"Rhythm as Language": A Cognitive Analysis of Krzysztof Penderecki’s “Cadenza for Solo Violin” Based on Lerdahl and Jackendoff’s Theory

Krzysztof Penderecki’s Cadenza for Solo Violin, characterized by its free structure and absence of fixed meter, poses a significant challenge for analyses and performers of contemporary music. This study investigates the application of the Tonal Music Generative Theory of Lerdahl and Jackendoff, a framework inspired by Chomsky’s generative grammar in the 1980s, which seeks to represent the cognitive processes underlying musical perception through a hierarchical and systematic model. The theory emphasizes four core components - grouping structure, metrical structure, time-span reduction, and prolongational structure - each capturing a different dimension of musical organization, collectively offering a comprehensive tool for understanding the layers of perceptual experience in music. By analyzing these structures, it becomes evident that music, like language, is organized according to well-formedness rules and transformational principles. However, fundamental differences remain: whereas linguistic meaning depends on syntactic combinations and transformational operations, musical meaning primarily emerges from perceptual relationships such as tension and release, stability and instability, or motion and stasis. Therefore, although musical syntax draws inspiration from linguistic models, elements unique to music - such as timbre, dynamics, and texture - prevent a complete one-to-one correspondence. The generative theory of music thus represents not a mere “musical translation” of linguistic principles, but an independent analytical framework grounded in cognitive processes. Analytical findings indicate that grouping and metrical rules are applicable not only in tonal classical music but also, with certain limitations, in contemporary and atonal compositions. The prolongational structure, which accounts for tension–release relationships throughout a piece, provides a particularly flexible tool for analyzing modern and experimental works, as it is not strictly dependent on tonal or metric conventions. Conversely, time-span reduction relies more heavily on tonal hierarchies and harmonic stability, naturally constraining its applicability in non-tonal contexts. From a practical perspective, adopting the Lerdahl–Jackendoff framework can assist performers and educators in clarifying perceptual structures for students. Understanding hierarchical grouping and metric relationships enables musicians to achieve not only technical accuracy but also musical coherence. Prolongational analysis further allows performers to interpret moments of tension, relaxation, and forward motion, guiding listener experience through informed expressive choices. Consequently, the theory functions both as an analytical tool and as a practical guide for musical interpretation and expression. At a research level, this study demonstrates that interdisciplinary approaches - here combining linguistics and music cognition - can open new avenues for understanding. Comparative analysis of language and music highlights shared hierarchical organization and cognitive mechanisms, though non-hierarchical musical dimensions, such as timbre and dynamics, remain formally unmodeled, representing opportunities for future investigation. In conclusion, the Lerdahl–Jackendoff theory constitutes a foundational step toward a cognitive understanding of music, with significant implications for analysis, performance, and pedagogy. It reveals that the musical listening experience arises not solely from the written score or technical execution but from complex, unconscious mental processes. Applying this framework can enrich analytical insights, performance practices, and pedagogical strategies, offering musicians and scholars alike a deeper engagement with both tonal and contemporary repertoires.