arXiv:2510.27530cs.SDcs.LG2025-10

用认知模型构建音乐图谱,揭示听众感知的结构规律。

Representing Classical Compositions through Implication-Realization Temporal-Gestalt Graphs

  • 将旋律分段并标注预期模式,生成含认知信息的图结构。
  • 图相似性分析显示不同作品间存在显著结构差异。
  • 能捕捉风格特征,超越作曲家身份,适合音乐分析研究者。

理解音乐作品的结构与认知基础仍是音乐理论和计算音乐学的关键挑战。传统方法侧重和声与节奏,而认知模型如意涵-实现(I-R)模型和时间格式塔理论则揭示了听众所感知与预期的音乐结构机制。本文提出一种基于图的计算方法,将旋律分割为感知单元,并标注I-R模式;通过动态时间规整比较片段,构建k近邻图以建模段内与段间关系。每个片段作为图中节点,节点标签来自Schellenberg的两因素I-R模型,量化音高接近度与音高反转程度,从而编码结构与认知信息,反映听众体验中的张力与解决。利用Weisfeiler-Lehman图核评估图间与图内相似性,结果表明段内与段间结构存在统计显著差异。多维缩放分析确认图级结构相似性对应段级感知相似性。Graph2vec嵌入与聚类显示该表示可捕捉超越作曲家身份的风格与结构特征。这些发现表明,基于图的方法为计算音乐分析提供了一种结构化、认知驱动的框架,使音乐结构与风格的理解更贴近听众感知。

原文摘要 · Abstract (English)

Understanding the structural and cognitive underpinnings of musical compositions remains a key challenge in music theory and computational musicology. While traditional methods focus on harmony and rhythm, cognitive models such as the Implication-Realization (I-R) model and Temporal Gestalt theory offer insight into how listeners perceive and anticipate musical structure. This study presents a graph-based computational approach that operationalizes these models by segmenting melodies into perceptual units and annotating them with I-R patterns. These segments are compared using Dynamic Time Warping and organized into k-nearest neighbors graphs to model intra- and inter-segment relationships. Each segment is represented as a node in the graph, and nodes are further labeled with melodic expectancy values derived from Schellenberg's two-factor I-R model-quantifying pitch proximity and pitch reversal at the segment level. This labeling enables the graphs to encode both structural and cognitive information, reflecting how listeners experience musical tension and resolution. To evaluate the expressiveness of these graphs, we apply the Weisfeiler-Lehman graph kernel to measure similarity between and within compositions. Results reveal statistically significant distinctions between intra- and inter-graph structures. Segment-level analysis via multidimensional scaling confirms that structural similarity at the graph level reflects perceptual similarity at the segment level. Graph2vec embeddings and clustering demonstrate that these representations capture stylistic and structural features that extend beyond composer identity. These findings highlight the potential of graph-based methods as a structured, cognitively informed framework for computational music analysis, enabling a more nuanced understanding of musical structure and style through the lens of listener perception.

音乐分析认知模型图神经网络结构建模

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