Nomos Alpha of Iannis XENAKIS for cello solo : guide for performers [NOMOS ALPHA of Iannis XENAKIS for cello solo: guide for performers

Name: Josquin Buvat Main subject: Cello Supervisor: Patrick van Deurzen Master circle leader: Martin Prchal Title: Nomos Alpha of Iannis Xenakis: guide for performers Research question: how build one's interpretation of Nomos Alpha ? And practice it? Summary of result: Today, Nomos Alpha (1965-66) is greeted with loud applause each time it is performed. And the piece is considered one of the greatest pieces of the 20th century's cello solo repertoire, still it's also one of most difficult and “avant-gardiste”. Furthermore, the piece remains 'Difficult' for the listener: it is submerged in the torrent of 144 micro-events, an extreme fragmentation accentuated by the presence of many silences. That's why Nomos is only rarely played. Since the piece's creation in 1966, lot of cellists were aware of the existence of Nomos Alpha. Many cellists had the score, but hardly anyone played it. It seemed important to me to begin my research with an analysis of the piece and an explanation of the historical musical context of that time. Indeed, Nomos alpha is one of Xenakis’s most ‘formalised’ pieces, the structure and all the parameters are calculated down to the last details. For cellists, these knowledges are essential to understanding the piece and making the necessary choices to build its interpretation of Nomos Alpha. In last the last part of this research, I have maked a guide for performers for the cellist who would like to play Nomos Alpha. For this guide I will try to concentrate on some essentials aspects of the piece for the performers. To illustrate this guide I did an critic comparative analysis of the different versions of the piece. And finally to complete this guide I did some videos of tutorials on how to practice the piece. Biography After completing his studies at Pôle Supérieur Paris Boulogne-Billancourt in Michel Strauss's cello class, as well as his Bachelor's degree in Musicology at Paris-Sorbonne University, Josquin Buvat continued his studies in a Master's degree in Performance at the Koninklijk Conservatorium Den Haag. Josquin gives a special place to modern music and contemporary creation in his repertoire. Since 2017, he has been a member of the Nomos ensemble, with which he has appeared at several festivals, including the Presences festival at Radio France, a concert that will be recorded. He performs regularly in chamber music as well as in orchestra, with Les Siècles, Ensemble Appasionato, Ensemble A-letheia the OJIF, the JOEHB. In addition to his musical activities Josquin is also involved in the field of associations, for two years including one as President of the Students Office of the PSPBB.

Path A :
Formalized compositions
Fragmented music
Micro-events

Why this title ?

In greek Nomos could have several meanings:

“The rule”, “the law”: this understanding refers to the use of mathematics for the conception of this piece, acting as a rule governing the whole work.
“Mode” or sometime “special melody”: this aspect is less obvious than the first one. But as we have seen in chapter on the context of the genesis of Nomos Alpha, we know that during the period of the composition, Xenakis had a special interest for the demonic music -the ancient greek music- and more especially for the working of the scale system. Using the sieves theory is for him a method to create many scales -modes- in its own way.

In this preface we find some important notions to understand the piece, that we are going to develop. On one hand the “extra-temporal architecture” and on the other hand two main concepts - “rules”- of Nomos Alpha: the “theory of groups” and “theory of “sieves”".

The "sieve" gives the "store of pitches" to Xenakis for the first three sections

First part we listened

Nomos Alpha (1965-66), analysis presentation

Source:Fernand Vandenbogaerde,
analysis of Nomos Alpha of I.Xenakis

A-/Initial contact with Nomos Alpha: listen to it!

As we have seen above, the perception of sound and the experience of the listener are very fundamental elements of Xenakis' music Therefore, I invite you to listen to the first part of the piece with the score before talking about the analysis of Nomos Alpha. Recording of Christophe Roy

C-/ The Path A, composition with the basic sounds

B-/ The Form

Beginning of the second section

Beginning of the third section

New cube position for the second section

1 ) The macro-strucure : the Paths

Nomos Alpha is comprised of six parts. We just heard the first of them which is the first line of this table. To compose each part, Xenakis uses two Paths :

the Path A: the principal one, 6 parts each comprising 3 sections
the Path B: 6 intermezzi between the Path A sections.

Each path has his own conception. The path A is the first "type of music", energetic and fragmented, composed with micro-events. In this path, all the parameters are formalized and calculated. Whereas the path B is the second type of music, in a more "free" conception. Xenakis usually uses in Path B long notes and explores the extremities of the cello registres.

Now we are going to look at the group theory in the next part: The organisation of the basic sounds: the group theory

To compose the path A, Xenakis uses eight basic sounds and organizes them with the theory of the groups: he uses here the 24 cube-transformations onto himself in the space. The eight basic sounds correspond to the eight apexes of the cube, and each transformation gives to Xenakis an order of appearance different from the basic sounds. In a same way, this process is used to organise the intensities, the durations and densities of the sounds. We will see later how these cube-transformations work. Now, we are going to look on the eight basic sounds.

The eight basic sounds:

The basic sounds are the “atoms” of the piece,sincethey are the ones who give Nomos Alpha his special sonorities and his indentity. We can find more informations about the creation and the transformations of these basic sounds on the page The basic sounds : theNomos Alpha's sound universe. Here is a list of the eight basic sounds with their symbols:

Comments: In this first part, we heard two very contrasting types of music:

The first: very energetic and fragmented, with a lot of rests between the different sounds, the Path A.
The second, just at the end: more continue and soft with very long notes, the Path B.

Now let's see how these two "types of music" are organised in the general structure of Nomos Alpha

Path A is constructed as a juxtaposition of micro-events that are in fact the different basic sounds, which produces a very fragmented music. This is accentuated by the presence of a lot of long or short rests between these micro-events. Therefore it's easy to see in the score the delimitation of each of them. You'll find in each section the eight basic sounds in the order given by the cube-transformation. When the eighth is played, a new section from a new cube transformation start.

"Symbolic music for solo cello, possessing an extra-temporal architecture based on the theory of groups of transformations. In it use is made of the theory of "sieves", a theory wich annexes the congruences modulo z and which is the result of an axiomatic theory of the universal structure of the music. This work is an act of homage to the imperishable work of Aristoxenes of Tarentum, musician, philosopher and mathematician and founder of the Theory of Music; of Evariste Galois, mathematician and foundre of Theory of Groups, and of Felix Klein, his worthy successor. Written for Siegfried Palm, it was commissioned by Hans Otte of Bremen Radio."

preface to the part writte by Iannis Xenakis

1 : ataxic cloud of sound-points

2 : Pizzicati ascending or descending

3 : Pizzicati on one note

4 : ataxic field of sliding sounds

(Or sound sustain with granulation or battement)

indication of the cube position

2) The Path B

Initially, "Xenakis wanted to make 6 paths and formalize them all, as he did for the Path A"1. But it would have been a huge work, and a too long piece. That's why he chooses to do just two paths and to formalize only one of them.

The sections of the path B are quite short, acting as intermezzi between the sections of Path A, contrasting with their long notes. The composition in the Path B is very free. The only rule is the pitches because Xenakis uses the sieves theory. But as we saw in the first part, the sieves give Xenakis a "store of heights" and every sieve used for Nomos Alpha is very big, more than seven octaves.And he makes wide use this freedom and these huge ambitus, and pushes the boundaries of the cello like the follow example:

Comments about the basic sounds organisation:

the order in the first section is: 2314 6758
the order in the second section is: 5687 1243

Form table of Nomos Alpha

5 : relatively ordered ascending or descending field

of sliding sounds

6 : Glissandi ascendin or descending

7 : Atom represented on a cello by interferences of a quasi-unison

8 : glissandi contraries

Preface in the score of Nomos Alpha by Iannis Xenakis

Example of Path B. Xenakis combines the two extremities of the cello's registres. On one side, very high with the harmonic sounds, and one the other, with the C string tuned one octave below.

First two pages of Nomos Alpha

Symbols abstract to : Fernand Vandenbogaerde,
analysis of Nomos Alpha of I.Xenakis2

Table abstract to : Fernand Vandenbogaerde,
analysis of Nomos Alpha of I.Xenakis3

Path B:
Free composition,
continue music

end of the first part

First section: containning the 8 basic sounds

Second section: new position of the cube. containning the 8 eight basic sounds

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