2) Read a graph
Now we are going to look the graph of the last section of Nomos Alpha: Xenakis uses this graph to compose, thereafter he has translated the on a music sheet, the score (example 6)
conclusion : After describe the general historical and musical context of the Nomos Alpha creation. And explain somes aspect to the creation and conception of the Xenakis music. Now we will see how Xenakis uses this different concepts in Nomos Alpha.
go to Nomos Alpha (1965-66) : Analysis presentation
B-/ Experience of Xenakis' music: an Avant-garde research
When he arrived in Paris in 1947, Iannis Xenakis attempted studying composition with various professors, none of which however, correspond to his personality: Honegger at the Ecole normale de musique, and later Milhaud. But in 1951 he meets Olivier Messiaen. It was a revelation for Xenakis, and Messiaen invited him to audit his classes in the Conservatoire de Paris. During this classes Xenakis met notably Karlheinz Stockhausen.
The first compositions of Iannis Xenakis date from 1950-51, at this period his language was very close to Béla Bartok or Zoltan Kodaly. As we can hear in Dhipli zyia duo for violin and cello composed in 1952 (example 1). The pieces of this first period are not published at the time, for example this duo was played for the first time in 2000. And these early works are totally different from the rest of his compositions that he will write from Metastasis (1952-53). But there are already some elements who will be later important parameters of Xenakis music as: the energy and more discreetly, his taste for traditional musics and modes.
1) "A music unlike any other"
Iannis Xenakis publishes in july 1955, "La crise de la musique sérielle" (The crisis of serial music) in the first issue of the Gravesaner Blätter. In this article, Xenakis denounces the very principle of the series and the polyphonic organization that is derived from it. For Xenakis the serial music has become so complex that it is impossible for the listener to hear all the polyphonic lines, and to understand this music without making an analysis of the piece. For him the serial music's conception is too intellectual. The Xenakis approach is totally different: for him the most important thing is the “masses of sound”, and the global sound perception by the listener. His music is at the opposite of the polyphonic music, there is no counterpoint but only sonorities juxtapositions. It is interessant to notice the difference between the sound and the sonority in Xenakis mind. The sounds are only an element of the sonority, as well as the rhythm. When he writes a very complex rhythm superposition, it's not to make a polyrhythmic effect but just to created special sonorities. In fact, all parameters serve the masses of sound creation.
Consequently, most of Xenakis' research is focused on finding new sonorities with radical modernity. Jean-Bernard Mâche, specialist and friend of the composer, defines Xenakis' works as "a music unlike any others"1. This music has a profound impact on the audience. The listener is totally immersed in many sounds as “geological noise that gushes in him”2 said Maurice Fleuret. Indeed, Xenakis has a taste for the harsh and “primitive” sonorities, what he calls the "granulation". In addition, Xenakis will work to develop a spatialized music with a sound conception in three dimensions, the pitch correspond at the vertical, the length at the horizontal and the intensity at the depth. In this way, he wrote several spatialized pieces like Retour-Windungen 1977 for 12 cellos. This piece was written for the 12 cellists of the Berliner Philharmoniker and it was especially thought for the hall of the Berlin Philharmony and it's fantastic acoustic. The twelve cellists are positionned in circle on the stage, and the audience can sit around the circle or inside. This piece is for the listener an incredible experience: we can hear the masses of sound in motion passing between the circle of cellos , giving us a real feeling of spatialization.
3) The "sieves" theory
The "sieve" theory is a very complicated concept and I do not have the necessary mathematical knowledge to explain exactly how it works. However, I can explain in which way Xenakis used it in his composition.
The importance of the intonation.
In Nomos Alpha, as in others piece of this period, Xenakis attached a great importance to the pitches and the intonation, as Makis Solomos explain it. After setting out the structures of pitch in Greek antiquity and Byzantine music at length, his article "towards a Metamusic" introduces the theory of pitch "sieves", which is to say, scales. He spent a lot of time on sieve-construction for Nomos Alpha. In the example 7, we can see the calculation sheet of the "sieves" of Nomos Alpha. It is a huge precision work. Pitch, then, is a crucial element in Nomos Alpha.
The use of "sieves"
The “sieve” gives to Xenakis a reservoir of pitches. To compose Xenakis chose in this reservoir the note he wished to use. In example 8, we can see the reservoir of pitches of Jonchaies (1977) a piece for 109 performers. In Jonchaies, the sieve has an ambitus of four octaves and a half and there is no quarter of a tone.
But he had a larger choice in Nomos Alpha, indeed, the “sieves” used in Nomos Alpha have an ambitus more than seven octaves, with lot of quarter tones. In all, he used twelve several “sieves” in the whole piece.
In this type of piece the main element used is the glissando. The X-axis (the horizontal line) corresponds to the time, and the Y-axis (vertical line) corresponds to the pitches. In Pithoprakta there are 46 separate solo parts, each line on the graph corresponds to one of these solo part. The graph is the main process of the composition, thereafter Xenakis will just have to “translate” on music sheet.
Especially with composition with graphs, Xenakis worked on glissandi speeds: the steeper the slope on the graph, the faster the glissando will be. For the performer of the Xenakis music it's important to know how to play the glissandi rightly. You can not play the glissandi like in Mahler's music, it is as in the graph straight line segment. That means the glissando speed must be constant between two notes (example 4) as it show in the video 3 How play the glissando. Sometime, the slope could be null, and in this case the line on the graph will be horizontal. Consequently, on a music sheet it will be a hold note. This aspect is important as we will see later in the chapter about the basic sounds.
I ) Iannis Xenakis music language
What is the main aspect of Xenakis's music ?
A-/ Some biographic information
Xenakis began to discover the music when he was ten in a English-Greek academy on the island of Spetsai. Later in Athens in 1938, he started composing and studying with Aristote Koundourov analysis, harmony and counterpoint. However, in this time the music was not his main priority. Iannis Xenakis has an another passion, the mathematicals and the architecture. In 1940, he succeeded in entering the Athens Polytechnique Institute. He studied there until January 1947 when he defends his final thesis on “Reinforced concrete”. During many years he had an semi-clandestine existence, he joined the Greek Resistance in 1941 and was imprisoned several times. And on the 1st of January 1945, a English shell hits him, smashing his jaw and poking out his eye.
In september 1947, Iannis Xenakis arrived in Paris. He fled from Greece with a falsified passport, intending to end up in the United States but finally he stayed in France. In Greece, he was given the death sentence in absentia for political terrorism. His father and brother were sent in prison. Xenakis will never be able to return to Greece until his death.
In Paris, it was his architectural skills that gave Xenakis his main job. He was hired as an engineer by Le Corbusier. He worked on several projects of the renowned architect especially Le Pavillon Philips for Brussels World Fair in 1958. This creation was a first meeting between music and architecture. On the one hand, Xenakis used his musical research on sound, including the graphical structure of textures glissandi Metastaseis (1952-53) to draw the blueprints of the Pavilion; inside, images and lights were to be projected and a spatialized electroacoustic work were to be proposed to the visitors/spectators. On the other hand, Edgar Varese composed an electronic poem specifically designed for the architectural properties of the building imagined by Xenakis.
2) The forms in Xenakis' music
On the contrary to the Webern heritage or in serial music, there is no concept of development in Xenakis' music. In serial music, the series is a fundamental element that structures the piece and ensures its coherence. The forms of Xenakis' pieces are quite simple, "we always know where we are"3. There are just juxtapositions of different independant sonorities with silences between each of them, as we can also see it in Nomos Alpha (example 2). In Xenakis' music the coherence of a piece is ensure by the process used to create the each sonorities. It is this process that will give the sound cohesion to the piece. Therefore, these are non-narrative forms, there is no "dramatic" progression. Even if some pieces of Xenakis give the feeling of a climax, it is actually a choice of Xenakis to place here more "powerful" sound than others. In any case, it is not a consequence of the form conception.
3)The formalisation concept
In his “avant-gardiste” research process, Xenakis will use many mathematical concepts to create new sonorities. It was often said during the fifties that Xenakis was a mathematician than a composer, and his piece more the result of calculation than a the resul of a composition process. Of course, this is a caricature: in fact his mathematics is a way to create new sound materials that a human mind could not imagined. In 1962 Xenakis developed especially the software program ST, with which he composed 4 pieces. This program is based on probability calculations (this is what Xenakis calls the stochastic music). Xenakis used the ST programm to create his “clouds of sound”. But the program gives only to him a catalog of sonorities. Like a "classical" composer uses the 12 notes of the chromatic scale, Xenakis composes with his sonorities. In addition, more often than not only some parts of the pieces are "formalized", that means composed with mathematical concepts.
From the sixties, Xenakis intended to compose a piece in which all the parameters would be formalized. There are five parameters in a sound: the pitch, the duration, the intensity, the density and the tone. This work will result to Nomos Alpha. where he will use several mathematical concepts like the groupe theory, and the “sieves” theory.
4) Context of the genesis of Nomos Alpha
In 1963-64 Xenakis lived in West Berlin on a grant from Ford Foundation, finnaly he was a recognized as a composer. During these years, thanks to the grant, Xenakis has plenty of time to compose a music and writes some articles and books. He wrote in 1964 his essay: La ville cosmique (The cosmic city). It is a text on a utopian vision of urbanism. In order to prevent any further suburban sprawl, he proposes a model of gigantic towers, several kilometers high, susceptible of containing high density human populations. Indifferent to climatic variations, this model would have a universal vocation. Itis also in Berlin that Xenakis is going attempt to create a new ambitious music. He was interested in the tonal structure in Demonic music and Byzantine music. He continued to use mathematics, he wanted to create a music where all the sound parameters would be formalized. There are five parameters in a sound: the pitch, the duration, the intensity, the density and the tone. These research will lead to Nomos Alpha.Indeed, "Nomos Alpha is the most "formalised" piece"4.To support his arguments his approach, he wrote two articles Towards a philosophy of music , and Toward a methamusic. Another important aspect of this new compositional idea is the distinction between the in-time music and outside-time music. In this extract he explains us what are these two type of music:
"It is necessary to distinguish two natures: in-time and outside-time. That which can be thought of without considering a before or an after is outside-time. Traditional modes are partially outside-time, logical operations or relationships imposed on classes of sounds, intervals, characters…are also outside-time. As soon as the discourse contains a before or an after, we are in-time. A series is in-time, as is a traditional melody. All music, in its outside-time nature, can be instantaneously delivered, struck. Its in-time nature is the relationship of its outside-time nature with time. In terms of a sonorous reality, there is no purely outside-time music; a purely in-time music does exist, it is rhythm, in it’s purest state."
from Preuves, n° 177, November 1965, p.34
As it were, the in-time music is the narrative music and the outside-time music is the music that you perceive instantly. Xenakis, with his taste for the global perception of sound, defends outside-time music, contrary to the serial music, for example, which is an in-time music because the serial concept gives an order.
C-/ The methods of compositions used in Nomos Alpha
Xenakis used several mathematical concepts and composition tools to write Nomos Alpha. For the tones, the durations, the intensities and densities he used the group theory. In this work I'm going to talk later about the group theory in the second part in the section the organisation of the basic sounds: the group theory. Here I intend to present more particulary two main tools of Xenakis' composition: the composition with a graph and next the “sieves” theory.
1) The composition with a graph:
Many pieces of his first composition period were written from a graph, as Metastasis (1953) or Pithoprakta (1955-56). As some pieces are entirely composed with a graph, though others only use the graph for some passages (like in Nomos Alpha), and sometime we find the same graph in several pieces or in architecture plan. He used again the Metastasis to draw the plans of the Pavillon Philips.
Here is the graph of Pithoprakta, example 3 :
This graph works the same way than the previous ones, the X-axis (horizontal) corresponds to the time, and the Y-axis (vertical) corresponds to the pitches. Here the unity is the bar. At the beginning, we can observe two lines, both starting on the same G. The first is an ascending 0.75 tone scale, froms a G (ground) and ending on a E (mi). The second one played in same time is a descending whole tone scale, starting on a G (sol) and ending on a C# (do#). If we look the score we can see these two polyphonic lines.
Example 7: sieves of Nomos Alpha.
Calculation sheet before the translation on a music sheet before the translation to a standard notation. I didn't manage to figure out how this translation works.
