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 operations. Recent approaches to melodic elaboration have converged to a representation based on intervals, which allows the elaboration of pairs of notes. However, two problems 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 operations 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 perspectives on latent structure behind melodies and music in general. The presented grammar is based on a graph representation that allows one to express elaborations on both notes and intervals, unifying and generalizing previous graph- and tree-based approaches.