The Role of Statistics in Computational Musicology

Part of the Computational Music Science book series (CMS)


Music analysis, broadly speaking, can be divided into commonality analysis (“what is common?”) and diversity analysis (“what is special?”). It is worth pointing out here that a statistician is essentially a commonality expert in the sense that the philosophy of statistics is to summarize and average and make inferences which are true on the whole and which describe a process rather than an individual entity. Fortunately, there are issues in music where this traditional mindset of the statistician finds a support. For example, a collection of recordings of the same artist if analyzed statistically will definitely reflect certain common features having to do with the style of the artist. But the statistician must realize that every single music piece will have something special to offer. Fortunately, again, there are issues even in statistics where the statistician does take an individual observation seriously—as in the case of an outlier or influential observation, for example. There is a whole literature in statistics to deal with outliers. When an outlier comes, the traditional philosophy of summarizing and averaging is brushed aside. The statistician goes after this individual influential observation exploring how it came and what it signifies. The case of outliers is an exception in statistics. It is the very grammar in music as music is a work of art! If the statistician can use his experience and mindset of handling outliers (regarding every musical piece as a musical outlier) along with his commonality expertise, he can be a very effective music analyst. Similar point of view has been expressed by Nettheim who has also provided a good bibliography of statistical applications in musicology (Nettheim 1997). For a sound statistical treatment of musical data, see Beran and Mazzola (1999). Additionally, we acknowledge the contributions from Meyer (1989), Snyder (1990), Winkler (1971), Wilson (1982), Todd and Loy (1991), and Morehen (1981). It is an irony that computational musicology in Indian classical music is still lagging behind the progress in Western classical counterpart, although we do appreciate the efforts of Castellano et al. (1984), Chordia and Rae (2007), and Sinha (2008) among others. We hope this book will provide some food for thought in that direction. Statistics is a useful tool both for analyzing a musical structure and quantitative assessment of a musical performance. The former helps in revealing features of a musical piece in general, while the latter brings the style of the artist into consideration as well in performing the musical piece.


Musical Performance Musical Piece Musical Structure Revealing Feature Musical Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. K. Adiloglu, T. Noll, K. Obermayer, A paradigmatic approach to extract the melodic structure of a musical piece. J. Music Res. 35(3), 221–236 (2006)CrossRefGoogle Scholar
  2. D. Benson, Music: A Mathematical Offering (Cambridge University Press, New York, 2007)Google Scholar
  3. J. Beran, Statistics in Musicology (Chapman and Hall/CRC, Boca Raton, FL, 2004)zbMATHGoogle Scholar
  4. J. Beran, G. Mazzola, Analyzing musical structure and performance – a statistical approach. Stat. Sci. 14(1), 47–79 (1999)CrossRefzbMATHGoogle Scholar
  5. M.A. Castellano, J.J. Bharucha, C.L. Krumhansl, Tonal hierarchies in the music of north India. J. Exp. Psychol. Gen. 113(3), 394–412 (1984)CrossRefGoogle Scholar
  6. S. Chakraborty, S.S. Solanki, S. Roy, S.S. Tripathy, G. Mazzola, A statistical comparison of performance two ragas (dhuns) that use the same notes, in Proceedings to the International Symposium on Frontiers of Research in Speech and Music (FRSM2008), held at Sir C. V. Raman Centre for Physics and Music, Jadavpur University, Kolkata on 20–21 Feb 2008, pp. 167–171Google Scholar
  7. S. Chakraborty, R. Ranganayakulu, S. Chauhan, S.S. Solanki, K. Mahto, A statistical analysis of raga Ahir Bhairav. J. Music Meaning 8, sec. 4 (Winter 2009a),
  8. S. Chakraborty, R. Ranganayakulu, S.S. Solanki, A. Patranabis, D. Ghosh, R. Sengupta, A.K. Dutta, N. Dey, Shadowing along the maestro’s rhythm. Revista eletronica de musicologia (Electron. Musicol. Rev.) XII (2009b)Google Scholar
  9. S. Chakraborty, M. Kumari, S.S. Solanki, S. Chatterjee, On what probability can and cannot do: a case study in Raga Malkauns. J. Acoust. Soc. India 36(4), 176–180 (2009c)Google Scholar
  10. S. Chakraborty, K. Krishnapryia, K. Loveleen, S. Chauhan, S.S. Solanki, K. Mahto, Melody revisited: tips from Indian music theory. Int. J. Comput. Cognit. 8(3), 26–32 (2010)Google Scholar
  11. S. Chakraborty, S. Tewari, G. Akhoury, S.K. Jain, J. Kanaujia, Raga analysis using entropy. J. Acoust. Soc. India 38(4), 168–172 (2011)Google Scholar
  12. P. Chordia, A. Rae, Raag recognition using pitch-class and pitch-class dyad distributions, in Proceedings of International Conference on Music Information Retrieval, 2007Google Scholar
  13. N.A. Jairazbhoy, The rags of North India: Their Structure and Evolution (Faber and Faber, London, 1971)Google Scholar
  14. C.S. Jones, Indian classical music, tuning and ragas,
  15. B. Klemens, Modeling with Data: Tools and Techniques for Scientific Computing (Princeton University Press, Princeton, NJ, 2008)Google Scholar
  16. L.B. Meyer, Style and Music: Theory, History, and Ideology (University of Pennsylvania Press, Philadelphia, PA, 1989) (Re statistics: 57–65)Google Scholar
  17. J. Morehen, Statistics in the analysis of musical style, in Proceedings of the Second International Symposium on Computers and Musicology, Orsay (CNRS, Paris, 1981), pp. 169–183Google Scholar
  18. N. Nettheim, A bibliography of statistical applications in musicology. Musicol. Aust. 20, 94–106 (1997)CrossRefGoogle Scholar
  19. P. Sinha, Artificial composition: an experiment on Indian music. J. New Music Res. 37(3), 221–232 (2008)CrossRefGoogle Scholar
  20. J.L. Snyder, Entropy as a measure of musical style: the influence of a priori. Assumptions Music Theory Spectr. 12, 121–160 (1990)CrossRefGoogle Scholar
  21. D. Temperley, Music and Probability (MIT Press, Cambridge, MA, 2007)zbMATHGoogle Scholar
  22. S. Tewari, S. Chakraborty, Linking raga with probability. Ninad J. ITC Sangeet Res. Acad. 25, 25–30 (2011)Google Scholar
  23. P.M. Todd, D.G. Loy, Music and Connectionism (MIT Press, Cambridge, MA, 1991)Google Scholar
  24. S.R. Wilson, R. Sue, Sound and exploratory data analysis, in Compstat Conf. Part I: Proc. in Compu. Stat., ed. by H. Caussinus, P. Ettinger, R. Tomassone (Physica, Vienna, 1982), pp. 447–450Google Scholar
  25. W. Winkler, Statistical analysis of works of art. Bull. Int. Stat. Inst. 44(2), 410–415 (1971)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Applied MathematicsBirla Institute of Technology (BIT), MesraRanchiIndia
  2. 2.School of MusicUniversity of MinnesotaMinneapolisUSA
  3. 3.Dept. of Computer ApplicationsNetaji Subhash Engineering Coll (NSEC)KolkataIndia

Personalised recommendations