Abstract
Music is a ubiquitous, complex and defining phenomenon of human culture. We create and analyze complex networks representing harmonic transitions in eight selected compositions of Johann Sebastian Bach’s Well-Tempered Clavier. While all resulting networks exhibit the typical ‘small-world’-characteristics, they clearly differ in their degree distributions. Some of the degree distributions are well fit by a power-law, others by an exponential, and some by neither. This seems to preclude the necessity of a scale-free degree distribution for music to be appealing. To obtain a quality measure for the network representation, we design a simple algorithm that generates artificial polyphonic music, which also exhibits the different styles of composition underlying the various pieces.
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References
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: Structure and dynamics. Phys. Rep. 424, 175–308 (2006)
Liu, X.F., Tse, C.K., Small, M.: Complex network structure of musical compositions: Algorithmic generation of appealing music. Physica A 389, 126–132 (2010)
Serrà, J., Corral, A., Boguñá, M., Haro, M., Arcos, J.L.: Measuring the Evolution of Contemporary Western Popular Music. Sci. Rep. 2, 00521 (2012)
Liu, L., Wei, J., Zhang, H., Xin, J., Huang, J.: A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling. PLoS ONE 8, e58710 (2013)
Zivic, P.H.R., Shifres, F., Cecchi, G.A.: Perceptual basis of evolving Western musical styles. Proc. Natl. Acad. Sci. U.S.A. 110, 10034–10038 (2013)
Nettheim, N.: On the Spectral Analysis of Melody. Interface 21, 135–148 (1992)
Boon, J.P., Decroly, O.: Dynamical Systems theory for music dynamics. Chaos 5, 501–508 (1995)
Voss, R.F., Clarke, C.: “1/f noise” in music: Music from 1/f noise. J. Acoust. Soc. Am. 63, 258–263 (1978)
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987)
Jennings, H.D., Ivanov, P.C., Martins, A.M., da Silva, P.C., Viswanathan, G.M.: Variance fluctuations in nonstationary time series: A comparative study of music genres. Physica A 336, 585–594 (2004)
Boon, J.P., Noullez, A., Mommen, C.: Complex Dynamics and Musical Structure. Interface 19, 3–14 (1990)
Zanette, D.H.: Zipf’s law and the creation of musical context. Music Sci. 10, 3–18 (2006)
Beltrán del Río, M., Cocho, G., Naumis, G.G.: Universality in the tail of musical note rank distribution. Physica A 387, 5552–5560 (2008)
Lerdahl, F.: Tonal Pitch Space. Oxford University Press (2001)
Tymoczko, D.: The Geometry of Musical Chords. Science 313, 72–74 (2006)
Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-Law Distributions in Empirical Data. SIAM Rev. 51, 661–703 (2009)
Deluca, A., Corral, Á.: Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions. Acta Geophys. 61, 1351–1394 (2013)
Artificially generated music is available on http://stoop.ini.uzh.ch/artmus
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Gomez, F., Lorimer, T., Stoop, R. (2014). Complex Networks of Harmonic Structure in Classical Music. In: Mladenov, V.M., Ivanov, P.C. (eds) Nonlinear Dynamics of Electronic Systems. NDES 2014. Communications in Computer and Information Science, vol 438. Springer, Cham. https://doi.org/10.1007/978-3-319-08672-9_32
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DOI: https://doi.org/10.1007/978-3-319-08672-9_32
Publisher Name: Springer, Cham
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