Introduction

We can think of musical sound as an entity which lives on the continuum between silence and white noise. Then, a composition becomes a procedure which defines a path along this continuum. Compositions usually start with silence, at some point get closer to white noise, and eventually return to silence. Due to the nature of infinity, a continuum can never be traversed by humans unless it is ``quantized''. Pitch scales quantize the continuum of frequency, while rhythms do the same for the continuum of time. In tonal form the quantization methods, as well as all the formal operations, are derived from the structures of the harmonic sound. In this paradigm - tonal form -- one can only create a single type of musical timbre. Schoenberg's theory of harmony[41] implies a new perspective on music and sound. According to this theory, music is capable of conveying any type of relationship, and not only that of harmonic sound, as discussed in the chapter 2 of this thesis.

Computers seem to be useful to the world of music in a few different ways. They make ideal mechanistic instruments and instrumentalists for the precision of their sound creation capabilities. The computation power of computers makes them ideal for algorithmic composition. Given the correct paradigm, computers are also capable of managing huge databases of information, and provide our imagination with enough primitives to build logical interfaces to the stored data. However, there is a certain dilemma in composing with computers, namely the extent of the freedom they provide.

When writing for acoustical instruments, the composer already uses a quantization of the continuum of timbres, which is defined by the available instruments. In electronic music, the act of composition is stretched to the micro structures of sound. The field of sound has no constraints, and therefore no shape. There are no defined timbres or scales. The point is not that we cannot define such things; currently different synthesis methods are capable of creating distinct sounds for computers. However, ``not having a defined sound'' is inherently part of the spirit of using computers for music, and perhaps in general is a major part of the spirit of modern music. In this domain, a musical idea has to define not only the organization but also the material of composition. Thus, material and organization become intimately interconnected (refer to chapter 2, Stockhausen[47] and Koblyakov[22]).

If we would like to take advantage of the freedom that computers provide us, we have to come up with paradigms of composition which treat material and organization in the same way, not only emotionally and spiritually, but also very precisely and logically. In this work, we have experimented with the principle of self-similarity which is very close to Lindenmayer's L-system[25] as a synthesis method^5.1The question of why self-similarity can be useful in music is discussed in chapter 2. Self-similarity provides us with a simple paradigm to view material and organization as a single parameter, and therefore, view sound and music as the same. Self-similarity also provides us with tools to control the perceptual continuum which exists between pitch, rhythm, and form. In this chapter we will explain the synthesis method we have devised and present some of its results.