Hidden assumptions of integer ratio analyses in bioacoustics and music
Widely adopted integer-ratio analyses in bioacoustics and music rhythm research suffer from critical methodological flaws: inadequate modeling of temporal noise, sensitivity of statistical inference to ratio formulation choices, and longstanding neglect of null-hypothesis appropriateness. Method: We formally characterize the temporal properties of empirically observed rhythmic ratios and introduce the first general-purpose statistical testing framework for integer ratios—flexibly accommodating arbitrary null hypotheses. This framework integrates mathematical modeling, probabilistic distribution analysis, and rigorous hypothesis testing to systematically identify the sources of statistical bias in prevailing approaches. Contribution/Results: The framework rectifies long-overlooked methodological shortcomings and provides a standardized, reproducible testing protocol. It substantially enhances statistical robustness and cross-study comparability in cross-species rhythmic analyses and music cognition research, enabling principled inference about rhythmic structure beyond ad hoc ratio assessments.