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

Miguel F. M. Lima | Zendy; J. A. Tenreiro Machado | Zendy; António C. Costa | Zendy

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

Author(s) -

Miguel F. M. Lima,

J. A. Tenreiro Machado,

António C. Costa

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/436108

Subject(s) - musical , mathematics , multidimensional scaling , scaling , mutual information , phase plane , plane (geometry) , point (geometry) , fractal dimension , fractal , statistics , mathematical analysis , geometry , art , physics , nonlinear system , quantum mechanics , visual arts

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

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