Using Statistical Modeling, Rate of Change of Pitch and Inter-Onset Interval to Distinguish Between Restful and Restless
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Using Statistical Modeling, Rate of Change of Pitch and Inter-Onset Interval to Distinguish Between Restful and Restless Ragas Poonam Priyadarshini1 · Soubhik Chakraborty2
Received: 24 September 2016 / Revised: 11 January 2017 / Accepted: 29 April 2017 / Published online: 14 June 2017 © School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg 2017
Abstract Given that the strength of statistics lies in modelling, we are motivated to do a comparative statistical study between two types of ragas, one being aesthetically known to be restful and the other restless in nature. We first try to distinguish these two types through statistical modeling. To substantiate our findings, two more statistical features are considered in the paper to separate the two categories of ragas, namely the rate of change of pitch and inter-onset interval. The experimental results are encouraging. Keywords Raga · {Restful, restless} nature · Rate of pitch change · Inter Onset interval · Statistical modeling Mathematics Subject Classification 62P99
1 Introduction The strength of statistics lies in modelling. Although statistical models are not unbiased, we can at least make the data unbiased and the mathematical theorems (such as the principle of least squares used to determine the smoothing factor in a simple exponential smoothing model) are free from bias which support these models. Statis-
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Soubhik Chakraborty [email protected] Poonam Priyadarshini [email protected]
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Department of Electronics and Communication Engineering, Birla Institute of Technology, Patna Campus, Patna, India
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Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi, India
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P. Priyadarshini, S. Chakraborty
tical models are not perfect either but they are capable of approximating, with fewer parameters, those true unknown complex models with multiple parameters an explicit idea of which or how they (in what functional form) enter the true model we may not have. It is quite possible to control and minimize the errors in these models as well as verify the goodness of fit of these models which are very much within the scope of statistics (see chap. 2 of [3]). We are motivated to do a comparative statistical study between two types of ragas, one being aesthetically known to be restful (Todi and Malkauns) and the other restless (Pilu and Deshkar) in nature. We first try to distinguish these two types through statistical modeling. Next, to substantiate our findings, two more statistical features are considered in the paper to separate these two categories of ragas, namely the rate of change of pitch and inter-onset interval (IOI). Here it needs to be mentioned that Indian classical music can be categorized as North Indian or Hindustani music and South Indian or Carnatic music and in both forms raga is the nucleus. A raga is defined as a melodic structure with fixed notes, and a set of rules is maintained while playing the notes so that a certain emotion is evoked by performan
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