Automatic Piano Reduction from Ensemble Scores Based on Merged-Output Hidden Markov Model

We discuss automated piano reduction from ensemble scores based on stochastic models of piano fingering and reduction process. Music arrangement including piano transcription is an important compositional technique, automation of which creates a challenging research field. As a starting point, we aim at a simple case of piano reduction which is playable and sounds similar to the original ensemble score. It is proposed to formulate the problem as an optimisation of fidelity to the original score under constraints on performance difficulty. First a model of piano fingering is presented to quantify performance difficulty. Next we construct a stochastic model for piano reduction based on the fingering model and probabilities to describe how notes in ensemble scores are likely to be edited, from which a piano reduction algorithm is derived. The models are constructed with merged-output hidden Markov model, which is a recently proposed model suited to describe a musical process involving multiple voice parts. It is confirmed that the constructed algorithm can control the performance difficulty of output reductions taking into account the density of notes and chords, the tempo, and the rhythm of the input ensemble score. The proposed formulation can be applied for more general music arrangement.