Music can be interpreted as a collection of meaningful events distributed in time. The construction introduced during the first seminar neglects this time-dependent interpretation. Temporal evolution allows the composer to introduce a musical idea, then shape it, and finally proceed to a new scenario. Would it be possible to refine our analysis by representing music in a variable geometry space? We will present a primal attempt to describe this time-dependency in topological terms. First, we will suggest an adaptation of the persistent homology formalism to the analysis and classification of time series. Second, we will analyse different dataset in order to understand the role played by the granularity at which we describe musical events, with respect to our perception. Keywords: Time series, persistent homology, vineyards, Dynamic Time Warping 75 minutes talk, 45 minutes discussion.