A dynamical approach to music analysis
Alberto Pinto · Journal of Mathematics and Music · 2012
It is possible to identify significant units of a piece of music, like salient motifs or tonally prominent pitch classes, by looking at the stable states of suitably defined dynamic systems associated with the piece and analytical paradigms assigned to the piece. The Lyapunov functions of these systems represent a paradigmatic energy around stable states and derive from eigenfunctions that reflect their centrality within a network of states. The theory presented here is illustrated through an experiment in paradigmatic motivic analysis. Furthermore, it is shown that the approach subsumes the usual repetition paradigm as a limiting case and that it can also be applied to the construction of tonally characteristic pitch class profiles from distance functions.