Complexity of frequency fluctuations and the interpretive style in the case study of a set of musical pieces of bass viola da gamba

Based on a computational musicology framework that bridges the gap between scientists and musicians, this case study investigates the feasibility of capturing the relationship between the presence of complex frequency fluctuations and the interpretive style. Because there is no well-known method for capturing such a relationship, we propose a preliminary formulation for identifying differences in musical interpretation. In particular, we focus on a set of musical pieces performed by the same interpreter on the bass viola da gamba. We analyzed digital audio data to best identify statistical regularities in audio frequencies (Hz) and their complex network properties in musical notation. Based on an interdisciplinary approach, we computed the spectral decomposition and translated its frequency components into a network of sounds. We applied a best-fit analysis for identifying the statistical distributions that most precisely describe the behavior of these frequencies, and we computed the centrality measures and identified cliques for characterizing such a network. Our findings reveal statistical regularities in the type of statistical distribution that best describes frequency fluctuations. The centrality measures confirmed the most influential and stable group of sounds in a piece of music, while the identification of the largest clique indicated functional groups of sounds that interact closely. Therefore, using musical signal processing, complex systems, and music theory, we can effectively translate musical audio signals into frequency components and complex networks. However, we cannot conclusively determine the relationship between the presence of complex frequency fluctuations and the interpretive style.