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]