This resource is designed for composers who are interested in exploring and creatively exploiting mathematical ideas in their music. It provides information on some potentially relevant mathematical algorithms and concepts, with a few thoughts on their musical possibilities. The list of algorithms covered can be found below, and will grow over time.

This material was first developed as a result of CNM’s New Structures in Composition project in 2017. We thank Prof. Pablo Padilla (UNAM) for kindly allowing us to use his algorithm descriptions.

Arithmetic procedures: Least common multiple and canonical forms

Combinatorial algorithms

Geometrical methods

Iterated maps: self-similarity and fractals

Music and image

Probabilistic ideas: dice games

Recursivity

Symbols and codes

Syracuse conjecture