Abstract
Today, the relationship between music and mathematics is a common factor. In the last two or three decades, the advances in mathematics, computer science, psychology, semiotics, and related fields, together with technological progress (in particular computer technology), lead to a revival of quantitative thinking in music [see, e.g., Archibald (1972), Babbitt (1961), Balzano (1980), Lewin (1987), Lendvai (1993), Forte (1964, 1973), Morris (1987, 1995), Johnson and Wichern (2002), Leyton (2001), Andreatta (1997), Solomon (1973), Beran and Mazzola (1999), Meyer (1989)]. Musical events can be expressed as a specific ordered temporal sequence, and time series analysis is the observations indexed by an ordered variable (usually time). It is therefore not surprising that time series analysis is important for analyzing musical data as it is always be the function of time. Music is an organized sound. But the equation of these sounds does not produce the formula of how and why sounds are connected. Statistics is a subject which can connect theoretical concept with observable phenomenon and statistical tools that can used to find and analyzing the structure to build a model. But applications of statistical methods in Indian musicology and performance research are very rare. There were some researches that had been done on Western musicology and mostly consist of simple applications of standard statistical tools. Due to the complex nature of music, statistics is likely to play an important role where the random variables are the musical notes which are function of time.
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References
M. Andreatta, Group-theoretical methods applied to music. Ph.D. thesis, University of Sussex, 1997
B. Archibald, Some thoughts on symmetry in early Webern. Perspect. New Music 10, 159–163 (1972)
M. Babbitt, Set structure as a compositional determinant. JMT 5(2), 72–94 (1961)
G.J. Balzano, The group theoretic description of 12-fold and microtonal pitch systems. Comput. Music J. 4(4), 66–84 (1980)
J. Beran, G. Mazzola, Analyzing musical structure and performance: a statistical approach. Stat. Sci. 14(1), 47–79 (1999)
J. Beran, Statistics in Musicology (Chapman & Hall, New York, 2004)
G.E.P. Box, G.M. Jenkins, Time Series Analysis, Forecasting and Control (Holden Day, San Francisco, 1976)
S. Chakraborty, R. Shukla, Raga Malkauns revisited with special emphasis on modeling. Ninad J. ITC Sangeet Res. Acad. 23, 13–21 (2009)
S. Chakraborty, M. Kumari, S.S. Solanki, S. Chatterjee, On what probability can and cannot do: A case study on raga Malkauns, in National Symposium on Acoustics 2009, Hyderabad, India, 26–28 Nov 2009
P. Desikan, J. Srivastava, Time series analysis and forecasting methods for temporal mining of interlinked documents. Department of Computer Science, University of Minnesota, www-users.cs.umn.edu/~desikan/publications/TimeSeries.doc, accessed on January 26, 2014
D. Dutta, Sangeet Tattwa (Pratham Khanda), 5th edn. (Brati Prakashani, 2006) (Bengali) (Kolkata, India)
A. Forte, A theory of set-complexes for music. JMT 8(2), 136–183 (1964)
A. Forte, Structure of Atonal Music (Yale University Press, New Haven, CT, 1973)
R.A. Johnson, D.W. Wichern, Applied Multivariate Statistical Analysis (Prentice Hall, Englewood Cliffs, NJ, 2002)
E. Lendvai, Symmetries of Music (Kodaly Institute, Kecskemet, 1993)
D. Lewin, Generalized Musical Intervals and Transformations (Yale University Press, New Haven, CT, 1987)
M. Leyton, A Generative Theory of Shape (Springer, New York, 2001)
G.M. Ljung, G.E.P. Box, On a measure of lack of fit in time series models. Biometrika 65, 297–303 (1978)
D. McDowall, R. McCleary, E.E. Meidinger, R. Hay Jr., Interrupted Time Series Analysis (Sage Publications, Thousand Oaks, CA, 1980)
L.B. Meyer, Style and Music: Theory, History, and Ideology (University of Pennsylvania Press, Philadelphia, PA, 1989). Re statistics: 57–65
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. 169–183
R.D. Morris, Composition with Pitch-Classes (Yale University Press, New Haven, CT, 1987)
R.D. Morris, Compositional spaces and other territories. PNM 33, 328–358 (1995)
L.J. Solomon, Symmetry as a determinant of musical composition. Ph.D. thesis, University of West Virginia, 1973
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Chakraborty, S., Mazzola, G., Tewari, S., Patra, M. (2014). Modeling Musical Performance Data with Statistics. In: Computational Musicology in Hindustani Music. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-11472-9_7
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