Modelling the Syntax of North Indian Melodies with a Generalized Graph Grammar

Hierarchical models of music allow explanation of highly complex musical structure based on the general principle of recursive elaboration and a small set of orthogonal op- erations. Recent approaches to melodic elaboration have converged to a representation based on intervals, which al- lows the elaboration of pairs of notes. However, two prob- lems remain: First, an interval-first representation obscures one-sided operations like neighbor notes. Second, while models of Western melody styles largely agree on step- wise operations such as neighbors and passing notes, larger intervals are either attributed to latent harmonic properties or left unexplained. This paper presents a grammar for melodies in North Indian raga music, showing not only that recursively applied neighbor and passing note oper- ations underlie this style as well, but that larger intervals are generated as generalized neighbors, based on the tonal hierarchy of the underlying scale structure. The notion of a generalized neighbor is not restricted to ragas but can be transferred to other musical styles, opening new perspec- tives on latent structure behind melodies and music in gen- eral. The presented grammar is based on a graph represen- tation that allows one to express elaborations on both notes and intervals, unifying and generalizing previous graph- and tree-based approaches.