The majority of computer music today is undertaken using commercial software that does not require knowledge of mathematics, algorithms, etc. However, such systems have a limited scope: sequencers, accompaniment systems, recording and playback gear. This book intends to broaden the horizons for those musicians who want to go further: hence the need to become familiar with fundamental computer music concepts and be prepared to use systems that either embody some interesting compositional model, allow for programming, or both.

Whilst geometry, numerical proportions and esoteric numbers served to scaffold great compositional minds in past centuries (James 1993), logic, probabilities, set theory and algorithms inspire some contemporary composers. This chapter begins by introducing fundamental mathematical concepts that are crucial for mastering computer music, from discrete mathematics and set theory, to logic and formal grammars. Then, it gives a primer in general computer programming with examples followed by an overview of two historical landmarks for the development of computer music: Schoenberg's serialism and Xenakis' formalised music.