A network perspective on J.S Bach's 6 violin sonatas and partitas, BWV 1001 - 1006

Complex networks and statistical physics have been proposed as powerful frameworks and tools in the analysis of the properties of complex systems and in particular musical pieces. They can reveal variations in musical features such as harmony, melody, rhythm as well as the composer's style. The empirical study of a wide range of digitized scores of Western classical music and their corresponding networks brought to light quantitative evidence for changes in harmonic complexity. We complement the common topological analysis of these networks with musicological or music-theoretical considerations. We illustrate this by studying J. S. Bach's sonatas and partitas for solo violin by constructing duration-weighted transition matrices between notes, or melody networks, as well as harmony networks, which are transition matrices between the chords, or equivalently synchronously played notes. We further propose statistical physics measures that were first introduced in the study of socio-economic networks: the partition function and communicability and provide evidence for their significance. Our findings and observations include: the detection of three main communities centered around the tonic, the dominant, and submediant in most of the pieces; the association of the nodes with the highest betweenness centrality, the lowest clustering coefficient and highest in and out degrees respectively with the tonic and the dominant; the high similarity between pieces which share the same key or when the key of one is the dominant of the other; finally, the association of the highest partition function, the shortest average path length, and the highest communicability with the Fugues.