We present a new probabilistic model for transcribing piano music from audio to a symbolic form. Our model reflects the process by which discrete musical events give rise to acoustic signals that are then superimposed to produce the observed data. As a result, the inference procedure for our model naturally resolves the source separation problem introduced by the the piano's polyphony. In order to adapt to the properties of a new instrument or acoustic environment being transcribed, we learn recording specific spectral profiles and temporal envelopes in an unsupervised fashion. Our system outperforms the best published approaches on a standard piano transcription task, achieving a 10.6% relative gain in note onset F1 on real piano audio.