Statistical Piano Reduction Controlling Performance Difficulty

TL;DR

This paper introduces a probabilistic approach to convert ensemble scores into piano scores with controllable performance difficulty, balancing musical fidelity and player skill through optimization and statistical modeling.

Contribution

It develops a novel statistical framework that quantifies difficulty and fidelity, enabling adjustable piano reductions based on probabilistic models and iterative inference.

Findings

Difficulty and fidelity increase monotonically with difficulty constraints.

Sequential pitch and fingering models improve high-difficulty reductions.

Iterative optimization enhances the quality of piano reduction scores.

Abstract

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.