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Part of the book series: Current Research in Systematic Musicology ((CRSM,volume 2))

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Abstract

The analysis of self-organization and chaoticity of musical sounds and instruments needs powerful tools to analyze sounds in terms of their fine structures. As the slavery principle, where one subsystem forces others to vibrate with its eigenfrequencies of the other holds for the quasi-steady state of the sound to most extend, the initial transient is clearly the struggling between the two subsystems until the slaving has been achieved.

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References

  1. Abarbanel, H.D.I.: Analysis of Observed Chaotic Data. Springer, NY (1996)

    Book  MATH  Google Scholar 

  2. Arom, S.: African Polyphony and Polyrhythm: Musical Structure and Methodology. Cambridge University Press (1991)

    Google Scholar 

  3. Bader, R.: Berechnung fraktaler Strukturen in den Études für Klavier von György Ligeti [Calculating fractal structures in the Études for piano of György Ligeti]. In: Stahnke, M. (ed.) Mikrotöne und mehr. Auf György Ligetis Hamburger Pfaden. Bockel-Verlag Hamburg (2005)

    Google Scholar 

  4. Balatoni, J., Rényi, A.: Über den Begriff der Entropie, Arbeiten zur Informationstheorie I (gekürzte deutsche Übersetzung 1957) [About the notion of entropy, works in information theory I]. Math. Forschungsberichte IV, pp. 117–134. Deutscher Verlag der Wissenschaften, Berlin (1957)

    Google Scholar 

  5. Beuermann, A., Schneider, A.: Struktur, Klang, Dynamik. Akustische Untersuchungen zu Ligetis Atmosphères [Structure, timbre, dynamics. Acoustical investigations of Ligetis Atmosphères]. Hamburger Jahrbuch für Musikwissenschaft 11, 311–334 (1991)

    Google Scholar 

  6. Floquet, G.: Sur les équations differentielles linéaires à coefficients périodiques. Ann. Sci. École Norm. Sup. Ser. 2 12, 47 (1883)

    MathSciNet  MATH  Google Scholar 

  7. Gibiat, V.: Phase space representations of acoustical musical signals. J. of Sound and Vibration 123(3), 529–536 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gibiat, V., Castellengo, M.: Period Doubling Occurences in Wind Instruments Musical Performance. Acustica 86, 746–754 (2000)

    Google Scholar 

  9. Haken, H.: Synergetics, vol. 3. Springer, Auflage (1990)

    Google Scholar 

  10. Haken, H.: Advanced Synergetics. Springer (1983)

    Google Scholar 

  11. Kowalik, Z.: Biomedizinische Zeitreihen und nichtlineare Dynamik [Biomedical time series and nonlineare dynamics]. Lit-Verlag, Münster (2002)

    Google Scholar 

  12. Kolmogorov, A.N.: A new metric invariant of transient dynamical systems and automorphisms of Lesbesgue spaces. Dokl. Akad. Nauk SSSR 119, 861–864 (1958)

    MathSciNet  MATH  Google Scholar 

  13. Kratzky, K., Wallner, F.: Grundprinzipien der Selbstorganisation [Foundations of self-organization]. Wissenschaftliche Buchgesellschaft (1990)

    Google Scholar 

  14. Kubik, G.: Die Amadinda Musik in Buganda. Musik in Afrika, 139–156 (1983)

    Google Scholar 

  15. Leissa, A.W.: Vibration of Plates. 2nd edn. American Acoustical Society (1993)

    Google Scholar 

  16. Mahnke, R., Schmelzer, J., Röpke, G.: Nichtlineare Phänomene und Selbstorganisation [Nonlinear phaenomena and self-organization]. Teubner Studienbücher Physik (1992)

    Google Scholar 

  17. Moon, F.C.: Chaotic and Fractal dynamics, NY (1992)

    Google Scholar 

  18. Paluš, M., Albrecht, V., Dvořák, I.: Information - theoretic test for nonlinearity in time series. Phys. Lett. 175, 203–209 (1993)

    Article  MathSciNet  Google Scholar 

  19. Reich, S.: Foreword to Michael Tenzer: Gamelan gong Kebyar. University of Chicago Press, Chicago (2000)

    Google Scholar 

  20. Rényi, A.: On the dimension and entropy of probability distributions. Acta Mathematica 10, 193–215 (1959)

    MATH  Google Scholar 

  21. Shannon, C.E.: Mathematical theory of communication. Bell Syst. Tech. J. 27, 379–432 (1948)

    MathSciNet  MATH  Google Scholar 

  22. Tenzer, M.: Gamelan Gong Kebyar. The Art of Twentieth-Century Balinese Music. University of Chicago Press (2000)

    Google Scholar 

  23. Vandenhouten, R.: Analyse instationärer Zeitreihen komplexer Syteme und Anwendungen in der Physiologie [Analysis of instationary time series of complex systems and applications in physiology]. Shaker Verlag, Aachen (1998)

    Google Scholar 

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Correspondence to Rolf Bader .

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Bader, R. (2013). Embedding Representations. In: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology. Current Research in Systematic Musicology, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36098-5_3

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  • DOI: https://doi.org/10.1007/978-3-642-36098-5_3

  • Publisher Name: Springer, Berlin, Heidelberg

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