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Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments

Carpentier, T. & Einbond, A. ORCID: 0000-0003-1734-6641 (2023). Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments. Acta Acustica, 7(40), article number 40. doi: 10.1051/aacus/2023033


We investigate the use of spherical cross-correlation as a similarity measure of sound radiation patterns, with potential applications for their study, organization, and manipulation. This work is motivated by the application of corpus-based synthesis techniques to spatial projection based on the radiation patterns of orchestral instruments. To this end, we wish to derive spatial descriptors to complement other audio features available for the organization of the sample corpus. Considering two directivity functions on the sphere, their spherical correlation can be computed from their spherical harmonic coefficients. In addition, one can search for the 3-D rotation matrix which maximizes the cross-correlation, i.e. which offers the optimal spherical shape matching. The mathematical foundations of these tools are well established in the literature; however, their practical use in the field of acoustics remains relatively limited and challenging. As a proof of concept, we apply these techniques both to simulated radiation data and to measurements derived from an existing database of 3-D directivity patterns of orchestral instruments. Using these examples we present several test cases to compare the results of spherical correlation to mathematical and acoustical expectations. A range of visualization methods are applied to analyze the test cases, including multi-dimensional scaling, employed as an efficient technique for data reduction and navigation. This article is an extended version of a study previously published in [Carpentier and Einbond. 16th Congrès Français d’Acoustique (CFA), Marseille, France, April 2022, pp. 1–6.].

Publication Type: Article
Additional Information: © The Author(s), Published by EDP Sciences, 2023. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher Keywords: Radiation patterns, Spherical acoustics, Rotational matching, Musical instrument directivity
Subjects: M Music and Books on Music > M Music
Departments: School of Communication & Creativity > Performing Arts > Music
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