  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 ten 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.
