An Analysis of Musical Instruments Directivity Based on Spatial Complexity

Characterizing and modeling the spatial radiation of musical instruments is a challenging task in acoustics due to the complex and high-dimensional nature of their directivities. In this paper, we address this challenge by presenting a comprehensive analysis of musical instrument directivities using Spatial Complexity, a novel metric that quantitatively describes how energy is distributed across spherical harmonics coefficients. Lower Spatial Complexity values indicate a concentration of energy in lowerorder spherical harmonic components, corresponding to nearly isotropic radiation patterns, while higher values reflect energy distributed across higher-order harmonics, denoting highly directional and intricate beam patterns. To demonstrate the utility of this metric, we analyze an extensive dataset of measured instrument directivities, uncovering systematic correlations between complexity and physical radiation properties. Further, we train a rotation-equivariant neural network designed to preserve the geometric symmetries of spherical harmonics representations. The model's latent space organizes directivities along gradients tightly aligned with complexity, showing the metric's ability to capture fundamental attributes of spatial radiation. These findings highlight the effectiveness of complexity as a concise and interpretable analytical tool for comparing and categorizing instrument directivities, with potential applications in acoustic research, instrument design, and spatial audio technologies.