematical game enables the composer to create a dynamic situation in which all parties involved select courses of action that will optimize their possibilities of reaching a desired goal. Xenakis introduced the first musical applications of such games. In contrast, the interactive design of this, and, indeed, many other compositions by Christian Wolff consists of a set of blueprints that enable a group of performers to interact with one another. Thus, both compositions involve the formulation of a framework for interaction among a group of performers. One, however, is based upon mathematical rules; the other is not. In their respective works each composer shifts the focus away from himself--away from his own personal experiences and internal conflicts--toward the literal interactions of the performers on stage. Consequently, these interactions no longer reflect the composer's personal tastes and biases. Rather, the interactions themselves are transferred to the performers as abstractions. The subject of each of these works is the nature of interaction itself; not the specific responses, (emotional, intellectual) of one person to a specific set of stimuli, but the generalized give and take that accompanies any gathering of individuals regardless of the particularities of the situation. Each work, then, becomes an examination of the nature of discourse, and each composer reveals a different dimension of discourse. Xenakis's work, since it is based upon a model provided by mathematical game theory, is goal oriented. It externalizes a conflict of oppositions. His performers literally become opponents. In contrast, the indete rminate designs of Wolff are in no way goal oriented. Performers connect with one another within the framework of a musical design the sole purpose of which is to aid in and encourage the discovery of new points of intersection. The performers remain in a perpetual state of renewal. Each of these compositions reveals a very different facet of human interaction. The polarities of directed and nondirectional interplay (and all that they represent: competition vs. cooperation, etc.) reflect very different views of behavior. Once again, composers who might initially appear to be radically different from one another actually complement one another.

The foregoing comparisons reflect similarities and differences of a conceptual nature, relating to general issues such as determinism, chance, et al. It is, however, also revealing to look at parallels that arise from more specific, concrete interactions with sound. I have found it most revealing, for example, to compare works that share as a common source the microstructure of a single tone: Xenakis's Empreintes (1975) for orchestra, and the first movement of Gyorgy Ligeti's Cello Concerto (1966)--not to mention such equally important works as Giacinto Scelsi's Quattro Pezzi (su una nota sola) (1959) and the seventh etude from Elliott Carter's Eight Etudes and a Fantasy (1949). Any structural similarities exhibited by these very different works are therefore not so much the result of overlapping conceptual frameworks as they are a product of each composer's direct interaction with the same particular sonic matter. As such we will discuss these works from a slightly different perspective.

Empreintes opens with one note sustained by brass and strings for ninety seconds, prolonged through a succession of crescendos and diminuendos, as well as a variety of rhythmic articulations. The elaboration of this tone constitutes the most important thread in the multilayered texture of the piece. Whenever it grows louder upper partials are introduced. Conversely, whenever it gets softer these partials disappear. The composition, then, opens with a succession of ascending and descending waves of sound, resulting from the repeated crescendos and diminuendos (Example 1). (6) These somewhat "hidden" contours, embedded within a single tone, are soon enlarged into a stream of ascending and descending string glissandi (examples of what Xenakis has labeled arborescences). In a sense, the subtle arching shapes produced by the rising and falling partials of that first tone are made concrete by the ensuing glissandi. As the piece develops, these shapes unfold in counterpoint to one another. Near the end of the compos ition, the partial structure of the opening tone is rendered concrete in yet another way. As we've noted, whenever the initial tone grows louder its higher partials grow stronger and more audible. At its loudest moments we actually start to hear a dense cluster of overtones forming in the upper registers. The work ends with a long succession of repeated pitches and clusters (fundamentals), which seem to resemble those dense bands of upper partials. The distribution of both pitches and intervals in these clusters resembles that of the upper partials of the initial tone, leaving the listener with the sense that the composer has taken those bands of upper partials down a few octaves, removed their fundamental and turned them into a series of repeated chords. Thus, the clusters first introduced as internal components of a single tone are rendered concrete, as actual chords. The form of the piece traces a transformation of the inner life of a single tone into complex masses of sound, articulated as both continuous and discontinuous gestures (glissandi and repeated chords respectively).

The first movement of Ligeti's Cello Concerto also opens with a single tone, sustained for a little over a minute and a half, first by the soloist alone, then by a steadily growing array of instruments. As with Empreintes all that follows is an outgrowth of the timbre of this opening note (Example 2). Here too the sweeping arches of ascending and descending partials that repeatedly appear and disappear inform the rest of the composition. For example, the sustained octaves that become so prominent later in the movement literally emerge from the overtone series of the opening pitch; each time it grows louder its component octaves become more audible. Though the literal octaves heard later in the piece are of a different pitch class than those of the opening tone, they still bear a strong aural connection to them. Thus, over the course of this movement, we hear, not a shift from a single pitch to a set of octaves, but a shift from a set of octaves buried within the overtone series of a single fundamental frequen cy to a set of fundamental frequencies themselves spaced in octaves.

To be sure, the opening of each of these compositions, though derived from the same basic materials (the overtones of a single tone), imprints a different sonic signature. One begins with the fragile sound of a single, nearly inaudible cello that seems to pull a tone out of thin air. The other opens quite forcefully with massed brass dominating. Also, each evolves in quite different ways. Here again, we encounter two composers whose general intentions are similar--to explore the inner life of one tone and to transform that rarefied sonic world into a large-scale musical design--but whose intentions are realized in very different ways.

Many other connections can be found between the music of Xenakis and that of his greatest contemporaries. Indeed the list of such connections goes on and on. One thinks of his earliest computer-assisted compositions which still today influence many working in algorithmic composition; the unique spatial designs of Terretektroh (1965) which beautifully complement those of Stockhausen's Gruppen (1955-7), revealing another, very different way of integrating space into our experience of sound; the total theater (Xenakis's term) of Oresteia (1965), which resonates in so many interesting ways with Harry Partch's similarly conceived music/theater works; the array of vocal colors and textures of the textless choral work Nuits (1967) which traverses a path similar to that of Ligeti's beautiful Aventures (1962); and, of course, his Polytopes (1967, 1972, 1977), those unparalleled interpenetrations of sound, light and space to which virtually all multimedia experiments of the present day are indebted. Of how many other c omposers can it truly be said that their work touches our musical experiences in so many different ways, and resonates in the work of so many, diverse contemporaries?

Of course, Xenakis did not necessarily inspire these composers. Nor did their work necessarily inspire his. This is not the point. The question of influence is not a particularly interesting one, even from a historical perspective. Ideas are often "in the air." Frequently, we hear of physicists, artists, philosophers and writers, in different parts of the world, reflecting very different cultural perspectives, working along the same lines unbeknownst to one another. The more diverse the group of individuals exploring a specific idea, the more sharply that idea comes into focus. Clarity is achieved when each facet of a problem is examined from an array of different perspectives. This is certainly true when a number of great composers touch upon the same idea (chance, determinism, et al.). Our understanding of the world comes, not from the work of one or two composers, but from the work of many, very different composers as they complement one another in often startling and unexpected ways. That Xenakis's work r esonates so deeply with that of so many others is, in my view, a tribute to his greatness.

In pointing out these and many other similarities I in no way wish to suggest that Xenakis was merely eclectic. Achoripsis, Nomos alpha, Duel, Empreintes, Oreteia, Terretektorh and the rest, could never be mistaken for the work of anyone else. The foregoing comparisons reveal that, for Xenakis (perhaps alone among the great figures of twentieth-century music) the larger picture does not end with chance alone, to the exclusion of determinism. Nor does it end with non-linearity alone, to the exclusion of linearity. Rather, it includes all of these principles, and more. As his music eloquently teaches, it is through the interweaving of each of these seemingly contradictory ideas that we begin to comprehend our world. "Everything happens as if there were one-to-one oscillations between symmetry, order, rationality, and asymmetry, disorder, irrationality in the reactions between epochs and civilizations." (7)

In my view, a musical composition is not an expression of a preordained worldview, but a record of the process of a mind working toward the formulation of a worldview, a formulation that can never be fully realized for, I think, obvious reasons. This process begins with an interaction with the physical world. The nature of that interaction determines the particularities of each artist's work. When a composer such as Varese, Cage, or Xenakis embraces sounds new to the world of music, his ability to shape those sounds is necessarily challenged, for a composer's way of acting on materials is, first and foremost, determined by what he chooses as materials. As Xenakis's biographer Nouritza Matossian has rather poetically put it: "Certainly it is hard to imagine how Herma [Xenakis's first piano piece], complete and newly formed as though from a state of nature, could have been born in a composer's imagination without some strange parentage such as the unlikely terra firma of logic." (8) For music theorists, the tas k posed by Xenakis is immense. To conceptualize processes, wherein both materials and methods are so radically new requires a virtual tabula rasa. (Of course, Xenakis's own writings do help in this regard, but, as anyone who has tried to analyze his compositions understands, those theoretical writings provide only a point of entry into the complex structural designs that one encounters in his music.)

Composers like Xenakis challenge us to reevaluate from scratch our most basic assumptions about music--a very good thing for us to do periodically. Every generation produces a few artists who force us to return to the beginning, to strip away all existing notions of art and reconceptualize it from the ground up. In my view, every time a new composer forces us to undertake such a complete reevaluation we have reached one of the pinnacles of music's evolution. Xenakis was just such a composer. He leaves us a body of music staggering both in its intellectual depth and its emotional range.

At the time of Varese's death Xenakis noted:

Varese worked on the very flesh of sound .... His music is color and sonorous force. No more scales, no more themes, no more melodies, to the devil with music called "musical," he delivers in the flesh that which is more generally called "organized sound." His dimension is not in the proportion of the combinatory elements. It is in those parts of music which are not yet utterable. (9)

The music of Xenakis conveys much of the same elemental force as that of Varese. Not merely because its sounds may seem harsh to our ears, nor because its forms are riddled with deliberately discomforting contradictions and disruptions; but because his music teaches us that those contradictions and disruptions form the basis of our understanding. It teaches us that any attempt to comprehend and explain our experience of the world must be rooted in that fabric of discontinuities which constitutes the very essence of that experience. It is for this that we mourn the passing of Xenakis, one of our greatest explorers.

THOMAS DeLIO is a distinguished composer and scholar. His music is recorded on the Wergo, Neuma, Capstone, 3D Classics (Paris), and Spectrum labels. His compositions are published by Smith Publications/ Sonic Art Editions (USA) and Editore Semar (Rome). He is the author of numerous essays and books on the music of the 20th century including the widely celebrated Circumscribing the Open Universe and The Music of Morton Feldman. He is Professor of Music at the University of Maryland School of Music, College Park, MD.


(1.) Jacob Brownowski, The Origins of Knowledge and Imagination (New Haven: Yale University Press, 1978), 4-5.

(2.) Charles Bernstein, A Poetics (Cambridge: Harvard University Press, 1992), 1.

(3.) William Carlos Williams, Paterson (New York: New Directions, 1963), 2.

(4.) Iannis Xenakis, Formalized Music (Bloomington: Indiana University Press, 1971), 4.

(5.) Daniel Charles, For the Birds, (London: Marion Boyars Ltd., 1981), 147.

(6.) Spectrographs allow us to examine the internal components of each sound and to view each work more in terms of what is actually heard than only what is notated in a performance score. The spectrographs used in this paper were created with the aid of the Sound Technology Inc., Spectra Plus FFT Spectral Analysis System. The vertical axis of each of these graphs represents frequency in Hz, while the horizontal axis represents time. The relative darkness of the various images in each picture reflects their relative amplitude levels (a lighter image reflects a soft sound; a darker image, a louder sound). On these spectrographs frequency is plotted logarithmically. The spectrographs used is this paper are based upon the following recorded performances: Iannis Xenakis, Empreintes, Orchestra Philharmonique du Luxembourg, Arturo Tamayo, Timpani 1C1057, 2000; Gyorgy Ligeti, Cello Concerto, Siegfried Palm, Hessischen Rundfunks, Frankfurt Symphony Orchestra, Michael Gielen, Wergo 60163, 1967.

(7.) Xenakis, Formalized Music, 25

(8.) Nouritza Matossian, Xenakis (London: Kahn & Averill, 1986), 156.

(9.) Iannis Xenakis, "Article on Varese," Tribune de Lausanne, 14 November 1965, as cited in Matossian, Xenakis, 179.

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Title Annotation:Iannis Xenakis
Author:Delio, Thomas
Publication:Perspectives of New Music
Geographic Code:4EUGR
Date:Jan 1, 2001
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