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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abarbanel, H.D.I.: Analysis of Observed Chaotic Data. Springer, NY (1996)
Arom, S.: African Polyphony and Polyrhythm: Musical Structure and Methodology. Cambridge University Press (1991)
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)
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)
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)
Floquet, G.: Sur les équations differentielles linéaires à coefficients périodiques. Ann. Sci. École Norm. Sup. Ser. 2 12, 47 (1883)
Gibiat, V.: Phase space representations of acoustical musical signals. J. of Sound and Vibration 123(3), 529–536 (1988)
Gibiat, V., Castellengo, M.: Period Doubling Occurences in Wind Instruments Musical Performance. Acustica 86, 746–754 (2000)
Haken, H.: Synergetics, vol. 3. Springer, Auflage (1990)
Haken, H.: Advanced Synergetics. Springer (1983)
Kowalik, Z.: Biomedizinische Zeitreihen und nichtlineare Dynamik [Biomedical time series and nonlineare dynamics]. Lit-Verlag, Münster (2002)
Kolmogorov, A.N.: A new metric invariant of transient dynamical systems and automorphisms of Lesbesgue spaces. Dokl. Akad. Nauk SSSR 119, 861–864 (1958)
Kratzky, K., Wallner, F.: Grundprinzipien der Selbstorganisation [Foundations of self-organization]. Wissenschaftliche Buchgesellschaft (1990)
Kubik, G.: Die Amadinda Musik in Buganda. Musik in Afrika, 139–156 (1983)
Leissa, A.W.: Vibration of Plates. 2nd edn. American Acoustical Society (1993)
Mahnke, R., Schmelzer, J., Röpke, G.: Nichtlineare Phänomene und Selbstorganisation [Nonlinear phaenomena and self-organization]. Teubner Studienbücher Physik (1992)
Moon, F.C.: Chaotic and Fractal dynamics, NY (1992)
Paluš, M., Albrecht, V., Dvořák, I.: Information - theoretic test for nonlinearity in time series. Phys. Lett. 175, 203–209 (1993)
Reich, S.: Foreword to Michael Tenzer: Gamelan gong Kebyar. University of Chicago Press, Chicago (2000)
Rényi, A.: On the dimension and entropy of probability distributions. Acta Mathematica 10, 193–215 (1959)
Shannon, C.E.: Mathematical theory of communication. Bell Syst. Tech. J. 27, 379–432 (1948)
Tenzer, M.: Gamelan Gong Kebyar. The Art of Twentieth-Century Balinese Music. University of Chicago Press (2000)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-36098-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36097-8
Online ISBN: 978-3-642-36098-5
eBook Packages: EngineeringEngineering (R0)