# Rhythm-Based Attention Analysis: A Comprehensive Model for Music Hierarchy
## 5 Discussion  
Our experimental results demonstrate that the fractal-driven approach to hierarchical music analysis achieves state-of-the-art performance in phrase segmentation tasks, outperforming both rule-based and machine learning baselines on the Essen Folksong Collection. The model's superior F1-score (83%) and balanced precision-recall profile (83% precision and 84% recall) highlight its ability to reconcile the competing demands of boundary detection accuracy and structural coherence preservation. A key strength of our fractal-driven approach is its capacity for transparent structural visualization, as exemplified in Figure 8. This visualization demonstrates how our model parses a music piece into hierarchical segments while simultaneously quantifying the \"rhythmic attention\" contribution of individual notes. The figure displays the original score annotated with phrase boundaries (V in figure) and segment divisions (+ in figure), revealing the model's ability to capture the underlying structure of the melody. The rhythmic attention values are represented as a color gradient, with red indicating higher attention. This visualization not only aids in understanding the model's decision-making process but also provides a valuable tool for musicologists and composers to analyze and interpret musical structures. Our experimental outcomes systematically validate the four research hypotheses. Hypothesis 1 is confirmed through the model's consistent hierarchical segmentation across meters (Table 5), where nested phrase boundaries exhibit self-similar rhythmic patterns aligning with [PERSON]'s hierarchical principles. Hypothesis 2 gains support from the fractal characteristics analysis, and we prove that the fractal dimension \(D_{f}\approx 2-0.496=1.504\) for our proposed quantization scheme for rhythmic attention. The 7.75% F1-score drop when removing rhythmic grouping operators (Table 6) corroborates Hypothesis 3, proving operator-driven detection surpasses conventional similarity measures. The proposed model outperforms existing baseline models, demonstrating its potential for advancing music analysis and understanding. The integration of rhythmic grouping operators and the quantization scheme allows for a more nuanced representation of musical structure, paving the way for future research in this area. The research questions posed at the beginning of this study have been addressed through the proposed model and its evaluation. The model's ability to accurately segment musical phrases and capture hierarchical structures provides a solid foundation for further exploration of music analysis tasks. The findings suggest that the proposed approach can be extended to other aspects of music analysis, such as similarity detection and composition. Our model adapts robustly to a wide spectrum of metrical types. When confronted with non-standard meters (e.g., 5/8), the \(k\)-value detection algorithm introduced in Section 3.1.3 dynamically selects the most appropriate subdivision value and partitioning pattern on the basis of the incoming note-level rhythmic features before passing control to the subsequent hierarchical parsing stages. In parallel, the KL-divergence-guided tree-construction heuristic steers the model toward a merger strategy that balances information compression with structural fidelity, ensuring that the resulting segmentation tree remains both parsimonious and musically plausible. Moreover, our work may aid socio-emotional music education, music-influence assessment, and speech-in-noise training [48, 49, 50]. We contend that fractal characteristics of the musical structure are not confined to rhythmic organization; they also manifest in melodic contour and harmonic progression. Rhythm was chosen as our entry point because, in symbolic music, temporal information is explicitly encoded and, therefore, readily extracted, affording clear visualizability and interpretability.