Unbounded Space

O God! I could be bounded in a nutshell, and count myself a king of infinite space, were it not that I have bad dreams --- William Shakespeare from Hamlet

This piece explores further all the instruments that were used by Richard Boulanger in his well known Trapped in Convert, and also in his later At Last...Free. The instruments are played in the same order and same proportions as appear in Trapped. However the timing, pitches, and durations and other parameters are chosen by values generated by the Henon (chaotic) equation. This equation
x{n+1} = y - a x{n}^2 + 1
y{n+1} = b x{n}
is one that interests me as it generates sequences that are never quite the same, but retain a high degree of similarity; so they go round, never quite repeating themselves. The piece opens with a short quotation from the start of Trapped in Convert to set the scene as it were, and there is a further quotation after about 200 seconds, but the repetitions of the Henon equation dominate the work. A short, three note motif emerges from the process and dominates the closing moments. Unlike the first work in this series which used the Henon equation, here the pitches are taken from a conventional twelve note equal temperament scale, so the motif repeats the pitch if not the rhythm.

The question that lies behind the work and the Hamlet quotation is the starting point; are we really in boundless space or just trapped in a nutshell? Is this reality or just bad dreams?

The piece was algorithmically generated using a C program to calculate the Henon process with a=1.3 and b=0.21, and to map the results to the parameters to control a Csound score for instruments that are minor modifications of the Boulanger orchestra. The algorithm was developed and modified, partly with closer reference to Trapped in Convert and the use of instruments there, and partly on composer's choice. Composed in September-November 2002.

Csound score and orchestra (score was generated by a C program, not yet available).

WAV file, MP3 and OGG

First performed in Boston 2002.

jpff@cs.bath.ac.uk

Last modified: Mon Aug 30 20:50:24 BST 2004