Quantification of stylistic differences between musical artists is of academic interest to the music community and is also useful for other applications, such as music information retrieval and recommendation systems. Information about stylistic differences can be obtained by comparing the performances of different artists across common musical pieces. In this article we develop a statistical methodology for identifying and quantifying systematic stylistic differences among artists that are consistent across audio recordings of a common set of pieces, in terms of several musical features. Our focus is on a comparison of 10 different orchestras, based on data from audio recordings of the nine Beethoven symphonies. As generative or fully parametric models of raw audio data can be highly complex and more complex than necessary for our goal of identifying differences between orchestras, we propose to reduce the data from a set of audio recordings down to pairwise distances between orchestras, based on different musical characteristics of the recordings, such as tempo, dynamics and timbre. For each of these characteristics, we obtain multiple pairwise distance matrices, one for each movement of each symphony. We develop a hierarchical multidimensional scaling (HMDS) model to identify and quantify systematic differences between orchestras in terms of these three musical characteristics and interpret the results in the context of known qualitative information about the orchestras. This methodology is able to recover several expected systematic similarities between orchestras as well as to identify some more novel results. For example, we find that modern recordings exhibit a high degree of similarity to each other, as compared to older recordings.
"Hierarchical multidimensional scaling for the comparison of musical performance styles." Ann. Appl. Stat. 14 (4) 1581 - 1603, December 2020. https://doi.org/10.1214/20-AOAS1391