3.7 Martin Bastiaans
In the 1980's Bastiaans
went through all the mathematics from the two articles that Gabor published
in the 1940's. He verified that the mathematics Gabor used had been correct.
Bastiaans discussed Gabor's sliding window analysis of a short-time Fourier
analysis. He reduced this idea to a function with just two variables -
a discrete time index and a continuous frequency variable. These two variables
form a rectangular lattice. The rectangular cell produced by the window
can only focus on one variable at a time, i.e. The finer the sampling frequency
the courser the sampling in time and vice versa. (Bastiaans 1985: 873)
Fig 3.6 The first diagram shows time as the dominant domain, in which the frequency becomes coarser. The second shows frequency as the dominant domain, in which the time becomes much coarser.
In the 1960's, before Gabor's
theory had been verified by Bastiaans, Xenakis came across this idea. He
was the first to look at Gabor's theory of communication and use it in
a compositional format. Using an integration of the grains described by
Gabor, Xenakis composed with the aid of stochastics. Xenakis said each
grain has a threefold nature: duration, frequency and intensity. He proposed
that all music is composed of a large number of elementary grains. (Xenakis
1971: 43) Xenakis also goes into detail about how these grains can be used
together. This was represented in a three dimensional context using frequency,
time, and grains as the three axis. He compared them to galactic masses,
in which all parts move but one must decide if they want to concentrate
on the movement of the whole galaxy, or one star. (Xenakis 1971: 46-50).
This idea of a galaxy of sound makes one think of sound as a three dimensional
object, whereas before it had mostly been considered two dimensional. It
is this idea that allows sound signals to become textures, sounscapes and
galaxies. These terms imply that sound must exist in a three dimensional
context. It allows the composer to think of music in another way of abstraction
from the conventional forms of abstracting sound in order to compose music.
The next chapter will discuss the compositions produced by Xenakis and those that followed him.