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

  • Nandini Sarma
  • Pranita Sarmah
Chapter
Part of the Asset Analytics book series (ASAN)

Abstract

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.

Keywords

Graph theory Indian classical music Markov chain Musical graph Musical cycle 

References

  1. 1.
    Peusner L (2002) A graph topological representation of melody scores. Leonardo Music J 12:33–40. MIT Press, USAGoogle Scholar
  2. 2.
  3. 3.
    Szeto MW, Wong HM (2006) A graph-theoretical approach for pattern matching in post-tonal music analysis. J New Music Res 35(4):307–321CrossRefGoogle Scholar
  4. 4.
  5. 5.
    Santhi B, Sairam N (2011) Melakartha, raga generation through breadth first search algorithm. J Theor Appl Inf Technol 31(2):88–90Google Scholar
  6. 6.
  7. 7.
    Haus G, Pinto A (2004) A graph theoretic approach to melodic similarity. In: Proceedings of the second international conference on computer music modeling and retrieval, pp 260–279. Springer, Denmark (2004)Google Scholar
  8. 8.
    Haus G (2005) A graph theoretic approach to melodic similarity. Lecture Notes in Computer ScienceGoogle Scholar
  9. 9.
    Bhatkhande VN (1993) Hindustani Sangeet Paddhati: Kramik Pustak Mallika, vol 1–6, Sangeet Karyalaya, HathrasGoogle Scholar
  10. 10.
    Shetty S, Achary KK (2009) Raga mining of indian music by extracting arohana—avarohana pattern. Int J Recent Trends Eng 1(1):362–366Google Scholar
  11. 11.
  12. 12.
    en.m.wikipedia.orgGoogle Scholar
  13. 13.
  14. 14.
    Ghosh D, Sengupta R, Sanyal S, Banerjee A (2018) Musicality of human brain through fractal analytics. SpringerGoogle Scholar
  15. 15.
  16. 16.
  17. 17.
    The Physics Hypertextbook. http://physics.info/music/
  18. 18.
    Jairazbhoy NA (1972) Factors underlying important notes in North Indian music. Ethnomusicology 16:63–81CrossRefGoogle Scholar
  19. 19.
    Liu WY, Field ES (2002) Modeling music as Markov chains: composer identification. Music, 254 Final Report, Stanford University. https://ccrma.stanford.edu
  20. 20.
    Chakraborty S, Mazzola G, Tewari S, Patra M (2014) An introduction to Indian classical music. Springer. Chapter 1Google Scholar
  21. 21.
    Bondy JA, Murty USR (1976) Graph theory with applications. The Macmillan Press Ltd, Great BritainCrossRefGoogle Scholar
  22. 22.
    Sarma N, Sarmah P (2013) Grammatical structures of the ten common thaats of North Indian classical music: a graph theoretic approach. Assam Stat Rev 25:62–76Google Scholar
  23. 23.
    Vir RA (2000) Theory of Indian ragas. Pankaj Publications, New DelhiGoogle Scholar
  24. 24.

Copyright information

© 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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