Volume 121, Number 3, February 2018
|Number of page(s)||7|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||09 April 2018|
The complexity of classical music networks
1 Institute for Pure and Applied Mathematics (IMPA) - Rio de Janeiro, 22460-320, Brazil
2 School of Fine Arts at the Federal University of Rio de Janeiro (UFRJ) - Rio de Janeiro, 21941-972, Brazil
Received: 24 November 2017
Accepted: 14 March 2018
Previous works suggest that musical networks often present the scale-free and the small-world properties. From a musician's perspective, the most important aspect missing in those studies was harmony. In addition to that, the previous works made use of outdated statistical methods. Traditionally, least-squares linear regression is utilised to fit a power law to a given data set. However, according to Clauset et al. such a traditional method can produce inaccurate estimates for the power law exponent. In this paper, we present an analysis of musical networks which considers the existence of chords (an essential element of harmony). Here we show that only 52.5% of music in our database presents the scale-free property, while 62.5% of those pieces present the small-world property. Previous works argue that music is highly scale-free; consequently, it sounds appealing and coherent. In contrast, our results show that not all pieces of music present the scale-free and the small-world properties. In summary, this research is focused on the relationship between musical notes (Do, Re, Mi, Fa, Sol, La, Si, and their sharps) and accompaniment in classical music compositions. More information about this research project is available at https://eden.dei.uc.pt/~vitorgr/MS.html.
PACS: 89.75.-k – Complex systems / 89.75.Da – Systems obeying scaling laws / 89.75.Fb – Structures and organization in complex systems
© EPLA, 2018
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