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A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane

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  • Miguel F. M. Lima
  • J. A. Tenreiro Machado
  • António C. Costa

Abstract

This paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles the MDS technique is used. The MDS is calculated based on two alternative metrics obtained from the PPP, namely, the average mutual information and the fractal dimension. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical sounds.

Suggested Citation

  • Miguel F. M. Lima & J. A. Tenreiro Machado & António C. Costa, 2012. "A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, July.
    • Handle: RePEc:hin:jnlaaa:436108
    DOI: 10.1155/2012/436108
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    Cited by:

    1. Danutė Krapavickaitė, 2022. "Coherence Coefficient for Official Statistics," Mathematics, MDPI, vol. 10(7), pages 1-20, April.
    2. Ferreira, Paulo & Quintino, Derick & Wundervald, Bruna & Dionísio, Andreia & Aslam, Faheem & Cantarinha, Ana, 2021. "Is Brazilian music getting more predictable? A statistical physics approach for different music genres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

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