An algorithmic approach to South Indian classical music
We develop a theoretical framework for representation and automated generation of South Indian classical music. The foundational part of the latter is based on symbolic dynamics and is implemented by translating the lexicographic rules for a rāga to constraints on a Markov chain whose state space is a layered graph. We analyze the statistical properties of this Markov chain from the point of view of information theory. We also develop several tools in music signal processing, such as, (a) a procedure for automated generation of gamakas or ornamental notes, unique to South Indian classical music, (b) rhythm synchronization, and (c) an algorithm for perceptual scale shifts. The Online Supplement has computer synthesized music from Śankarābharaṇa rāga, rhythm synchronized music for a Mōhana rāga composition, original and synthesized gamakas over madhyama for Begaḍa and Nīlāmbari rāgas, and perceptually scale shifted rāgas Hindoḷa, Madhyamāvati, Śuddha sāveri, and Udaya ravi chandrikā rāgas from the base Mōhana rāga.