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.