In 1967 Xenakis becomes teacher of
music at the Indiana University, in Bloomington, U.S. He' not
completely keen on teaching, but he accepts since he wants to realize
a centre of research devoted to the relationships between music and
mathematics. Unluckily almost all of the funds are redirected for the
Vietnam war. In 1966 the composer resigns, and he comes back to Paris
where he found the CEMAMu (Centre d'Etudes Mathématiques et
Musicales, a non-profit organization dedicated to the study of the
application of information technology to music). During these years
he will realize the Polytopes, architectural spaces that today would
be defined 'multimedia centre' and 'site-specific', dedicated to
performances involving compositions made of light and sound.
The Polytopes (from the Greek
'poli'=multi and 'tòpos'=space) represent an idea of art that
integrates sound, light and space. In that sense, polytopes are not
only ancestors of the soundart, since the sound sculptors of our
times are always working in a given space, and they sculpt it after
choosing it, not before projecting it, and this is Xenakis' most
complete realization, today not overtaken. The architecture of
specific spaces created to enjoy live music and the creation of its
own tools so to realize electronic music come together in Xenakis'
mind and activity. When reading his writings of the 1980s, it is
clear that what pushes the composer towards this form of total art is
the same anxiety he has since the days of stochastic compositions:
"Can we do tabula rasa of all the known compositional rules?",
and "what a rule is?".
Since 1952 to 1956 Xenakis elaborates
in first person in Fortran language a program in order to obtain
scores that realize on cartesian axes analitic geometry, composing
the pieces of the ST Series. The use of the computer as a
compositional tool helps him to overtake 'the art of the fugue',
which is transforming a theme following the rules of transposition,
augmentation, temporal decrease, etc. inventing, instead, his own
musical forms. The ST Series comes from applying to the stochastics
the 'Markov chains' (responsible of the developing of computer
science and of linguistics, at least until Noam Chomsky proved they
were useless in that field).
Not only probability, but also
repetition, determinism, so to measure the symmetry of a composition
(Nomos Alpha is an example, again): 'repetition' is the definition of
one of the smallest conditions to have a 'rule', following Newton.
Nomos Alpha is also the best example of 'symbolic music' realized by
the composer. Unsatisfied by the structures of Western music, for its
limits in polyphonic development, as far as the time logic, Xenakis
points at the popular music, in particular the Bizantine popular
music, for his use of the pedal in vocal polyphony so that it creates
a new tension, the same that will occurr in the music of Debussy or
Schoenberg. The composition is divided in 24 sections, and it is
composed by two layers: the first is composed by a group of 24
elements, while the second, in contrast, is no more determined by the
group theory but it follows a continuous, evolving movement.
Commissioned in 1965 by Radio Bremen for cellist Sigfried Palm, and
dedicated to the mathematicians Aristossenus, Evariste Galois and
Felix Klein, Nomos Alpha represents perfectly the dialectic of
transformation of time between en temps and hors temps from which the
idea of 'amnesia' comes ('to leave at the entrance the emotional and
qualitative burdens passed on by musical traditions' taking under
exam only 'the abstract relationships in every event' [Iannis
Xenakis, Musiques Formelles, 1963]) and that represents the attempt
to recover in music the 'ubiquity' typical of subatomic physics.
The Polytopes are the places in which
to present music not only composed, but also played by computers. The
Polytope of Montreal has been realized in 1967. Commissioned for that
year Expo, it has been realized with wide concave and convex mirrors
suspended to electric cables reproducing 'visual melodies' through
lightning sources. The music created for the polytope will lead to
Kraanerg, a piece of 75 minute of lenght, without any inner
subdivision, including instead 20 moment of silence of different
lenghts integrals to the development of the piece itself. The first
section of Kraanerg contains equal portions of live orchestra and
recorded tape, the second section is mostly live orchestra, and the
third is almost entirely recorded tape. Performed for the first time
at the National Arts Center in Ottawa in 1969, and conceived as
accompaniment for Roland Petit's ballet company, Kraanerg has been
performed until 1972 and then forgotten until 1988, when a new
version coreographed by Graeme Murphy took it at a new peak, with a
performance almost exclusively instrumental. The title of the piece
comes from Greek, and it means 'accomplished act', referring to the
youth movement of those years and the socio-political changes wished
for.
The Polytopes diverge the one from the
other for the spatial-temporal disposition of music and listeners.
The Polytopes of Persepolis and Micenae are the only ones with a
fixed stationing for the listeners while sound and light sources are
dispersed. Works as Terretektorh and Nomos Gamma presuppose, on the
contrary, the listeners to be dispersed between the musicians. The
Polytope of Montreal sees the audience at the center of the
architecture, with the light and sound sources around the audience.
During the 1970s Xenakis teaches
composition and gives public lectures. He creates an atelier as the
IMAMu at the University of Indiana, he teaches at the Sorbonne since
1973 to 1989, at the Gresham College in London since 1975 to 1978,
and he can see his works performed even in Iran. His last work,
O-mega, is accomplished before Alzheimer prevents him to compose. He
falls into a coma at the beginning of February, 2001 and he dies in
Paris few days later.
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