We present a statistical-modelling method for piano reduction, i.e.<br />
converting an ensemble score into piano scores, that can control performance<br />
difficulty. While previous studies have focused on describing the condition for<br />
playable piano scores, it depends on player&#039;s skill and can change continuously<br />
with the tempo. We thus computationally quantify performance difficulty as well<br />
as musical fidelity to the original score, and formulate the problem as<br />
optimization of musical fidelity under constraints on difficulty values. First,<br />
performance difficulty measures are developed by means of probabilistic<br />
generative models for piano scores and the relation to the rate of performance<br />
errors is studied. Second, to describe musical fidelity, we construct a<br />
probabilistic model integrating a prior piano-score model and a model<br />
representing how ensemble scores are likely to be edited. An iterative<br />
optimization algorithm for piano reduction is developed based on statistical<br />
inference of the model. We confirm the effect of the iterative procedure; we<br />
find that subjective difficulty and musical fidelity monotonically increase<br />
with controlled difficulty values; and we show that incorporating sequential<br />
dependence of pitches and fingering motion in the piano-score model improves<br />
the quality of reduction scores in high-difficulty cases.