用概率模型分析音乐动机的变形规律,揭示贝多芬钢琴奏鸣曲中的创作逻辑。
Probabilistic Multilabel Graphical Modelling of Motif Transformations in Symbolic Music
- 将动机变形建模为多标签变量,统一标注不同变体。
- 通过条件随机场发现不同变形类型常协同出现。
- 适合研究音乐结构与作曲风格的学者使用。
音乐动机在作品中常以变化形式重复出现,保持部分身份特征的同时发生局部变异。本文研究符号音乐中此类动机变形如何在其音乐语境中发生。为此,我们构建了一个概率框架,整合旋律、节奏、和声及动机信息,应用于贝多芬钢琴奏鸣曲。通过将每个动机实例与局部上下文中的指定参考版本对比,实现跨变形家族的一致标签化。引入多标签条件随机场,建模动机层面特征如何影响变形发生,并揭示不同变形家族之间的共现模式。目标是提供可解释的、分布式的动机变形分析,支持对结构性关系与风格变异的研究。该框架结合计算建模与音乐理论,促进符号语料库中音乐结构与复杂性的量化探究,有望拓展对作曲模式与创作实践的分析。
原文摘要 · Abstract (English)
Motifs often recur in musical works in altered forms, preserving aspects of their identity while undergoing local variation. This paper investigates how such motivic transformations occur within their musical context in symbolic music. To support this analysis, we develop a probabilistic framework for modeling motivic transformations and apply it to Beethoven's piano sonatas by integrating multiple datasets that provide melodic, rhythmic, harmonic, and motivic information within a unified analytical representation. Motif transformations are represented as multilabel variables by comparing each motif instance to a designated reference occurrence within its local context, ensuring consistent labeling across transformation families. We introduce a multilabel Conditional Random Field to model how motif-level musical features influence the occurrence of transformations and how different transformation families tend to co-occur. Our goal is to provide an interpretable, distributional analysis of motivic transformation patterns, enabling the study of their structural relationships and stylistic variation. By linking computational modeling with music-theoretical interpretation, the proposed framework supports quantitative investigation of musical structure and complexity in symbolic corpora and may facilitate the analysis of broader compositional patterns and writing practices.
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