Quantifying the directivity patterns of sound sources provides not only deeper insights into understanding the source and its acoustical properties but also the potential to simulate the propagation of its sound in various settings. Being able to describe the detailed 3-dimensional directivity of highly complex and dynamic sound sources such as musical instruments and human speech in a simple way while at the same time preserving the fine details of the directivity patterns has broad applications. By using seventeenth-order spherical harmonic expansions of data collected on a 2,664-point spherical array, large amounts of the measured directivity of musical instruments and human speech was condensed in a simple, accurate, and powerful tool for understanding these complex systems.