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2012 A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
Miguel F. M. Lima, J. A. Tenreiro Machado, António C. Costa
Abstr. Appl. Anal. 2012(SI01): 1-14 (2012). DOI: 10.1155/2012/436108

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.

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Miguel F. M. Lima. J. A. Tenreiro Machado. António C. Costa. "A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane." Abstr. Appl. Anal. 2012 (SI01) 1 - 14, 2012. https://doi.org/10.1155/2012/436108

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1246.00018
MathSciNet: MR2947683
Digital Object Identifier: 10.1155/2012/436108

Rights: Copyright © 2012 Hindawi

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