Complex network approach to classifying classical piano compositions

Complex network has been regarded as a useful tool handling systems with vague interactions. Hence, numerous applications have arised. In this paper we construct complex networks for 770 classical piano compositions of Mozart, Beethoven and Chopin based on musical note pitches and lengths. We find prominent distinctions among network edges of different composers. Some stylized facts can be explained by such parameters of network structures and topologies. Further, we propose two classification methods for music styles and genres according to the discovered distinctions. These methods are easy to implement and the results are sound. This work suggests that complex network could be a decent way to analyze the characteristics of musical notes, since it could provide a deep view into understanding of the relationships among notes in musical compositions and evidence for classification of different composers, styles and genres of music.

[1]  V. Menon,et al.  Musical rhythm spectra from Bach to Joplin obey a 1/f power law , 2012, Proceedings of the National Academy of Sciences.

[2]  Luciano da Fontoura Costa,et al.  Concentric network symmetry grasps authors' styles in word adjacency networks , 2015, ArXiv.

[3]  Xinyu Jin,et al.  Dynamic behavior of the interaction between epidemics and cascades on heterogeneous networks , 2014, 1405.3009.

[4]  J. Kurths,et al.  Estimating coupling directions in the cardiorespiratory system using recurrence properties , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  Jürgen Kurths,et al.  Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems. , 2015, Chaos.

[6]  Manfred Schroeder,et al.  Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise , 1992 .

[7]  Xin Jiang,et al.  Identify the diversity of mesoscopic structures in networks: A mixed random walk approach , 2013 .

[8]  Xinyu Jin,et al.  Dynamical interplay between epidemics and cascades in complex networks , 2014 .

[9]  Marcus T. Pearce,et al.  The construction and evaluation of statistical models of melodic structure in music perception and composition , 2005 .

[10]  Luciano da Fontoura Costa,et al.  Using complex networks for text classification: Discriminating informative and imaginative documents , 2016 .

[11]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Ying-Cheng Lai,et al.  Motif distributions in phase-space networks for characterizing experimental two-phase flow patterns with chaotic features. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  T. Rogers,et al.  Assessing node risk and vulnerability in epidemics on networks , 2015, 1502.00901.

[14]  Michael Small,et al.  Impact of asymptomatic infection on coupled disease-behavior dynamics in complex networks , 2016, 1608.04049.