Vol. 7, Issue 2, Part E (2025)

A vivid illustration of the intricate relationship that exists between mathematics and music is provided by the Indian tala system, which has rhythmic patterns that are highly improvisatory, recursive, and very organized. In this study, the Kaidas and Paltas, two of the most fundamental rhythmic compositions in Indian classical music, are the topic of analytical modeling using mathematical techniques. The complicated chains of bols, also known as mnemonic syllables, are described in a systematic manner by using formal approaches such as deep pushdown automata and state grammars. These techniques capture the structural and cross-serial interactions between the bols. The findings of this research demonstrate that computer technologies have the potential to preserve the logic of classical compositions while simultaneously precisely assessing, producing, and verifying rhythmic variations. As a result of the study's focus on the educational and creative implications of such modeling, music students, instructors, and composers now have access to a tool that allows them to better comprehend, explore, and create within existent rhythmic frameworks. Despite the fact that the mathematical modeling is extremely precise, it is not capable of capturing the nuances of performance in terms of expression, improvisation, and emotion. The way in which creative techniques and computational methods complement each other is now brought to light. In conclusion, this research contributes to the disciplines of musicology and computational music by combining the knowledge of traditional Indian music with the mathematical and computational methods that are now in use. The findings provide the platform for additional study into advanced talas, melodic integration, and interaction in music education, analysis, and composition since they give the foundation for such research.