Abstract and Applied Analysis

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

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

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 436108, 14 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168367

Digital Object Identifier
doi:10.1155/2012/436108

Mathematical Reviews number (MathSciNet)
MR2947683

Zentralblatt MATH identifier
1246.00018

Citation

Lima, Miguel F. M.; Machado, J. A. Tenreiro; Costa, António C. A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 436108, 14 pages. doi:10.1155/2012/436108. https://projecteuclid.org/euclid.aaa/1365168367


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