A variable neighborhood search algorithm to generate piano fingerings for polyphonic sheet music

Abstract

A piano fingering indicates which finger should play each note in a piece. Such a guideline is very helpful for both amateur and experienced players in order to play a piece fluently. In this paper, we propose a variable neighborhood search algorithm to generate piano fingerings for complex polyphonic music, a frequently encountered case that was ignored in previous research. The algorithm takes into account the biomechanical properties of the pianist's hand in order to generate a fingering that is user‐specific and as easy to play as possible. An extensive statistical analysis was carried out in order to tune the parameters of the algorithm and evaluate its performance. The results of computational experiments show that the algorithm generates good fingerings that are very similar to those published in sheet music books.

Statistical learning and estimation of piano fingering

“…In this paper, we introduced a newly released dataset (PIG Dataset) and studied statistical learning and estimation methods for piano fingering. The statistical modeling approach has the advantage of enabling efficient parameter estimation from data and even the first-order HMM outperformed the representative constraint-based method [3] in terms of the estimation accuracies, when the model was trained with a sufficient amount of data. Incorporating longer-range sequential dependence by means of higher-order HMMs further increased the accuracies and achieved the current state-of-the-art performance.…”

“…Among the methods proposed in previous studies reviewed in Section 2, only the VNS method [3] has public source code provided. This method, which is a refinement of [28], can be considered as a representative constraint-based method.…”

“…From a computational viewpoint, finding an appropriate fingering for these musical instruments often involves a complex combinatorial optimization problem. Automatic fingering estimation [1,3,8,11,13,18,21,23,28,39,41] has been a topic of music information processing with the aim of understanding the computational process of music performance and is used both in performance assistance and education systems [16,31,34,38] as well as for music arrangement [12,24]. There are also a growing number of public repositories 1 related to piano fingering generation, indicating the general interests in this topic.…”

MorpheuS: Generating Structured Music with Constrained Patterns and Tension

“…In this research, we chose to implement a VNS algorithm because it has been shown to outperform several other heuristics (including genetic algorithms) on a range of problems [82]. Since its inception in the late 90s, it has been successfully applied to problems in combinatorial optimization including project scheduling [83], finding extremal graphs [84], vehicle routing [85], graph coloring [86], and piano fingering [87].…”

Generating Fingerings for Polyphonic Piano Music with a Tabu Search Algorithm

“…Parncutt's original cost factors for piano fingering have been expanded by Jacobs [15] and Lin and Liu [16]. More recently, some improvements and additions were made by the authors [17]. It is that set that is used in this Preprint accepted for publication in Mathematics and Computation in Music.…”