Categorization of Indian Classical Music Using MB-BE Distributions

Abstract

Abstract: Information is usually made up of repetitive arrangements of basic patterns. The presence of such sequences contributes to the unique style/behaviour the information congregation represents. Various such congregations like music, language, biological signals exhibit this kind of repetitive patterns of symbolic sequences. The problem of categorizing such information collection is that the usual methods used are mostly nonquantifiable. In this study, its has been quantify that such abstractness using measurable parameters. For that, we introduce methods based on well-known concepts used in Statistical Physics (especially thermodynamics), namely Maxwell-Boltzmann (MB) statistics and Bose-Einstein (BE) distribution, in an attempt of categorization and classification of musical information present in Hindustani classical music. Both MB and BE statistics have wide applications outside the realm of describing the energy level occupation of elementary particles. For example: the usage of statistical physics in the domain of linguistics or social sciences. Here, statistical methods based on these distributions have been applied to find new parameters (equivalent to ‘temperature’ in physical systems) to distinguish between different features of different ragas in Hindustani classical music. To apply MB statistics to music, it is assumed that different notes (combined with their durations) with different occurrence frequencies are at different energy levels, the distribution of which follows the MB distribution pattern. Emerging ‘temperature’ parameter shows how close the said rendition is with the traditional grammatical structure of the said raga (or the amount of improvisations/creativity present in the rendition). In case of BE statistics, a rank-frequency distribution of the time durations of various notes occurring in different ragas is studied to obtain ‘temperature-alike’ statistical parameters, unprecedented in any previous studies. This novel method of analysis is then applied on different renditions of the same Raga. Music clips chosen were the Vandish part of the same raga sung by three legendary classical music maestros. The resulting analysis gives a number of parameters (they come from the analogy between the rank-frequency distribution and the respective statistical distribution) that help categorize the singing styles of the three renditions and parameters which are indicative of abstract ideas such as individual improvisation pattern. The results found shed new lights on the characterization of different ragas and their performances across different eras and artists. The methods studied here are novel in the music research field and are found to be effective in their projected goals. Hence, they can prove to be useful in the fields of music and speech as quantifying parameters for qualitative research questions such as style identification and speaker recognition.

Keywords: Maxwell-Boltzmann distribution, Bose-Einstein distribution, Indian classical music, Raga, temperature

Cite this Article: Souparno Roy, Archi Banerjee, Shankha Sanyal, Dipak Ghosh, Ranjan Sengupta, Categorization of Indian Classical Music Using MB-BE Distributions. Journal of Software Engineering Tools & Technology Trends. 2019; 6(3): 9–15p.