Xenakis in Kyoto (1997)
TAKAHASHI Yuji

1. On the Compositional Methods of Xenakis

When John Cage and many other composers started to seek
for the chance, indeterminacy or improvisation in the late 1950s,
Xenakis proposed the stochastic music.
It is a mathematical method to construct
unknown, but overall controlled complex sound movements
from the repeated random trials.
Without any musical premises
such as theme, tone row or rhythmic patterns,
using only Poisson distributions and other probability functions,
one can determine every phase
from the pitch, duration,
density (number of sound within a unit time), timbre distribution
to the overall structure (macro composition).
With this method Xenakis composed a series of instrumental music
starting with "Achorripsis"(1958) for 21 instruments
and then "ST10", etc. with a computer program.

On the other hand, when one considers the "complete continuum,"
without gap in time nor in space
it can be both Being and non-Being at the same time.
Articulating little by little this primordial space-time without void,
or total random state,
we arrive at the "sieve theory"
which provides the combined filters
based on the group theory and logical operations.
Pitches filtered through a "sieve" create a gapped space,
while the set of time points selected with a "sieve" creates rhythm.
Instead of traditional theories of scale, melody, harmony or rhythm,
such a method allows one to compose
more general, abstract and complex events.

In this way, from the complete randomness (chaos)
an order is established through strict logical and mathematical methods.
In the computer sound synthesis,
unlike the usual way of staring from the most elementary sine wave
"to create infinite variations through a finite number of operations,"
Xenakis sought the method of gradually providing a regularity
to the random waves created with various stochastic functions
(dynamic stochastic synthesis).
This is the computer program GENDY which creates every phase
from the sound synthesis (micro composition)
to the overall structure (macro composition)
through the accumulated stochastic processes.
It is employed to compose "la légende d'Eer" for 7-track tape,
the music to the spectacle of sound and light "Diatope" (1978)
with optical patterns derived from complex numbers
and stochastic calculations
of 4 laser beams and 1600 flash lights reflected on 400 mirrors,
performed in a red tent having the shape of hyperbolic parabloids
in front of the Ponpidou Center.
Such complicated calculations cannot be processed in real time
with the computer of today,
and it is almost impossible to estimate the result.
The creater of this program, however, seems to be interested
rather in finding out the musically efficient initial conditions.

In CEMAMu
(Center for the Studies in Mathematics and Automation of Music)
established in the building of
French Ministry of Telecommunications in Paris,
another system, UPIC (Unité Polygogique Information), was created.
It is an equipment to convert the lines and figures
drawn on the digital board into sounds.
Many pieces by Xenakis and other composers using this system
have been performed.
In addition to composing, it can also be used
for children's music education
as well as the acoustic experiments and musicological researches.

The ideas and musical theories
which gave birth to these methods and systems
may have their sources
in ancient Greek philosophy
(especially Pythagoras, Parmenides, Plato and Epicurus),
theories of interval of ancient Greek and medieval Byzantine music,
and the modern mathematics of probability and group theories.
But the violent movements of timbre groups created with those methods
could be the memory of the resistance movement against Nazis
and the following Civil War in Greece.
Or he may have sought the way to keep those events in memory,
found such technique,
and developed it into the theories and ideas.
Staring from nothing or minimum premises,
the strong will of creation tries to construct the entire work
all at once without any intervention
with the ideal automaton which could realize this will.
It can integrate the science and art
"creating a catalyst for the individual thrown into the dark space
to arrive at the higher intelligence
in order to see through and understand the world"
Music is not a language.
it is likened to a gigantic rock
on which enigmatic ancient symbols are inscribed
and can be interpreted in various ways.
Composing music is "to endure the trials of fate and to question Being."
It is also said to be an "atheistic asceticism"
to reach beyond the limit of the human intelligence.

Once possible combinations
and the variety of dense sound complex ("clouds of sounds")
are created through theories,
the actual composing in many cases
seems to consist of the graphical montage from these forms
freely drawn on the two-dimensional space of pitch and time.
The crossing glissandi
and the sound space made of numerous scintillating points
of the early orchestral works of Xenakis
influenced the Polish and Japanese composers of 1960s.
Later he composed with a huge wall of sounds with many entangled lines
("Aborescences" or "Medusa's hair").
The intervals and timbres consisting these lines
are reminiscent of the East Mediterranean traditions.
It seems as if he keeps a distance
from the West European contemporary music.

 

2. What I learned from Xenakis

In the suburb of Berlin, I remember,
from your house which does not exist anymore,
walking along a path in the forest to the post office,
you gave me a lecture on the history of ancient Greek philosophy
from Parmenidean 'Being,' Pythagorean 'number,'
through Platonic 'polyhedra' to Epicurean 'chance'.

I also remember what you said in a cafeteria at the New York Airport
as if it were just yeaterday,
"Human being is bound by its own perception of time and space.
Is it possible to escape from the labyrinth in this sad glass box,
and be awakened to Being
which envisages the 'now' as the 'forever'
and the 'here' as two hundred million light years away?"

At the only one formal lesson you gave me in Berlin,
your criticism of my piece composed with stochastic calculus
and timbre structure:
"There are two redundant sections in this piece.
Shall I lend you an eraser?"
I interpreted it as the method does not always guarantee the result.

Thirty years later, in a studio in Paris,
you played back the sounds of less than one minute,
which computer had calculated overnight,
then changing a single figure,
reset the computer for another calculation
and said:
"I am testing each data until I find the efficient combination."
At that time, I renewed my understanding that
not seeking the universal which manifests itself beyond chance,
you were looking for the road sign
to get out of the labyrinth of time and space
where we fell into,
looking for the Moebius ring
which returns from 'chance' back to 'Being' at the origin
by reversing the ancient history of phylosophy.
Is it but another misinterpretation?
With probability, as for Pascal,
was God or the Absolute at stake?

Could music,
that is a gigantic rock with enigmatic ancient symbols inscribed,
be a clue to recover Parmenidean 'Being'?
For an individual, having no certaintity anywhere
and only drifting in the dark universe,
where is the assurance that the method to construct the world
once again , facing the ruin of the history of ancient philosophy,
is not a mere illusion?

In 1962 you composed "Polla ta dhina" for children's chorus and orchestra based on the song of Choros in Sophocles' "Antigone".
There, the word 'dhinon' or 'deinon' is translated as
something terrifying, strong, difficult, and furthermore, skillful.
Heideggar has translated it as 'unheimlich',
that is 'who cannot stay at home.'

An adventurer is 'to deinataton,' the superlative of 'deinon'.
He sets out into the difficulties, and creates something terrifying
with violence, with skill.
It, however, is the same as being thrown into the difficulties,
exposed to the violence of the world, lured toward nothingness,
and never invited to the home and hearth of happy people.

Music, thus, is able to touch the world.
Coming in contact with the suffering of the world is
the process unavoidable to an adventurer.
Suffering of the world gives the authenticity to the sound of this music.

November 12, 1997

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