A Compact Statistical View of Musical-Instrument Directivity

Directivity is a defining feature of musical-instrument radiation and is known to vary strongly with frequency. With the growing availability of measured directivity datasets and their use in sound-field simulation and spatial audio, there is a practical need for representations that are both compact and comparable across sources. This work addresses that need by proposing a statistically grounded description of frequency-dependent directivity that reduces complex radiation patterns to a small set of meaningful descriptors. The approach enables directivity patterns to be summarized in an interpretable way and compared consistently across frequency bands, even when the radiation is not well described by a single dominant direction. The resulting representation supports tasks such as analysis, categorization, and model building, providing a bridge between detailed measurements and higher-level descriptors useful for musical acoustics and audio rendering. Experiments on a corpus of 41 orchestral instruments show that the proposed method preserves the distance geometry well while reducing the full order-4, 30-band corpus from about 492~kB to about 100~kB in double-precision storage.