Musical Algorithms - By Paul Doornbusch

An algorithm is a precise step-by-step procedure to solve a problem, often of a mathematical or computational nature. A recipe is like an algorithm. Musical algorithms specify ways to generate musical parameters. Typically these parameters are the large-scale specification of musical events, such as frequency, intensity, duration, density and so on. Broadly, musical algorithms can be classified into two groups; those that attempt to implement some part of music theory and those that take a more general approach towards composition. The music theory approach has attracted the most attention, but the musical results have been less than aesthetically compelling. In the 1950s and 60s two composers took the other approach and were successful in creating compelling musical works, they were Iannis Xenakis and Gottfried Michael Koenig. Xenakis used probabilities and probability theory to compose free stochastic music by controlling shapes, densities, contours, areas and so on. The force of Xenakis’ vision and music established these ideas as compositionally useful abstractions. Koenig took a different approach where he generalised from his current composition practice into simple abstractions and building tools (Project 1 and Project 2) to implement the ideas.

As musical algorithms are ways to generate musical data, there is little point in distinguishing between signal processing algorithms and musical algorithms designed for a higher level of organisation, as the two are very closely linked. Musical signal processing algorithms may be considered musical algorithms for the micro-form or micro-scale, and the ideas and abstractions of both the micro and macro forms often overlap.

There are many types of musical algorithm and these may be classified by the type of abstraction they represent. There are many which generate random numbers using statistical theory, such as linear, gauchy and beta distributions of random numbers. Others may filter their input to impose a “shape” on the (unstructured) data, such as tendency masks. Other examples of abstractions useful for musical algorithms are; genetic recombinatorial algorithms which generate musical data with processes based on genetic models, cellular automata algorithms may generate musically useful data and chaotic functions may be musically interesting. Other musically useful algorithms exist and there will undoubtably be many more developed. It is worth noting that using data generated or structured through and algorithm usually provides the data with some structure and composers and performers seek to use this to provide new structural possibilities to their music.