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Dynamical analysis of compositions

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Abstract

This paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus on a large number of compositions classified along three sets of musical styles, namely “Classical”, “Jazz”, and “Pop & Rock” compositions. Without lack of generality, the present study describes the application of the tools and the sets of musical compositions in a methodology leading to clear conclusions, but extensions to other possibilities are straightforward. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments toward a dynamical analysis of musical compositions.

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Authors and Affiliations

  1. Dept. of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

  2. Dept. of Informatics Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    António C. Costa

  3. Dept. of Electrical Engineering, School of Technology of Viseu, Campus Politécnico de Repeses, 3504-510, Viseu, Portugal

    Miguel F. M. Lima

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  1. J. A. Tenreiro Machado
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  2. António C. Costa
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Correspondence to J. A. Tenreiro Machado.

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Tenreiro Machado, J.A., Costa, A.C. & Lima, M.F.M. Dynamical analysis of compositions. Nonlinear Dyn 65, 399–412 (2011). https://doi.org/10.1007/s11071-010-9900-6

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