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. It posits that undecidability, a principle traditionally associated with theoretical computer science, extends its relevance to the music industry. The study adopts a multidimensional approach, focusing on five key areas: (1) the Turing completeness of Ableton, a widely used digital audio workstation, (2) the undecidability of satisfiability in sound creation utilizing an array of effects, (3) the undecidability of constraints on polymeters in musical compositions, (4) the undecidability of satisfiability in just intonation harmony constraints, and (5) the undecidability of "new ordering systems". In addition to providing theoretical proof for these assertions, the paper elucidates the practical relevance of these concepts for practitioners outside the field of theoretical computer science. The ultimate aim is to foster a new understanding of undecidability in music, highlighting its broader applicability and potential to influence contemporary computer-assisted (and traditional) music making.

翻译：本文深入探讨了计算理论与音乐的交叉领域，考察了不可判定性这一概念及其在现代音乐创作与制作中重要却常被忽视的启示。文章认为，不可判定性这一传统上与理论计算机科学相关的原理，其相关性已延伸至音乐产业。研究采用多维度方法，聚焦于五个关键领域：（1）广泛使用的数字音频工作站Ableton的图灵完备性；（2）利用一系列效果进行声音创作时的可满足性不可判定性；（3）音乐作品中复节奏约束的不可判定性；（4）纯律和声约束的可满足性不可判定性；以及（5）“新排序系统”的不可判定性。除了为这些论断提供理论证明外，本文还阐明了这些概念对于理论计算机科学领域之外的实践者的实际意义。最终目标是促进对音乐中不可判定性的新理解，突显其更广泛的适用性及影响当代计算机辅助（及传统）音乐创作的潜力。