Yannis Xenakis was a Greek-French
avant-garde composer, who was
a music theorist and also
an architect. He worked as
an assistant of the famous French
architect Le Corbusier for many years.
And he was an engineer and a performance
director. Xenakis pioneered the use
of mathematical models in music,
such as the application of set theories,
stochastic processes, game theory and
he was extremeley influential in
the development of electronic music
in computer music.
I am going to describe and discuss here
two pieces of Xenakis: one that is
actually a piece meant to be, and written
for, an architectural space, where
he combines the two expertise
of engineering, architecture and music.
Xenakis left numerous writings about music
and the formulations of a compositional
structure aesthetics for music, that are
highly mathematical and very interesting
to read if one has an interest in
high-level mathematics. But he also left
us with some ideas on how we can formalize
music in terms of different elements, and
here, it kind of connects with what I was
talking about when we discussed the work
of Pierre Boulez.
So for Xenakis, formalized music starts
with an initial conception, that is
the idea, the framework, the nominal
content of the composition; a definition
of the sonic entities and their symbolism
that need to be part of the communication
of the composition itself, so sounds,
electronic sounds, musical instruments,
ensemble, or if it's electronic music,
the kind of sounds and kind of effects
on the sounds that one wants to utilize
in the framework of the composition;
the definition of the transformation of
these entities, so in a way Xenakis was
not a follower of integral serialism,
but again in composition - and you will
see this also in future units - operations
on the sonic elements are always used by
the composers so there is an aspect of
manipulation that is common to all music,
basically.
And then, he defines those two scales in
the composition. And this is interesting
because it is the first time that we see
in this music and complexity course,
the concept of microscale and macroscale.
So on the microscale, or the microcompo-
sition, this is the choice of the way in
which the elements are related within
a particular aspect of the composition,
and so we go from one note to another
according to some specific rules.
And then there is a macro aspect, that is
putting all of this together into
the larger framework, that implies
decisions at a higher level from
the composer to determine the structure
of the piece.
Then, once you have done all of this
in again a feedback loop, you go from
the microscale to the macroscale
continuously in the composition,
and then you end up with a final product
that you put to the score, recording
the performance and so on.
Now, I want to stress again that, although
these ideas were defined by Xenakis for
his own work, they apply to all of music
composition, whatever genre, whatever
culture and whatever function
the music has.
The first piece that I encourage you
to listen and try to understand, is called
Pithoprakta, that in Greek translates to
"actions through probability". And here,
Xenakis actually uses a physical model,
the statistical mechanics of gases,
and draws an analogy between the movement
of a gaz molecule through space and
the movement of a string instrument
through its pitch range. And so he maps
these two processes in this composition
and it basically utilizes also a concept
like temperature and pressure to modify
the way in which this virtual molecule
is mapped into the musical space.
And it's interesting to see - so now we
can listen to this piece, you'll find
a link in the PowerPoint of this video.
In this page, you see the graphic
notations and the notes that Xenakis
used in the composition. On the right,
we have these graphs that are actually
mappings of a molecular motion through
space and how these trajectories are
mapped to a particular
pitch range or pitch space,
and on the left is a translation of all
these behaviors and all these graphical
analyses into an actual score, written on
staff and using a traditional notation
for the composition.
The second piece that I want to introduce
you to, is called Concret PH and is
a piece that Xenakis wrote in 1958 for
the Philips Pavilion of the World's Fair
that was actually designed by Le Corbusier
and Xenakis himself as his assistant.
This is a piece of what we call "musique
concrète", that means music that is made
using ordinary sounds that are recorded
and manipulated, and it's a large scale
composition that was heard by the audience
in entering into this pavilion that you
can see at the bottom right picture
of this slide. Inside the pavilion, there
was another electronic music piece,
again very pioneering concept,
from another very influential and famous
composer of the 20th century,
Edgard Varèse and this piece is called
Poème électronique that you can find
in many different places, YouTube, or
any streaming app, if you want to listen
to it. The sound source for Concret PH is
the recording of burning charcoal, so that
is the concrete sound that Xenakis uses
for this composition, that is transformed,
and there are overdubbings and there are
effects applied to it, remember this is
1958, there was no digital sound
processing, everything was done
analogically using actual tape, recording
tape, in slicing and gluing different
pieces together.
The other novelty and interest for this
piece, is that for the time, it was
broadcasted over more than 400 speakers
in this space, and so it was the first
example of using sound reproduction
to create an immersive space of sound,
and so in many respects this is a very
influential and kind of pioneering
musical experience for Xenakis.
And you can listen to the recording of
this on the PowerPoint, and also in
the associated notebook, I'll guide you
through a version of this piece that is
obtained by purely algorithmic means
in Python.