Musical pitch has multiple psychological geometries

Pitch perception is central for both speech and music, and the representation of musical pitch has intrigued scholars for centuries. In his seminal work, Roger Shepard proposed a series of increasingly complex geometrical models to approximate the psychological representation of pitch, most famously the pitch helix which is often used in textbooks. The pitch helix represents the logarithmic scaling of the periodicity of tones and the similarity between tones separated by an octave. However, support for geometrical models of musical pitch derives from studies that are small-scale and sometimes contradictory. Moreover, research suggests that the representation of pitch is influenced by task context and expertise raising the question of whether any single integrated geometric approximation is sufficient. Using multi-dimensional scaling analysis, we revisit this problem through nine experiments involving participants with varied levels of musical expertise (N = 592) and paradigms covering both perception and production, as well as implicit and explicit measures of perceptual similarity. We show that, depending on task and musical experience, the best geometrical approximation can exhibit an array of structures ranging from linear to double-helical structures, providing strong evidence that a simple helical model, or in fact any fixed geometrical model, cannot explain the data. To explain these large variations, we then show that they can be captured by different reweightings of a small set of perceptual factors suggesting a composite representation. These findings highlight the importance of examining diverse tasks and populations to address the classic question of how perceptual representations are organized.