The mathematical analysis of the structure of some songs

Date

2005-11-15

Author

Gunduz, G
Gündüz, Ufuk

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The mathematical structures of six songs were studied by treating them as complex systems. The studies were based on (i) scattering diagram, (ii) spiral structure, (iii) graph theory and animal diagrams, and (iv) entropy and organization. In (i), the fractal dimension and the radius of gyration was determined for each melody. In (ii), it was shown that the total number of notes used in a song display a spiral, which can be expressed by a mathematical equation. In (iii), the animal diagram was obtained by using the pathways between the consecutive notes of the song. A ratio defined as 'the number of edges to the total number of unit edge' for the animal diagram was used as a parameter to characterize a melody. In (iv), the entropy, the maximum entropy, and the negentropy or the organization of the songs were determined. In addition, the rate of change of organization of the songs was also determined.

Subject Keywords

Music, Fractal, Graph, Animal, Entropy, Organization

URI

https://hdl.handle.net/11511/31161

Journal

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

DOI

https://doi.org/10.1016/j.physa.2005.03.042

Collections

Graduate School of Natural and Applied Sciences, Article

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Citation Formats

G. Gunduz and U. Gündüz, “The mathematical analysis of the structure of some songs,” PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, pp. 565–592, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31161.