In this paper, we investigate the problem of real-time polyphonic music transcription by employing non-negative matrix factorization techniques and the beta-divergence as a cost function. We consider real-world setups where the music signal arrives incrementally to the system and is transcribed as it unfolds in time. The proposed transcription system is addressed with a modified non-negative matrix factorization scheme, called non-negative decomposition, where the incoming signal is projected onto a fixed basis of templates learned off-line prior to the decomposition. We discuss the use of non-negative matrix factorization with the beta-divergence to achieve the real-time decomposition. The proposed system is evaluated on the specific task of piano music transcription and the results show that it can outperform several state-of-the-art off-line approaches.