When I started to compose, after the war, there were many different directions in musical research which had been prepared by the great masters Schoenberg, Webern, Berg, Stravinsky, Bart�k, Var�se. I had to go to the roots of their individual work, and find an underlying unity. It fell to me to synthesize all these different trends for the second half of the century, perhaps in a similar way that Heisenberg, in the first half of the century, had the role of bringing together the discoveries of Planck and Einstein in atomic physics.

My debut as a composer came in 1951. I was twenty-three, studying music and piano and doing my final exams at the state music conservatory in Cologne. At the end of my studies I wrote a piece called KREUZSPIEL, 'Cross-Play', which was performed in public at Darmstadt the following summer. I had composed other pieces but considered them simply stylistic exercises. We were given assignments to write a piece in baroque style, a fugue in Bach style, pieces for piano in Beethoven style, and I went further and composed a piece in Schoenberg style, which was not set by the professors, but just something I wanted to do. Another piece I wrote in Hindemith style. I never considered these as compositions: I was extremely conscious of the difference between imitation and originality, and much too intellectual to accept these plagiarisms of mine as original works, so studies in style they remained.

KREUZSPIEL did not just fall out of the sky. I was informed by a Belgian composer, Karel Goeyvaerts, about the work of Messiaen. There was a very special moment at this time when Messiaen's students - Boulez, Barraqué, Philippot, Michel Fano, Yvonne Loriod and Yvette Grimaux - persuaded him to synthesize the different influences that he had already incorporated in his own work; influences from the Viennese school, because they were more interested in them than in their own tradition of Debussy and Ravel, and the techniques of Indian raga and tala that Messiaen had learned from Indian music.

This led to the composition of a number of piano pieces, among them Mode de valeurs et d'intensités 'Mode of values and intensities', and lie de feu 'Fire Island', in which, following Messiaen's researches in early renaissance music, we find duration formulae and pitch formulae treated with equal importance, and the length of silences having the same importance in the musical structure as the measured durations of the sounds. We also find influences of his researches in twentieth-century music, in particular the music of Anton von Webern, in which the motif and musical themes are ultimately reduced to formulae of two notes, so-called intervals.

From Goeyvaerts I learned about this synthesis process in Messiaen's music. He also introduced me to Webern's music, which I didn't know before because no scores or records were available. Rend Leibowitz was the only one in Paris who owned scores of the Viennese composers, and we all shared and made copies of Schoenberg, Berg and especially Webern, by hand. Goeyvaerts explained the technique of Webern for me, and analyzed his own piece, the Sonata for two pianos, which I did not understand at all. This was terribly exciting, to discover that there was music which I couldn't make sense of. Webern's two-note formulae were reduced even further, extending the idea of a melody of tone-colours, represented by different instruments, or vowels, to one of giving each note a different duration, a different dynamic, a different pitch, a different form of attack.

For all of us who were students of Messiaen during this time this was the point of departure: a music in which all the possible characteristics were differentiated from note to note. The description 'star music was used casually by a music critic in Cologne, Herbert Eimert, after hearing these piano pieces of Messiaen, because the music sounded like stars in the firmament. The term 'punktuelle Musik' ('point music') was one I was using at the time.

At the 1951 Darmstadt summer school for new music Goeyvaerts and I played his piano sonata. Only the middle movement: the two fast movements were too complicated for me to learn so quickly. We played it in public during the open seminar on composition, and it was violently attacked by Theodor Adorno. At the time Adorno was considered to be an authority on the avant-garde movement: he had just written The Philosophy of the New Music and in this book had literally destroyed Stravinsky as a reactionary, Schoenberg being the only name he would accept. Adorno was actually conducting the seminar in place of Schoenberg, who was very ill and died later in the year, and he attacked this music of Goeyvaerts, saying it was nonsense, it was only in a preliminary state, was not through-composed, but only a sketch for a piece that was still to be written.

The second movement of this Sonata was indeed 'point music : just isolated tones, though nowadays it sounds strangely melodic. Adorno couldn't understand it at all. He said, there is no motivic work. So I stood there on the stage in short pants, looking like a schoolboy, and defended this piece, because the Belgian couldn't speak German. I said, but Professor, you are looking for a chicken in an abstract painting. That's when I began to have my doubts about intellectuals and so-called specialists, even among the avant-garde. It showed that even though Adorno had been a student of Alban Berg and had composed a great deal, and though he wanted to be known as a composer more than as a philosopher, he was not basically a creative person. A creative person is always most excited when something happens that he cannot explain, something mysterious or miraculous. Then he is very nervous.

Now a lot could be said about relationships between our work and the Modulor of Le Corbusier, who tried to lay the foundation of a new method of architecture based on the blue and red series of proportional measures. The word 'series in a context of structural design comes up again and again in architecture and other fields of constructivist art. We could speak of the strong influence on musicians during the early fifties, of certain books for the general reader by Einstein, or Heisenberg, of biologists like Weizsäcker, or Norbert Wiener.

There was similar thinking everywhere: reduction of the process of forming to the smallest possible element. When I use the word 'forming', I mean it in the sense of the crystallized result of the creative act, the form being just an instant in a process, and that what was happening among scientists as well as artists in the early fifties was that attention was increasingly focussing on the process.

According to Viktor von Weizsäcker, a German medical specialist and biologist, things are not in time, but time is in things (Gestalt und Zeit, Verlag Vandenhoek & Ruprecht, Göttingen, 1960). That is very important, in leading away from objective astronomical time to a consideration of organic, biological time. It was especially important for the musicians who started anew, after the war, working very systematically with individual notes. The evolution of electronic music did not happen by accident either, but literally as a result of discussions between Goeyvaerts and myself on achieving the objective of synthesizing even the individual notes, the timbre of the individual sound. The preformed nature of instrumental sounds - clarinet, piano, and so on - and of the way these sounds are produced, their physical limitations of breath, fingers and speed, were too restrictive for what we wanted to do. We wanted to achieve a unified musical structure, and therefore to make our own timbres, in order to find a coherent system to derive the macrostructure from the microstructure, and vice versa.

I use the words 'point', 'group', and 'mass in order to generalize what is happening in music, and to make it clear that each is a particular manifestation of a larger trend. Point music flourished for only a relatively short period. We should have composed many more pieces and gone into point music more thoroughly; there is still a lot to be done in the future and opportunities to be much more daring than we were. I should like to see point music being composed in the future in which individual notes and sound events are spread out into a much larger timespan than we ever dared to do at the time. But then, people were absolutely shocked. They said, what do individual notes mean? And we were naturally somewhat influenced by this. Even I thought the distance between notes was enormous. A silence of two seconds was something I could barely accept myself: I felt it was too long, the next note should begin. Nowadays a silence of ten or twelve seconds is something most composers are terribly afraid of, because the audience would start talking and not listen to the music any more. So the longest silences I have used in my pieces are up to a minute in length (though in my theatre piece ORIGINALE of 1961 I did include a silence of two minutes.) A radio broadcast would be switched off if that happened, because the engineers are instructed that when a silence is longer than fifteen seconds they have to switch off because something is wrong with the equipment. We have certain conven-tions about sound and silence, and these conventions are only changed very slowly and gradually.

The drawback of point music is that if one wants the music to be different all the time, it becomes very monotonous because trying to be different from element to element becomes something they all have in common. I composed a work for orchestra in 1952, called PUNKTE 'Points', in which the relationship of notes and silences is not always clearly audible, because some notes are longer than others, or louder than others, and they overlap with shorter and softer notes, and mask them completely. And if you cannot hear the softer sound, you cannot say how soft it is, or how long, or where there is a silence. There is a problem of how to give the elements equal importance which people can hear. For example, I would have to make the softest elements very long, and the loudest elements very short.

After PUNKTE I composed KONTRA-PUNKTE 'Counter-Points'. The term has a completely new meaning, because it literally means point against point, not melody against melody, which is what counterpoint has meant since the fifteenth century, and which is associated with a particular sort of musical mind. The beginning of KONTRA-PUNKTE is point music, with a maximum of differentiation. That's natural, because I had to start the composition with pure point music in order to break away, so to speak, from my own system. As the work progresses, more and more small groups appear, that is, sequences of notes played by the same instrument, and eventually the piano comes to the fore playing a whole mass of notes.

The second stage of that process of musical thinking that I'm trying to describe, brought the introduction of groups. It arose as a result of the composers having to be the teachers, and continuing to formulate a systematic approach to musical composition.

By group I mean the number of notes that can be separately distinguished at any one time, which is up to seven or eight. And they have to have at least one characteristic in common. A group with only one characteristic in common would have a fairly weak group character. It could be the timbre, it could be the dynamic: let's say for example you have a group of eight notes which are all different in duration, pitch and timbre, but they are all soft. That common characteristic makes them a group. Naturally, if all the characteristics are in common, if all of the notes are loud, high, all played with trumpets, all periodic, all in the same tempo, and all accented, then the group is extremely strong, because the individual character of each of the eight elements is lost.

So what is happening now is that more and more groups are combining with individual notes, and from that time on the point doesn't exist as a separate category any more, because it becomes one of the definitions of the group: if I have three notes, four notes, two notes, one note, five notes, six notes, then the one note is the smallest group. It's a question of context.

It might appear, from the way I am describing it, that I was following some divinely pre-ordained plan for twenty years. That was not the case: I did not talk in these terms at that time, it is only now that I can simplify things by classifying them in this way.

My composition GRUPPEN 'Groups', you may know is a work for three orchestras which surround the public in a horseshoe form. Each group of players has its own conductor, because they play in different tempi superimposed, which is impossible for one conductor and orchestra to realize. We say individual notes have their own durations; here, the important aspect is that the groups have their own modes of time, or tempi. That is something that has never occurred in Western music since the introduction of the common beat into music in order to control the vertical dimension of polyphony. In group compositions we come more and more to distinguish regions by their metronomical time, and I use chromatic scales of tempi corresponding to pitch, between MM=60 and MM=120, which is a ratio of 1:2, like an octave on the keyboard. Since then I've composed many times with chromatic tempi as composed with chromatic pitches.

The notion of group is transcended in GRUPPEN, just as in KONTRA-PUNKTE the notion of point was transcended by introducing groups. This is always happening, and is always very interesting. If one concentrates on something, or on a certain aspect, then one transcends it, because one cannot be content to remain permanently in a closed system.

What seems to be interesting in this context is this: whereas all music up to that historical moment, even the music of Webern, had been made by using certain Gestalten (figures), objects like a theme or a motif, and then transforming this object, varying it, transposing it, putting it into sequences, even destroying it or developing it further, in the music written since 1951 there was an explicit spirit of non-figurative composition. We tried to avoid all repetition of figures, and through this it became very clear to us that the way sounds were organized was the most important aspect, and not the particular Gestalt that occurred in a given moment.

The fact that certain notes were composed as points, and others as groups, that was what mattered: being recognizably points, or being groups, or a mixture of both. The groups could be completely different in their intervals or in their shape, and the points could be in different regions and of different overall quality, generally shorter or longer or higher or lower. I once made the comparison with sonata form, first-movement form in traditional music, where the best examples are the most through-composed, where the development is most advanced. As you know, the fifth symphony of Beethoven is always quoted as the example: there is just one figure which recurs all the time. As I say, always the same object in different lights. Whereas since 1950 it has been always new objects shown in the same light, and that light is, for example, a series of proportions.

There is a unity underlying all the different events which occur. That is why, when we listen to this music, we shouldn't become caught up too much with their differences, but try to sense and discover the underlying proportioning principle - the genetic principle - that gives birth to them all.