Estimation Algorithm Of Playable Piano Fingering By Pitch Difference-Fingering Matching Model

The expressiveness and appeal of keyboard instrument music is often directly related to fingering,so finding suitable fingerings for music scores is the first challenge for players.Nowadays fingering is determined mostly dependent on experience via trial and error,it is non-trivial for novice,even for virtuoso.From a computational point of view,automatic labeling of piano fingering is a typical combinatorial optimization problem.Therefore,research on automatic labeling of piano fingering is valuable in theory and is one of the most important tasks for machines to understand musical symbols.The existing piano fingering labeling statistical models usually consider the constraints among the fingers and the correlation between fingering and notes,while rarely include the relationship among the notes directly.The learned finger-transfer rules often cause that some parts of the fingering cannot be playable in fact.And traditional models often foucus on the original notes,which fails to reflect the nature of the mapping relationship between pitch and fingering to a great extent.To address this problem,we proposed a pitch-difference fingering(PdF)matching model.And bidirectional recurrent neural network is used to fit the relationship between pitch difference and fingering.And to get playable fingering,besides learned finger-transfer rules,prior finger-transfer knowledge is especially combined into the model.We use the PIG data set,the only public piano fingering data set currently published,which contains only 309 samples.In order to improve the generalization ability of the model,we propose a method for expanding the pitch-difference fingering data set.In order to characterize the playable performance of the model,we also present a new evaluation measure named incapable-performing fingering rate(IFR).Experimental results show that compared with the existing state-of-the-art third-order hidden Markov labeling model,the general and the highest matching rate of our model increases by 3% and 1.6% respectively,and the fingering for all scores can be playable.In addition,in order to examine the effect of each improved point in the model,we did an ablation experiment.The original note sequence and pitch difference(Pd)sequence were used for training.With the same data size,both the general and the highest matching rate of the Pdf model are more than 10% higher than that of the original note fingering one.The design of the bidirectional recurrent network,the introduction of learned fingering transfer relations,the addition of prior fingering knowledge and the addition of expansion sets all contribute to the improvement of fingering estimation results.Experiment results show that the pitch difference with time and physical distance information is more suitable for fingering estimation than original musical note information.Combined with the fingering transfer constraint,the BILSTM network is more like the way of manually fingering determinination,and can get better results.The context instead of one-sided information is more helpful to predict the fingering.And prior fingering transfer knowledge can ensure the playability of fingering.