A city floating outside of time

Iannis Xenakis and Conlon Nancarrow were the first two modern composers whose work completely blew me away. I was eighteen years old and had just begun listening to the music of contemporary composers, and I encountered the work of these two in quick succession. Two revelations. Two portals giving access to a world of intensities, of physical energy as well as intellectual mystery, two promises, visions of a time other than time.

It has taken me long to start noticing some remarkable coincidences in their biographies. Both Xenakis and Nancarrow had joined communist movements; both have taken up arms against the fascists; both lost their respective struggles after enduring great hardship; both have had to flee and to live a large part of their lives in political exile. Both imagined a better world, worth fighting for, but both had to let go of it. Without, however, disavowing their political beliefssimilarly, both have refused to accept the Soviets as keepers of their ideals.

Dutch author Sybren Polet writes: ‘Utopian imagination is qua utopia now behind us for good, as a floating city in the distance. […] The real, i.e. unreal utopia is past without ever having been present.Perhaps, in the twentieth century, you had to be a communist outside of the Party, an exile, to experience this most sharply – and to transmute it into artistic form. Their war experiences, and thereby their political convictions, have had a profound influence on the development of the work of both Xenakis and Nancarrow.

The specific musical innovations of both have to do with thinking about time. Both have managed to shape time as such in music so as to make it seem to point towards the outside of time. I’m inclined to read this outside-time in both cases as an artistic transmutation of the non-real time of lost utopia. It is however striking to see that the approaches to time of the two differ greatly, to the point of being each others complement.


Massive motion is a core characteristic in the work of Iannis Xenakis (1922-2001). His music is overpowering, violent even, a music about which one usually speaks in terms such as eruptionsand sound masses’. Xenakis’s pieces evoke the unsentimental violence of nature, often using complicated mathematical models. The physical and mental challenges with which they present their performers are extreme: to play Xenakis is to wage a battle against the elements.

That, at least, is what is most striking when first encountering the work. Xenakis’s music however also always has a subtle and lyrical side. Regularly, out of the frenzied whorls of sound, curious, at times seemingly archaic, hymn-like melodies emerge. Always, between the eruptions, there are passages of an invigorating, albeit just as unsentimental beauty. Many of his pieces end with a mysterious gesture of fading away or sliding off the scene, as if the violence of nature has found other, shadowy, dimensions into which to continue.

Even Xenakiss most massive eruptions contain a rough, colorful, rich relief in sound. Xenakis is not only interested in the grandeur of the gesture, as expressed by every orchestral crescendo. What concerns him really is the motion of a mass. In the early orchestral work Pithoprakta (1956) independent parts were composed for every player in the string section, each with its proper details, in which the development was modeled after Brownian motion. Every musician follows another path; as a listener one might possibly follow every individual contribution, although probably you would rather focus on the flowing massiveness of the resultant whole. Another piece that is strong in my memory is Ata, the first orchestral work of Xenakis that I managed to hear in live performance. A piece full extremely loud, enormous, dissonant, cluster-like chords, but I had the sensation that I could hear the sound laid out in space, that if I would like to and be given the time, I would be able to determine the isolated nature of every component, every player, within the immense whole. This is the very opposite of the classical symphonic ideal of a blend of timbres. What I heard was compressed contradiction. A sound of rare power and depth.

Xenakis derives his models for this massiveness from mathematics and physics. But they have a political significance as well, as witnessed by a key passage from his theory book, Formalized Music:

Everyone has observed the sonic phenomena of a political crowd of dozens or hundreds of thousands of people. The human river shouts a slogan in a uniform rhythm. Then another slogan springs from the head of the demonstration; it spreads towards the tail, replacing the first. A wave of transition thus passes from the head to the tail. The clamor fills the city, and the inhibiting force of voice and rhythm reaches a climax. It is an event of great power and beauty in its ferocity. Then the impact between the demonstrators and the enemy occurs. The perfect rhythm of the last slogan breaks up in a huge cluster of chaotic shouts, which also spreads to the tail. Imagine, in addition, the reports of dozens of machine guns and the whistle of bullets adding their punctuations to this total disorder. The crowd is then rapidly dispersed, and after sonic and visual hell follows a detonating calm, full of despair, dust, and death. The statistical laws of these events, separated from their political or moral context, are the same as those of the cicadas or the rain. They are the laws of the passage from complete order to total disorder in a continuous or explosive manner. They are stochastic laws.1

He knew what he was talking about. During World War II, Xenakis, then a student at the polytechnic, had joined the radically left-wing resistance against fascist domination. After the withdrawal of the fascists a conflict started between the communists and the new government supported by the British, leading to a civil war. A British grenade hit the building which Xenakis was defending along with some comrades; Xenakis was left for dead, but he survived, though from that moment on he had to make do with only one eye. In 1947 he escaped to France, with final destination the United States, but he remained in Paris, there becoming a collaborator of Le Corbusier, and also taking up musical composition. The new dictatorship in Greece meanwhile condemned him in absence to death.

During his activist years Xenakis read Plato, Marx and Lenin. He later wrote in an autobiographical notice about this political education that he became a marxist thanks to Plato. He admired Marx’s quest, ‘as it seemed to me nearly the only still valid one’, for the rediscovery of harmony of humankind, and that of humankind and nature. Marx, as he puts it, ‘taught me a sense for contradiction, the true motor of mind and world, such that the mortal sin of marxism, if one could put it like that, to my eyes consists of the belief that one day there will be a society in which all contradictions have been abolished.’2

In his mature work, direct references to political ideologies receded into the background, but the values that are indicated here have remained important motives. In his later thinking he would consistently return to the ancient Greeks, including those before Plato, and he would always honor the ‘harmony’ of contradiction, especially in his quest for a balance between a Heraclitean and a Parmenidean conception of time, with mathematical thinking being given a mediating role. Xenakis remained true to his revolutionary aspirations, but displaced them (in a passage referring to Plato’s famous cave) to the level of space and time itself:

All of a sudden it is unthinkable that the human mind forges its conception of time and space in childhood and never alters it. Thus the bottom of the cave would not reflect the beings who are behind us, but would be a filtering glass that would allow us to guess at what is at the very heart of the universe. It is this bottom that must be broken up. Consequences: 1. It would be necessary to change the ordered structures of time and space, those of logic, … 2. Art, and sciences annexed to it, should realize this mutation.

Humankinds liberation is not based on acceptance of stable categories. Every category is an emanation of an underlying tension that is yet to be explored. Behind time and space itself unknown, deeper worlds lie hidden. These depths precede the universe of our awareness, and they have to be sounded, with all artistic and scientific devices available to the imagination. All harmony rests on contradiction.

The influence of Parmenides lies at the origin of Xenakis’s creative metaphysics. He paraphrases the presocratic thinker from Elea in one of his first poetical texts. First, he quotes from Parmenides’s Poem: ‘For it is the same to think and to be’, and then he writes his paraphrase: ‘For it is the same to be and not to be.3 He continues:


In a universe of nothingness. A brief train of waves, so brief that its end and beginning coincide (negative time) disengaging itself endlessly.

Nothingness resorbs, creates.

It engenders being.

Time, Causality.

The reference is not obvious. The Poem of Parmenides forms the foundation for our notion of logic as a timeless, unchangeable world. But the musical universe founded by Xenakis in this brief text is in fact one of complete randomness and change. A true modernist, Xenakis was dreaming of a music that would in no way be based on any pre-existent cultural idea or taste judgement. He was looking for a self-creating world of sound, and was hoping to abolish causality as such as the motor of musical form. It had to sound as if no single event would have a cause outside of itself. Sounds were not to be determined by a logic of their succession, as is the case in classical and every other traditional style. In this resides an affinity with the Elean. Indeed, by giving up such a logic, time itself as a medium for succession is suspended. Additionally, Xenakis could approach his dream of total contingency only by mathematical means. In the case of his sequence of ‘stochastic’ compositions, these means were provided by statistical theory. Early pieces like Achorripsis and the computer-calculated series of ST-pieces (the string quartet ST/4, 1-080262 and the orchestra piece ST/48, 1-240162) feature a shape that corresponds to a perfectly random distribution of events in time. If, for instance, some passages are denser than others, this is in accordance with the most probable distribution of events, but not caused by any other idea of form. The result is a highly dynamic music, in which every sound exists by itself and time is constantly starting all over. Sonic vacuum variation: pieces constructed from sounds that emerge spontaneously, breaches of silence that arise and wane without cause.

This way, at the outset of his oeuvre, Xenakis reached the zero degree of musical time. From that point on, he would develop in his later work a theory about the relation between music ‘in-time’ and music ‘outside-time’. This was necessary, because, even in an entirely stochastic composition, the events, which get lodged somewhere in time, are drawn from a particular reservoir of sonic possibilities: a collection of pitches, timbres, modes of playing, and so on – and this collection itself will always be governed by some type of structure (scales, meters, instrumental groupings…) After having abolished causality in-time, Xenakis became ever more interested in this organization outside-time, and the (mathematical) relations and transformations between potential sonic structures, which act in this outside-time realm. This organization would come to replace the causality determined by stylistic conventions in traditional music. Music in-time, then, is the product of a projection into time of relations between sonic possibilities outside-time. The potential relations, structures, and transformations that one can think of between sounds outside-time is vast, only restricted by the open space of mathematics itself. For that reason, the exploration of music outside-time became became a priority for Xenakis. This would enable humankind to rid itself of its accustomed sense of time.

It is remarkable that the examples of a complex outside-time organization that Xenakis gives in his writings stem from ancient Greek and Byzantine hymnal music. These traditions boast of very rich, stratified systems of scales and modes, and know subtle techniques to shift from mode to mode. In the course of Western musical history such rich tonal architectures have become increasingly schematized and reduced, being simplified first into the system of major and minor scales, to end up with the structurally impoverished, all too symmetrical twelve tone chromatic scale as a universal scheme. This scale increasingly dominates the world today: in every electronic keyboard commercially available this is the standard tuning, and thus through the distribution of technology it manages to invade everywhere more and more deeply into music.

To resist this kind of leveling, Xenakis found inspiration in ancient music theory. The major difference with the older tradition is that he was not concerned with developing a closed universe of scales, but rather aimed for an open system of endlessly mutable scales and rhythms, for which he developed a mathematical technique (‘sieves4). It is precisely the rigid, abstract, axiomatic formulation of that technique that allows for an infinite space of potential variations and applications: Xenakis’s sieves can generate harmonies in the greatest variety of tonal systems, but they can also determine rhythms or other patterns. The music from antiquity did keep haunting him, however, and in many pieces this can be heard as a hint of hymnal, ritual melody, interspersed between all the violence. His music outside-time, his floating city, indeed was behind him, full of promise of an other kind of time.


‘Time is the last frontier in music,’ Conlon Nancarrow said in an interview. For him, temporal structures were the starting point and main subject of all composition. Time itself becomes plastic and pliant in his work. First and foremost, this applies to tempo. His compositions combine multiple tempi sounding together, or they contain layers that accelerate and slow down independently. This leads to a music of exceptional rhythmical complexity and often at breathtaking speed, made possible by the instrument for which he composed the major part of his oeuvre: the player piano, the mechanically self-playing piano, which at the apex of its history used to be one of the main vehicles for bourgeois commercial music.

In contrast to Xenakis, Nancarrow has not left behind any theoretical texts filled with philosophical speculations. Other than in the case of the Greek it is not possible to find an explicit relationship between musical innovation and utopian thought. In his work, a metaphysical notion like the outside-time category has no role to play. What counts for Nancarrow are not the abstract relations and operations that can be projected into time, but the operations that can be applied to the course of time and tempo themselves. Put differently: it is about operations that are immanent to time, that do not stand apart from it. Even so, Nancarrow has managed to create points within the runtime of his pieces that are counter to the normal progress of time, that seem to point elsewhere.

Without political struggle, his music would most likely not have developed in the same way. Conlon Nancarrow was born in 1912 in Texarkana, Arkansas, in an extremely conservative environment, as the son of a prominent right-wing politician. However, at a young age, he discovered communism and became devoted to it. Musically he did not develop all too traditionally either: starting out playing jazz trumpet, he then found himself gripped by the modernism of Igor Stravinsky. In 1937, as civil war raged across Spain, he became convinced of the necessity to halt the advance of fascism. He interrupted his compositional education, left his trumpet with a friend, and joined the Abraham Lincoln Brigade, a group of left-wing volunteers fighting on the side of the Republicans against Franco. After two years of hardship, the Republicans were beaten, and Nancarrow managed to escape back to the United States. There, he was to discover that his membership in the Brigade had made him into a politically suspect individual. He heard from fellow combatants about difficulties that they found in renewing their passports. Nancarrow decided to go into exile, moving into Mexico, where he has lived the rest of his life. Even though he could no longer support the Soviet line he remained true to his earlier idealism: in 1985 he tried to remigrate for health reasons, but he refused to sign a declaration in which he would renounce his earlier communist sympathies as a youthful error, and so he remained in Mexico City until his death in 1997.

As a consequence of his activism, he was cut off from music life in the United States. This was a problem, to the extent that his music has developed in an increasingly experimental direction. Especially rhythmically his scores provided challenges to performers that were far above the norms of the day, and musicians who were willing to take them on could hardly be found in Mexico at that moment. But Nancarrow remembered the idea, from the theoretical treatise New Musical Resources by the composer Henry Cowell, that it should be possible to use a pianola in order to write music in highly complex rhythms. So in 1947 Nancarrow returned one more time to the United States to buy himself a player piano, as well as a machine for punching piano rolls.

This was the start of a long adventure of exploration like nothing else in music history. Nancarrow now could write every rhythm he liked. He embarked upon a series of Studies for Player Piano that would take the possibilities of the instrument very far. The first piece he wrote – a brief composition that was later to receive the title Study #3a – was a boogie-woogie, though for eight-handed virtuoso pianist who can play in multiple temporal layers at the same time. Still, those first pieces were conceived with human limitations in mind, possibly to be transcribed for regular chamber ensembles, something that would indeed come to pass some decades later. But after some time, Nancarrow became more interested in the proper idiom of the mechanical instrument. Rhythms became ever more daring, speeds were raised to extreme levels, until sonic textures would arise that had up to that point never been heard5. Study for Player Piano #21 Canon X is one of the most famous examples: there are two voices, with one voice starting very fast (some thirty notes a second) and gradually slowing down, and the second voice starting quite slow (about two notes per second) and gradually speeding up – over the course of three minutes up to some two hundred notes a second, creating a sound that even after repeated listenings remains impossible to believe even as you are hearing it.

The tempo canon is one of Nancarrow’s favorite devices. In a normal canon, like Frère Jacques, voices enter one by one with the same melody, in the same tempo, and form a harmonious counterpoint. A tempo canon follows the same principle, but the voices are each in a different tempo. A voice entering later at a higher tempo will then gradually overtake the earlier voices. In Nancarrow’s first tempo canons the tempo relationships are relatively simple: 3:4, 4:5, 3:5 – these are polyrhythms that could in principle also be performed by well-trained musicians. Later Nancarrow would shift his attention to much more complex structures. Canons began to appear in which the tempi would change in a regular, exponential way; canons with very close tempi, like 17:18:19:20; and even canons in irrational tempo relationships like 2:√2 and e:π.

The sounding result is sensational. In many pieces, one can hear a crazy mixture of jazzy melodic fragments or boogie-woogie-like basses in a rigidly stylized, disfigured swing rhythm, next to more abstract sounding lines, sudden explosions of chordal trills, sweeping glissandi and astonishingly erratic, whirling flashes of melody. All this in multiple layers mixed together, as in a Bach fugue, though here, the tempo differences confer an odd kind of depth to the experience of listening. Attention shifts from layer to layer and you constantly find yourself shifting gear; the mosaic of signals and melodies is transparent at times, sharply discontinuous at other times, entirely saturated at yet other times so that you find yourself immersed in an overpowering, but always exhilarating sonic complexity – often only to halt very suddenly, as the underlying clockwork completes all of its turns of the wheels at the same time.

This is very much a surface music. One might be forgiven to call the spectacular aspect of the gestures and the schematic nature of the idiom superficial. Nancarrow’s bluesy gestures for instance often have something hackneyed about them, and seemingly deliberately so, because he has good reasons for that. Indeed, one might see time itself as a ‘surface’, a stretch within which events happen. Nancarrows gestures are schematic and signal-like precisely to serve as marks on that surface, to make its passage audible, to make it manipulable for the composer. Nancarrow is hardly interested in deep harmonic structures or similar advanced relationships between musical objects outside-time, as Xenakis is.

Yet this surface music allows for curious experiences of ‘depth’, especially in the perception of different layers of temporal surfaces at once. It helps strongly that the music is using canons so much. You hear an event first in one layer, and then, perhaps a little faster, in another. Then, from a combination of two temporal layers, a new musical phenomenon is born: the interval in time itself, which starts acting like a kind of extra dimension to time itself, adding depth to its normally linear progress. What is so beautiful is how this depth is being created entirely ‘in-time’6. What distinguishes Nancarrow’s canons from ordinary canons is how this interval has its own dynamics: it can grow shorter or longer, as the different layers of the canon get closer to one another or run apart. This generates something like a movement of time in time. With this, so-called convergence points appear in Nancarrow’s canons, moments at which the voices overtake one another. These are extraordinary musical moments. What makes a convergence point so special is that it can be perceived as a moment of the music, but it does not possess temporal extension at all. The moment in which two voices pass one another is indivisibly brief, a moment that never sounds.

In many Studies, the convergence point is at the exact end of the composition, functioning as an effective and fully natural climax to the piece. Especially in the breathtaking works for two player pianos, such as Study for Player Piano #40a, b or Study for Player Piano #48a, b, c, in which two already very dense and complex rolls are played back on two different pianos at the same time, the convergence points at the end have a strong effect. As a listener you have been swept along by the multi-layered whirls of time and motion, you hear them gradually get together, and then, suddenly, everything is gone. The moment of convergence is also the final chord: generally a most simple major triad, played with staccato articulation. It tends to have a comical effect – I have often witnessed people, to whom I was playing Nancarrow’s music for the first time, couldn’t help but laugh. Indeed it is surprising, and in fact surprisingly rare in music: to have a piece that ends at the exact moment of climax (and not a bit after, as is more often the case). The moment of convergence in these works sounds as briefly as possible, and it is precisely the threshold moment at which as a listener you find yourself being catapulted out of the complex, layered temporal world of the piece. One moment you were fully submerged in it, the next moment everything is gone, and you find yourself in the everyday again – though with the wild, exhilarating physical and intellectual energy of piece still under your skin.

One of the most successful pieces in the sequence of Studies is number 36, subtitled Canon – 17/18/19/20. This piece starts innocently enough, with relatively slow melodies that enter voice by voice – though of course according to the highly complex rhythm of the subtitle. After a short while the texture accelerates, and wild glissandi start shooting up. These and other signals render the gradual mutual approaching of the four layers well audible. Gestures, explosions, glissandi follow one another faster and faster. You hear how the temporal intervals get ever more closely compressed, how the time frame of the canon narrows.

The convergence point of the piece is in its middle, and has been crafted in a very inventive way. At a point where the voices have come very close to one another, they all start playing quickly repeated, rising short glissando-figures, which, as the convergence point nears, themselves narrow down, shrinking to mere trills, and finally repeated notes. The passage only takes a couple of seconds, but the effect is tremendous: you hear, as it were, time itself vibrate and be compressed. It is one of the most intense moments that I know in all of music history. And then, at the precise moment in which all voices converge, they all shoot downwards and start running apart again. The point of total compression has passed at the exact moment that it was reached. You hear it approaching, you do perceive the moment, but it has never sounded. It has never been present. Like no other composer before him, Nancarrow has managed to compose the impossible: a musical event without the slightest temporal extension. A non-time, entirely within time.


1 Except where otherwise noted, all Xenakis quotes are from Iannis Xenakis, Formalized Music, Pendragon Press, Stuyvesant NY, 1992.

2 Translated by the author after the 1980 text Esquisse dauotiobgraphie as printed in Iannis Xenakis (ed. Sharon Kanach), musique de larchitecture, Éditions Parenthèses, Marseile, 2006

3 The sentence is in flagrant contradiction to another fundamental notion of Parmenides, according to which that which is is, and that which is not is not, and these two possibilities are never to be confused. It is to be pointed out however that it is precisely this error of the double-headedhumans which enables the world of appearances, which, too, is being developed in Parmenidess treatise.

4 This technique resembles a number theoretical idea from classical antiquity: Eratostheness Sieve, which allows one to sift through the numbers to find the prime numbers, by systematically removing all multiples (first those of two, then those of three, then of five, and so on) from the sequence of natural numbers. The sievesof Xenakis are constructed as regular patterns that interferewith one another to produce more complex patterns.

5 In recent years, thanks to the great advance of computational power of computers for the common market, comparable textures have started popping up in the folk music of the internet through the Black MIDI movement, a thriving genre of automatically performed music that has been named after the visual impression the scores make, chock full of notes as they are. These are very energetic, thrilling pieces, often arrangements of existing popular songs, that however do remain conceptually far behind the temporal operations of Nancarrow.

6 An echo functions in a similar way. Its perhaps no coincidence that it is precisely reverberant spaces like cathedrals that tend to be devoted to the eternal. There is a relationship between metaphysics and acoustics. The atmosphere of Nancarrows canons does remain much more earthly, probably due to his roots in jazz and his use of a commercial musical instrument.