Complexity of frequency fluctuations and the interpretive style in the bass viola da gamba
Igor Lugo, Martha G. Alatriste-Contreras, Rafael Sánchez-Guevara
TL;DR
This paper investigates how the complexity of frequency fluctuations in bass viola da gamba performances relates to interpretative style. It models audio signals as a network of sounds by performing $FFT$-based spectral decomposition to obtain Hz components and then applies a Kolmogorov-Smirnov ($KS$) test to compare candidate distributions, including an exponential distribution with PDF $f(x)=e^{-x}$, $x\ge0$. The network is analyzed via degree centrality and largest cliques, linking large-scale statistical regularities to small-scale frequency fluctuations. The results show a dominant exponential pattern across pieces performed by the same musician, with consistent centralities and clique structures that vary due to recording conditions, supporting a connection between interpretative style and measurable network features, with implications for computational creativity.
Abstract
Audio signals in a set of musical pieces are modeled as a complex network for studying the relationship between the complexity of frequency fluctuations and the interpretive style of the bass viola da gamba. Based on interdisciplinary scientific and music approaches, we compute the spectral decomposition and translated its frequency components to a network of sounds. We applied a best fit analysis for identifying the statistical distributions that describe more precisely the behavior of such frequencies and computed the centrality measures and identify cliques for characterizing such a network. Findings suggested statistical regularities in the type of statistical distribution that best describes frequency fluctuations. The centrality measure confirmed the most influential and stable group of sounds in a piece of music, meanwhile the identification of the largest clique indicated functional groups of sounds that interact closely for identifying the emergence of complex frequency fluctuations. Therefore, by modeling the sound as a complex network, we can clearly associate the presence of large-scale statistical regularities with the presence of similar frequency fluctuations related to different musical events played by a same musician.