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We describe a new approach for computing the similarity between symbolic musical pieces, based on the differences in shape between the interpolating curves defining the pieces. We outline several requirements for a symbolic musical similarity system, and then show how our model addresses them. Results obtained by an early prototype, tested with the MIREX 2005 Symbolic Music Similarity collections, show that this approach performs well. This new model opens a new and promising line for further research on the melodic similarity problem.