Representing Classical Compositions through Implication-Realization Temporal-Gestalt Graphs

TL;DR

This work introduces a cognitively informed graph representation for classical melodies by segmenting lines into perceptual units, annotating nodes with I-R expectancy and dominant symbols, and connecting segments via DTW-based k-NN graphs. It leverages Weisfeiler-Lehman graph kernels to compare intra- and inter-piece similarity, graph2vec embeddings for fixed-length representations, and MDS for segment-level validation, demonstrating that graph structure aligns with perceptual similarity and captures stylistic features beyond composer identity. The results show strong intra-piece coherence, meaningful cross-piece relations, and clustering driven by expressive and structural traits rather than solely by author, indicating the framework’s potential for nuanced computational music analysis. The approach offers a scalable, cognitively grounded method for analyzing musical structure and style, with implications for music information retrieval, stylistic classification, and theoretical modeling of listener-perceived musical form.

Abstract

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.

Figures (11)

• Figure 1: Methodology Flowchart
• Figure 2: An excerpt from Chopin’s Étude Op. 25 No. 11 ("Winter Wind"), annotated using the Implication-Realization (IR) model. Notes are color-coded and labeled to illustrate IR patterns.
• Figure 3: An excerpt from the first movement of Mozart’s Sonata No. 10 in C major (K. 330), illustrating the segmentation approach. Each color-coded group of notes indicates a distinct segment identified through Gestalt-based rules.
• Figure 4: A graph representation of Chopin's Waltz Op. 34 No. 2 in A Minor.
• Figure 5: Partitions of Chopin's Waltz Op. 34 No. in A Minor using the Kernighan-Lin algorithm.