A comparative analysis of the directional sound radiation of historical violins

The directivity pattern of a musical instrument describes the sound energy radiation as a function of frequency and direction of emission. Violins exhibit a rather complex directivity pattern, which is known to show rapid variations across frequencies, and whose behavior cannot be easily predicted except in the lowest frequency range. The acoustic behavior of the violin is a fascinating research topic that has prompted numerous published works, but a thorough, comprehensive, and comparative analysis of violin directivity patterns is long overdue. In this article, we propose a set of metrics for characterizing the radiative behavior of musical instruments and, in particular, for comparing their directivity patterns. We apply such metrics for a comparative analysis of the directivity patterns of some of the most prestigious historical violins ever made, including grand masters such as Antonio Stradivari, Giuseppe Guarneri "del Gesú"and members of the Amati family. The instruments are preserved in the Violin Museum of Cremona, Italy, where our lab is located. The analysis methodology introduced in this work allowed us to quantitatively evaluate the similarity of directivity patterns of such extraordinary instruments and draw some interesting conclusions.