  There has been an everlasting discussion around the concept of form in music.
This work is motivated by such debate by using a complex systems framework in
which we study the form as an emergent property of rhythm. Such a framework
corresponds with the traditional notion of musical form and allows us to
generalize this concept to more general shapes and structures in music. We
develop the three following metrics of the rhythmic complexity of a musical
piece and its parts: 1) the rhythmic heterogeneity, based on the permutation
entropy, where high values indicate a wide variety of rhythmic patterns; 2) the
syncopation, based on the distribution of on-beat onsets, where high values
indicate a high proportion of off-the-beat notes; and 3) the component
extractor, based on the communities of a visibility graph of the rhythmic
figures over time, where we identify structural components that constitute the
piece at a (to be explained) perceptual level. With the same parameters, our
metrics are comparable within a piece or between pieces.
