A Generative Model of Ragas Using Directed Graphs

This paper introduces melodic graphs—directed graphs with vertices representing individual notes and paths representing sequences of notes—to model note transitions in a context-specific and phrase-driven way. The generative capacity of melodic graphs is demonstrated here through the Carnatic raga Haṃsadhvani. A melodic graph was created by representing 16 short phrases in the raga as a connected graph with directed edges. A sample of 10 phrases generated using the melodic graph and 10 random sequences were evaluated by 8 musicians trained in Carnatic music. The phrases were rated on a scale of 1-10, with 1 representing no fit, and 10 representing a good fit of the phrase within the raga. The generated phrases received a significantly higher average rating than the random sequences (average rating of graph-generated sequences: 8.2/10; vs. random sequences: 3.6/10; p << 0.01). Thus, the melodic graph models Haṃsadhvani effectively. Future work with other ragas and using more sophisticated melodic graphs is needed to fully explore their applications in music education, raga representation and modelling, and computer-assisted music generation.