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In this paper, we address the task of semi-automatic music transcription in which the user provides prior information about the polyphonic mixture under analysis. We propose a non-negative matrix deconvolution framework for this task that allows instruments to be represented by a different basis function for each fundamental frequency (“shift variance”). Two different types of user input are studied: information about the types of instruments, which enables the use of basis functions from an instrument database, and a manual transcription of a number of notes which enables the template estimation from the data under analysis itself. Experiments are performed on a data set of mixtures of acoustical instruments up to a polyphony of five. The results confirm a significant loss in accuracy when database templates are used and show the superiority of the Kullback-Leibler divergence over the least squares error cost function.