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：摘要：本文深入探讨计算理论与音乐的交叉领域，审视了不可判定性这一概念及其在现代音乐作曲与制作领域中重要但常被忽视的意涵。论文主张不可判定性——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）利用系列效果器进行声音创作时满足性的不可判定性；（3）音乐作品中复节奏约束的不可判定性；（4）纯律和声约束满足性的不可判定性；以及（5）“新排序系统”的不可判定性。除为上述论断提供理论证明外，本文还阐明了这些概念对理论计算机科学领域之外从业者的实际关联性。最终目标在于促进对音乐中不可判定性的新认识，凸显其更广泛的适用性及对当代计算机辅助（及传统）音乐创作的潜在影响。