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