In this notebook, we explore in a very

simple way the procedural,

the compositional procedure that Boulez

used for the composition of these piano

pieces Structures that I discuss in

the lecture. So here everything is based

on the manipulation of a list of

12 numbers that are interpreted both

as pitches, or as durations, or other

parameters of the composition itself.

So this here is the original sequence,

the pitch sequence that Boulez used for

this piece, and this is actually

the tone row as it is called in musical

notation. So this row is actually used

to construct a matrix, where each row of

the matrix is a transposition of

the original list.

If you take this matrix

and you read in different ways so by

column, by row, from the bottom to the top

from the right to the left, then you

basically have all

the operations of transposition:

inversion and retrograde and retrograde-

inversion that manipulate this sequence

of notes and then they can be used in

different ways in the composition.

Same thing happens for durations,

durations are mapped to the same

12 integers and the choice -

the combination of choice - of

the row of pitches or the column

of pitches and the row, or column

or durations give rise to

the composition itself. So these are

the first three bars that are generated

using the simple manipulation of

these elements of the matrix that are

actually the exact same three bars

on the compositions by Boulez.

[Demonstration]