Abstract
Melodies can be treated as time series systems with the pitches (or frequencies of the notes) representing the values in subsequent intervals. The pattern of a melody can be revealed in a scattering diagram where pitches represent vertices, and the directed pathways which connect the former pitches to the next ones signify the relations established during the performance. The pathways form a pattern which is called animal diagram (or lattice animal) in the vocabulary of graph theory. The slopes of pathways can be used to characterize an animal diagram and thus to characterize a melody; and the scattering diagram can be used to find out the fractal dimension . In addition, the entropy , the maximum entropy , and the negentropy (or the order) of melodies can be determined. The analysis of Meragi songs in terms of fractal dimension and entropy was carried out in this work. It was found out that there is not a correlation between the fractal dimension and the entropy ; therefore, the fractal dimension and the entropy each characterizes different aspects of Meragi songs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Knopoff L, Hutchinson W (1983) Entropy as a measure of style: the influence of sample length. J Music Theory 27(1):75–97
Manzara LC, Witten IH, Jones M (1992) On the entropy of music: an experiment with Bach chorale melodies. Leonardo Music J 2(1):81–88
Gündüz G, Gündüz U (2005) The mathematical analysis of the structure of some songs. Physica A 357:565–592
Hsü KJ, Hsü AJ (1990) Fractal geometry of music. Proc Natl Acad Sci 87:938–941
Miller SL, Miller WM, McWhorter PJ (1993) Extremal dynamics: a unifying physical explanation of fractals, 1/f noise, and activated processes. J Appl Phys 73(6):2617–2628
Bigerelle M, Iost A (2000) Fractal dimension and classification of music. Chaos Solitons Fractals 11:2179–2192
Su ZY, Wu T (2006) Multifractal analyses of music sequences. Physica D 221:188–194
Su ZY, Wu T (2007) Music walk, fractal geometry in music. Physica A 380:418–428
Das A, Das P (2006) Fractal analysis of different eastern and western musical instruments. Fractals 14(3):165–170
Das A, Das P (2010) Fractal analysis of songs: performer’s preference. Nonlinear Anal Real World Appl 11:1790–1794
Voss RF, Clarke J (1975) ‘1/f’ in music and speech. Nature 258:317–318
Voss RF, Clarke J (1978) “1/f noise” in music: music from 1/f noise. J Acoust Soc Am 63:258–263
Madden C (1999) Fractals in music. High Art Press, Salt Lake City
Hazama F (2011) Spectra of graphs attached to the space of melodies. Discret Math 311:2368–2383
Gündüz G (2009) Viscoelastic properties of networks. Int J Mod Phys C 20:1597–1615
Gündüz G (2012) Thermodynamics of relation-based systems with applications in econophysics, sociophysics, and music. Physica A 391:4637–4653
Elinç E (2005) M.Sc. thesis (in Turkish), Abdülkâdir Merâği’nin eserlerinin makamsal açıdan incelenmesi (Study of the melodies of Abdülkâdir Merâği from the view point of their makams) Afyon Kocatepe Üniversitesi, Sosyal Bilimler Enstitüsü (Afyon Kocatepe University, Institute of Social Sciences)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Aydemir, A., Gündüz, G. (2014). Fractal Dimensions and Entropies of Meragi Songs. In: Matrasulov, D., Stanley, H. (eds) Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale. NATO Science for Peace and Security Series C: Environmental Security. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8704-8_6
Download citation
DOI: https://doi.org/10.1007/978-94-017-8704-8_6
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-8703-1
Online ISBN: 978-94-017-8704-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)