The musicological analysis of Carnatic music is challenging, owing to its rich structure and complexity. Automated \textit{rāga} classification, pitch detection, tonal analysis, modelling and information retrieval of this form of southern Indian classical music have, however, made significant progress in recent times. A causal analysis to investigate the musicological structure of Carnatic compositions and the identification of the relationships embedded in them have never been previously attempted. In this study, we propose a novel framework for causal discovery, using a compression-complexity measure. Owing to the limited number of compositions available, however, we generated surrogates to further facilitate the analysis of the prevailing causal relationships. Our analysis indicates that the context-free grammar, inferred from more complex compositions, such as the \textit{Mē\d{l}akarta} \textit{rāga}, are a \textit{structural cause} for the \textit{Janya} \textit{rāga}. We also analyse certain special cases of the \textit{Janya rāga} in order to understand their origins and structure better.