Automatically describing contents of recorded music is crucial for interacting with large volumes of audio recordings, and for developing novel tools to facilitate music pedagogy. Melody is a fundamental facet in most music traditions and, therefore, is an indispensable component in such description. In this thesis, we develop computational approaches for analyzing high-level melodic aspects of music performances in Indian art music (IAM), with which we can describe and interlink large amounts of audio recordings. With its complex melodic framework and well-grounded theory, the description of IAM melody beyond pitch contours offers a very interesting and challenging research topic. We analyze melodies within their tonal context, identify
melodic patterns, compare them both within and across music pieces, and finally, characterize the specific melodic context of IAM, the rāgas. All these analyses are done using data-driven methodologies on sizable curated music corpora. Our work paves the way for addressing several interesting research problems in the field of music information research, as well as developing novel applications in the context of music discovery and music pedagogy.