A Graph-Theoretical Approach for Comparison Between the Pair of Allied Ragas Bhupali and Deshkar of North Indian Classical Music

  • Nandini SarmaEmail author
  • Pranita Sarmah
Part of the Asset Analytics book series (ASAN)


Graph theory has been implicitly incorporated in musicology for discovering patterns in music and to provide a visual way to analyse a melodic sequence. In this paper, graph theory has been employed for understanding the grammar and for analysing the similarities and dissimilarities of a pair of allied ragas (Bhupali and Deshkar) of North Indian classical music. The comparison between the ragas has been performed with respect to the characteristics, viz. (a) ArohanaAvarohana, (b) Catch Phrase, (c) alap. Definitions of musical graph, musical walk, multi-musical graph, musical cycle and connectivity of musical graph are then used for explaining various digraphs of music theory. The transition of musical notes in sample alap of each of the ragas is modelled as a Markov chain. The corresponding weight matrices along with the estimated mean absolute difference of weights of sample alap of Bhupali and Deshkar have also been derived.


Graph theory Indian classical music Markov chain Musical graph Musical cycle 


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of StatisticsAIAS, Amity UniversityNoidaIndia
  2. 2.Department of StatisticsGauhati UniversityGuwahatiIndia

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