Science since antiquity has asked whether mathematical relationships among acoustic frequencies govern musical relationships. Psychophysics rejected frequency ratio theories, focusing on sensory phenomena predicted by linear analysis of sound. Cognitive psychologists have since focused on long-term exposure to the music of one’s culture and short-term sensitivity to statistical regularities. Today evidence is rapidly mounting that oscillatory neurodynamics is an important source of nonlinear auditory responses. This leads us to reevaluate the significance of frequency relationships in the perception of music. Here, we present a dynamical systems analysis of mode-locked neural oscillation that predicts cross-cultural invariances in music perception and cognition. We show that this theoretical framework combines with short- and long-term learning to explain the perception of Hindustani rāgas, not only by encultured Indian listeners but also by Western listeners unfamiliar with the style. These findings demonstrate that intrinsic neurodynamics contribute significantly to the perception of musical structure.