Manifold compositions: Formal control, intuition, and the case for comprehensive software

The paper defines the concept of manifold compositions and establishes that a comprehensive type of software based on solid formalism is required for such a project. Practical issues related to the use of randomness are discussed and tools used to compose three such manifold compositions are detailed. Arguments against the "black box" approach and formalism are reviewed and rebutted while insisting on the need for a flexible formal framework that does not neglect the role of intuition. Manifold compositions promote an experimental attitude and challenge tendencies toward commercialization of music.