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.