Modeling and Analysis of Indian Carnatic Music Using Category Theory

This paper presents a category theoretic ontology of Carnatic music. Our goals here are twofold. First, we will demonstrate the power and flexibility of conceptual modeling techniques based on a branch of mathematics called category theory (CT), using the structure of Carnatic music as an example. Second, we describe a platform for collaboration and research sharing in this area. The construction of this platform uses formal methods of CT (colimits) to merge our Carnatic ontology with a generic model of music information retrieval tasks. The latter model allows us to integrate multiple analytical methods, such as hidden Markov models, machine learning algorithms, and other data mining techniques like clustering, bagging, etc., in the analysis of a variety of different musical features. Furthermore, the framework facilitates the storage of musical performances based on the proposed ontology, making them available for additional analysis and integration. The proposed framework is extensible, allowing future work in the area of ra̅ga recognition to build on our results, thereby facilitating collaborative research. Generally speaking, the methods presented here are intended as an exemplar for designing collaborative frameworks supporting reproducibility of computational analysis and simulation.