A reformulation of Prior Subspace Analysis (PSA) is presented, which restates the problem as that of fitting an undercomplete signal dictionary to a spectrogram. Further, a generalization of PSA is derived which allows the transcription of polyphonic pitched instruments. This involves the translation of a single frequency prior subspace of a note to approximate other notes, overcoming the problem of needing a separate basis function for each note played by an instrument. Examples are then demonstrated which show the utility of the generalised PSA algorithm for the purposes of polyphonic pitch transcription.