Statistical Piano Reduction Controlling Performance Difficulty
This work addresses the challenge of creating playable piano reductions tailored to individual skill levels, which is an incremental improvement over previous methods that focused only on playability without continuous difficulty control.
The authors tackled the problem of converting ensemble scores into piano scores while controlling performance difficulty, by developing a statistical modeling method that quantifies difficulty and musical fidelity, and they found that subjective difficulty and fidelity increase with controlled difficulty values and that incorporating sequential pitch dependence and fingering motion improves quality in high-difficulty cases.
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.