Pierre Boulez was a French composer,

conductor and theorist who was also

a prominent figure in the music of

the 20th century and responsible

for a lot of innovations,

but also the establishment

of institutions that champion experimental

and new music. He was the founder and

has been the director, or was the director

for many years of IRCAM, Institut de

recherche et coordination

acoustique/musique in Paris, that is

still a landmark institution at the

forefront of musical experimentation.

Boulez was a composer that worked within

an aesthetic that we call the integral

serialism. Integral serialism is a way of

composing by making precomposition

decisions about the sequence of the notes,

the sequence of the rest, the sequence

of the dynamics, the sequence of all the

musical parameters and then strictly

adhere to these sequences, for the

production of the composition.

Of course, you can read a lot, I mean

you can find online a lot of information

about integral serialism, you'll see in

this example how these techniques

are established and evolve.

We are going to listen and analyze a piece

that is called Structures for two pianos

that was written in 1955. There are

actually two versions of this, we will do

Structure I (one), that is the first of

two from this series. And we can listen to

it here, in this PowerPoint, or on YouTube

or any other music streaming service.

In this slide, I am reproducing a few

important points about the way in which

Boulez uses automation and decisions as

two competing forces in the creation

of this piece and this analysis was

done by another very important influential

composer of the 20th century,

György Ligeti and he kind of summarizes

here this process of composing based

on the strict rules, and how the composer

navigates the rules

to create a piece that is interesting

and enjoyable.

So there are decisions that are made by

the composer like the selection of

the elements, the way in which elements

are arranged, and the choice of operations

that we are doing on the elements

in order to modify the structure, and this

is something that you do using

the same operators we have introduced

in the previous units, so it's

an application of, if you wish, all

the things that we have learned so far

about musical structure and manipulation.

And then, once the elements and operations

are selected, basically we get to a point

of automation where all the elements are

left to evolve according to the rules with

minimal intervention from the composer,

of course the composer is still there but

this is part of the automated part,

the algorithmic part of the composition.

And then again, you can go back and pass

it through a second phase of decision,

where you make choices depending on the

material that you have, and you do this

in a sort of feedback loop until you get

to the final version of the composition

that you are basically agreeing

and accepting.

This is a very general way that composers

work with, mostly when we talk about a

composition that is assisted by a computer

by a software or nowadays by

artificial intelligence, so it's never a

process where something is given

and accepted as is, it's always

a feedback loop, it's a self-consistent

loop that produces the final product

through the intervention of the composer

and its algorithmic constraints.

So, in Structure for two pianos,

Boulez utilizes a sequence of notes

that is here, in this slide. The notes

are always used in the order they are

listed here, so there is no choice

of exchanging one note for another,

this is called a tone row, and this is

the fundamental unit, or the fundamental

concept of serial music, that was

originally pioneered by composers like

Schönberg, and Webern, and Berg

at the beginning of the 20th century.

The tone row can be modified, can be

operated upon with operators

like transposition, and inversion,

and retrograde and so on. And so

that creates an enormous palette

of combinations for the composition.

Same for the duration of the notes,

the duration of the notes are also

mapped to twelve numbers like

pitches, and again also this series

of durations as you can see here

in this chart can be operated upon

with the same operators that we use

for the notes.

The way this works is combining and

constructing a matrix out of this

row of pitches or duration or,

in this case, numbers, and then taking

this row and apply to it all the possible

transpositions and forming a matrix

like the one in this slide.

The characteristic of this matrix

is that if I read it left to right and

by row, I get the original tone row and

all these transpositions going down row

by row, and if I look at the columns

what I get is the inversion of

the original row and so left to right

I have all the transpositions of

the inversions and, of course, if

I read it right to left, the row

is the retrograde of the original row

and bottom to top is the inverse

of the retrograde. So by constructing

these matrices I have at my disposal

all the possibilities that I can work with

in defining the different pitches in

the sequence of the composition.

What Boulez does is actually planning

a structure for the piece, and that is

the name that comes from there, Structure

by assigning a specific operation,

choosing specific rows or columns on

these matrices depending on the measures,

so that gives a kind of macroscopic

structure of the piece, but then

operates also on the microscopic

effects that come from the actual pitches

that you get. And so for instance, here

we have in red, I believe

the pitch structure and in green

the duration structure

that are combined into the first

section of the piece.

And this is the score, and you will

see in the associated notebook,

how we can actually produce a score like

this and the music that actually is

the same for the first few bars

of the composition, by encoding

all this in an algorithm that we can run

in the notebook.