Hindustani classical music revisited statistically: Does the order of Markov chain in the note dependence depend on the raga or the composition?

Soubhik Chakraborty; Aiman Habib; Prerna Singh

doi:10.59400/jam.v2i1.281

Hindustani classical music revisited statistically: Does the order of Markov chain in the note dependence depend on the raga or the composition?

Soubhik Chakraborty Department of Mathematics, Birla Institute of Technology Mesra, Ranchi 835215, India
Aiman Habib Department of Mathematics, Birla Institute of Technology Mesra, Ranchi 835215, India
Prerna Singh Department of Mathematics, Birla Institute of Technology Mesra, Ranchi 835215, India

Article ID: 281

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DOI: https://doi.org/10.59400/jam.v2i1.281

Keywords: Hindustani classical music; raga; stochastic process; order of Markov chain; AIC (Akaike’s information criterion)

Abstract

Rendering musical notes randomly does not create music. To generate music, there has to be a pattern that makes the musical notes dependent. It is therefore of interest to know whether the probability of the next note depends on the current note only or whether it depends on the note(s) prior to the current note. In other words, it is important to explore the order of the Markov chain in the musical piece. In the context of Hindustani classical music, does this order depend on the raga or the composition? The present work addresses this fascinating question and attempts to answer it through Akaike’s information criterion (AIC). It appears, interestingly, that the order of the Markov chain is dependent on the raga, which has a well-defined melodic structure with fixed notes and a set of rules characterizing a particular mood that is conveyed by performance. As long as these rules are maintained, as in a raga bandish, the order of the Markov chain is invariant over the raga compositions.

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Published

2024-01-23

How to Cite

Chakraborty, S., Habib, A., & Singh, P. (2024). Hindustani classical music revisited statistically: Does the order of Markov chain in the note dependence depend on the raga or the composition?. Journal of AppliedMath, 2(1), 281. https://doi.org/10.59400/jam.v2i1.281

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