A Few Remarks on Algorithmic Composition

Computer music is music that cannot be created without the use of computers. There are many examples of computer music that use the term in a less narrow sense, however. The performance of baroque music on digital equipment employs computers, but the very same compositions might be performed on other more suitable instruments. This article focuses on the use of computers for generating algorithmic compositions. I will define different categories of algorithmic compositions and discuss which of these deserve the designation computer music.

If one considers various methods of algorithmic composition, considerable importance can be allotted to differentiating between construction and resultant form, i.e., between compositional idea, its realization in the musical score, and its auditory perception. Computer-aided algorithmic composing consists of constructing or selecting algorithms to generate a composition. These constructions are then evaluated and assessed according to whether the resultant forms seem to work musically. To put it another way, computer-driven differentiation between algorithm and resultant--that is, the received form--is a peculiarity of computer-aided algorithmic composition. Only rarely is the process of generating the composition, and thus the construction of the algorithm, intentionally made visible.

The theory of algorithmic composition usually distinguishes between score synthesis (the computer-aided working out of a composition, usually for traditional acoustic instruments) and sound synthesis (the computer-aided working out of a synthetic sound that can only be heard through loudspeakers). This distinction has its roots in the traditional differentiation between score and instrument, but a computer-generated continuum between two different sounds, however, is both score and sound synthesis. In both types of synthesis, the appearance of events in time is structured, both globally (form) as well as locally (sound, timbre).

The present text is concerned for the most part with various methods of computer-aided score synthesis for orchestral instruments. It does not deal with the wide area of computer-aided interactive composition in real time, nor does it deal with algorithmic sound synthesis.

The term score synthesis is closely related to computer music, computer-aided composition, CAO (composition assistée par ordinateur, i.e., composition assisted by computer), and automatic composition or algorithmic composition. Algorithmic composition does not necessarily require the application of a computer. Algorithmic processes have also been shown to be at work in certain procedures in analog electro-acoustic music studios, where they were called semi-automatic and automatic composing (Stockhausen 1971). On the other hand, Arvo Pärt does not use a computer and calls those of his pieces in which a pattern is extended, shortened, or otherwise permutated according to an algorithm "computer music"(La Motte-Haber 1996a, p. 158; La Motte-Haber 1996b, p. 23). This illustrates how closely related both terms are.

The selection or construction of algorithms for musical applications can be divided into three categories:

1. Modeling traditional, non-algorithmic compositional procedures

2. Modeling new, original compositional procedures, different from those known before

3. Selecting algorithms from extra-musical disciplines

I will discuss each of these categories in terms of individual procedures and compositions. The third category receives greater weight, because, in my opinion, it contains the more recent developments in computer music.

Modeling Traditional, Non-algorithmic Procedures

The composer Lejaren A. Hiller's approach to form is characterized by a traditional attitude. In his early computer-generated compositions, which number among the earliest experiments in score synthesis, he simply borrows traditional forms and uses the computer to make the composing easier. But he works so skillfully with the computer that new dimensions are revealed. Hiller's first three experiments produced not just single pieces, but whole classes of compositions equivalent to the selected form. His fourth experiment generated new, unpredicted forms for the first time, which directly changed his own formal understanding. From these experiments arose the Illiac Suite for string quartet (1955-1956), by Hiller and Leonard M. Isaacson. The suite's four movements document the four experiments Mr. Hiller and Mr. Leonard carried out...