Although Algorithmic composition became popular with the rise of computers, algorithmic thinking is far older – it can be traced back to the ancient times of Pythagoras and the Jewish Kabbalah. It is a method of perceiving an abstract model behind the sensual surface, or in turn, of constructing such a model in order to create aesthetic works. Behind the various approaches there is one common denominator: a longing to create something infinite that exceeds the limited horizon of our individual knowledge. Seen in this light, algorithmic thinking and its application in the arts can become a way to gain experience and to overcome barriers that are either implicit in ourselves, or erected by our social environment.

In this article, I am focusing exclusively on the use of algorithms in the compositional process, leaving aside other approaches like the algorithmic simulation of musical styles, the computational modelling of music cognition and the application of artificial intelligence techniques (Cope 1996; Ebcioglu 1990). My primary aim is to demonstrate how the algorithmic spirit has evolved through the centuries – from medieval music theory to the interactive realtime-generated computer music of today.

Algorithm

The term algorithm was phonetically derived from the name of the Arab mathematician Muhammad ibn Musa al-Khwarizmi (ninth century) who introduced Hindu–Arabic numerals and the concepts of algebra into European mathematics. An algorithm can be defined as a predetermined set of instructions for solving a specific problem in a limited number of steps. Algorithms can range from a mere succession of simple arithmetical operations to more complex combinations of procedures, utilising more involved constructions from computer science such as rule-based grammars, recursion and probabilistic inference.