Most existing statistical models used to predict piano fingering apply explicit constraints among fingers and between fingers and notes; however, they disregard the relationship among notes. Furthermore, the state transfer matrix of HMM often makes the fingering of notes in compact scales unplayable without moving the hands. The direct adoption of notes interferes with mapping between specific pitches and the corresponding fingering. Inspired by human annotation and the note span constraints used in rule-based methods (in which fingering knowledge is acquired from span), we developed a model by which to match pitch difference and finger sequences (PdF). Playable fingering is achieved by combining learned finger-transfer knowledge with priori finger-transfer knowledge. The playability of the model was evaluated using a novel index, referred to as the irrational fingering rate (IFR). Experiment results demonstrate that the proposed model outperforms the third-order hidden Markov finger annotation model in terms of average match rate (by 4.06%) and highest match rate (by 2.87%). The proposed scheme also resolves the unplayable-without-hand-movement problem in compact scales.

中文翻译：

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用音高差指法匹配模型估计可演奏钢琴指法

大多数现有的用于预测钢琴指法的统计模型都在手指之间以及手指和音符之间应用了明确的约束；但是，他们忽略了音符之间的关系。此外，HMM 的状态转移矩阵经常使紧凑音阶中的音符指法无法在不移动手的情况下演奏。直接采用音符会干扰特定音高和相应指法之间的映射。受人类注释和基于规则的方法（其中指法知识是从跨度中获取）中使用的音符跨度约束的启发，我们开发了一个模型来匹配音高差异和手指序列（PdF）。通过将学习的手指转移知识与先验的手指转移知识相结合来实现可演奏的指法。模型的可玩性使用新的指标进行评估，称为非理性指法率（IFR）。实验结果表明，该模型在平均匹配率（4.06%）和最高匹配率（2.87%）方面优于三阶隐马尔可夫手指标注模型。所提出的方案还解决了紧凑尺度下无法播放的问题。