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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 436108, 14 pages
Research Article

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

1Department of Electrical Engineering, CI&DETS and School of Technology and Management of Viseu, Campus Politécnico de Repeses, 3504-510 Viseu, Portugal
2Department of Electrical Engineering, Porto Superior Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
3Department of Informatics Engineering, Polytechnic Institute of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal

Received 11 January 2012; Accepted 18 April 2012

Academic Editor: Juan J. Trujillo

Copyright © 2012 Miguel F. M. Lima et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.