Information content and human perception of note transitions in music composed by Bach

Music has a complex structure that allows one to express emotion and convey information. How can the information in a musical composition be quantified? Prior research has shown that humans, when presented with information (such as a sequence of notes) do not process the information accurately. Here, we analyze Bach's music through the lens of network science and information theory. Regarded as one of the greatest composers, Bach's work spans a wide range of compositions and is highly mathematically structured. Viewing each composition as a network of note transitions, we show that Bach's music networks contain more information than random transition structures, and that different kinds of compositions can be grouped together according to their information content. Applying a free energy model for how humans infer the network structure of information that accounts for inaccuracies in perception, we observe that the inferred versions of Bach's music networks maintain a low deviation from their true network, implying they convey information efficiently. We probe the network structures that enable these properties --- namely, high heterogeneity and clustering. Our study sheds new light on the properties of Bach's compositions. More broadly, we gain insight into features that make networks of information effective for communication.