Rhythm and form in music: a complex systems approach
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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.
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