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This paper delves into the intersection of computational theory and music,examining the concept of undecidability and its significant, yet overlooked,implications within the realm of modern music composition and production. Itposits that undecidability, a principle traditionally associated withtheoretical computer science, extends its relevance to the music industry. Thestudy adopts a multidimensional approach, focusing on five key areas: (1) theTuring completeness of Ableton, a widely used digital audio workstation, (2)the undecidability of satisfiability in sound creation utilizing an array ofeffects, (3) the undecidability of constraints on polymeters in musicalcompositions, (4) the undecidability of satisfiability in just intonationharmony constraints, and (5) the undecidability of "new ordering systems". Inaddition to providing theoretical proof for these assertions, the paperelucidates the practical relevance of these concepts for practitioners outsidethe field of theoretical computer science. The ultimate aim is to foster a newunderstanding of undecidability in music, highlighting its broaderapplicability and potential to influence contemporary computer-assisted (andtraditional) music making.

Undecidability Results and Their Relevance in Modern Music Making