Musical pitch has multiple psychological geometries

Abstract

Pitch perception is at the core of our experience of both speech and music1,2,3. Music theorists4,5, psychologists6,7, and neuroscientists8,9,10have sought to determine the psychological representation of musical pitch for centuries. The pitch helix, which jointly represents logarithmic scaling of the periodicity of a tone and the heightened similarity between tones separated by an octave, has been widely assumed to capture the psychological geometry of pitch6,7,11. However, empirical support for this structure is inconclusive, in part because it relies on studies with small sample sizes6,12,13,14,15. Here we revisit this problem using a series of comprehensive experiments involving musicians and non-musicians performing three established tasks based on similarity judgments and singing16,17,18. We show that a simple helical representation alone cannot explain the data. Rather, our results demonstrate that, depending on the task and musical experience10,19, the geometry of pitch can exhibit linear, degenerate-helical, and double-helical structures, suggesting a new, broader understanding of how we perceive pitch.