Music has a complex structure that expresses emotion and conveys information.
Humans process that information through imperfect cognitive instruments that
produce a gestalt, smeared version of reality. How can we quantify the
information contained in a piece of music? Further, what is the information
inferred by a human, and how does that relate to (and differ from) the true
structure of a piece? To tackle these questions quantitatively, we present a
framework to study the information conveyed in a musical piece by constructing
and analyzing networks formed by notes (nodes) and their transitions (edges).
Using this framework, we analyze music composed by J. S. Bach through the lens
of network science and information theory. Regarded as one of the greatest
composers in the Western music tradition, Bach's work is highly mathematically
structured and spans a wide range of compositional forms, such as fugues and
choral pieces. Conceptualizing each composition as a network of note
transitions, we quantify the information contained in each piece and find that
different kinds of compositions can be grouped together according to their
information content and network structure. Moreover, we find that the music
networks communicate large amounts of information while maintaining small
deviations of the inferred network from the true network, suggesting that they
are structured for efficient communication of information. We probe the network
structures that enable this rapid and efficient communication of
information--namely, high heterogeneity and strong clustering. Taken together,
our findings shed new light on the information and network properties of Bach's
compositions. More generally, our framework serves as a stepping stone for
exploring musical complexities, creativity and the structure of information in
a range of complex systems.Comment: 22 pages, 13 figure; discussion in section IV and VII expanded,
references added, results unchange