2025/06/15 by Fujiki, Yuichi
#FOS: Mathematics #Mathematics #Physical Sciences and Mathematics
paper · doi:10.17605/osf.io/gbr3p
This paper critically examines the hypothesis that mathematical constants such as π, e, and φ encode musically meaningful structure when mapped into musical domains using modular arithmetic and related procedures. Integrating robust statistical and information-theoretic analysis with direct comparison to random sequences and real musical works, the study finds no empirical evidence that mathematical constants contain latent musical structure beyond chance expectation. Instead, the case studies of real music highlight that musical structure is an emergent property of human culture, cognition, and creativity, not a mere byproduct of mathematics. Negative results are interpreted as a positive lesson for music theory and science, emphasizing the necessity of rigorous controls and theoretical clarity. The paper discusses the cultural relativity of musical meaning, the risk of category mistakes in pattern research, and the implications for future interdisciplinary studies at the boundary of mathematics, music, and information science. This negative result serves as a positive contribution.