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

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

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...

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Main Authors: Miguel F. M. Lima, J. A. Tenreiro Machado, António C. Costa
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/436108
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spelling doaj-f53a8e47bad74f569be10938acc648852020-11-24T22:12:46ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/436108436108A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase PlaneMiguel F. M. Lima0J. A. Tenreiro Machado1António C. Costa2Department of Electrical Engineering, CI&DETS and School of Technology and Management of Viseu, Campus Politécnico de Repeses, 3504-510 Viseu, PortugalDepartment of Electrical Engineering, Porto Superior Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, PortugalDepartment of Informatics Engineering, Polytechnic Institute of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, PortugalThis 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.http://dx.doi.org/10.1155/2012/436108
collection DOAJ
language English
format Article
sources DOAJ
author Miguel F. M. Lima
J. A. Tenreiro Machado
António C. Costa
spellingShingle Miguel F. M. Lima
J. A. Tenreiro Machado
António C. Costa
A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
Abstract and Applied Analysis
author_facet Miguel F. M. Lima
J. A. Tenreiro Machado
António C. Costa
author_sort Miguel F. M. Lima
title A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
title_short A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
title_full A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
title_fullStr A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
title_full_unstemmed A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane
title_sort multidimensional scaling analysis of musical sounds based on pseudo phase plane
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/436108
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