Harmonizations of Time with Non Periodic Ordered Structures in Discrete Geometry and Astronomy

  • Juan García Escudero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3310)

Abstract

Non periodic ordered tilings can be used for the generation of discrete structures in the time and frequency domains. The Fourier spectrum of impulse distributions ordered according with certain types of aperiodic ordered temporal sequences described by Lindenmayer systems shows a discrete part . In order to appy these ideas the main tools belong to discrete geometry and number theory. These techniques provide a connection between rhythms and harmonic fields which may have a natural phenomena basis when observational data of certain types of variable stars are analyzed. The pulsation of some semiregular and delta scuti stars is reflected in their light curves which can be modelled by means of sinusoidal sequences related with the golden number.

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References

  1. 1.
    Bombieri, E., Taylor, J.E.: Which Distributions of Matter Diffract? An initial investigation. Journal de Physique France, C3 47, 19–28 (1986)MathSciNetGoogle Scholar
  2. 2.
    Cowell, H.: New Music Resources. Cambridge University Press, Cambridge (1996)Google Scholar
  3. 3.
    Escudero, J.G.: La Tierra Ubèrrima for string quartet. CD Agenda Edizioni Musicali 001 (2004)Google Scholar
  4. 4.
    Escudero, J.G.: Grammars for Icosahedral Danzer Tilings. Journal of Physics A: Mathematical and General 28, 5207–5215 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Escudero, J.G.: Estudio del Tiempo Iluminado II for computer. CD MasterVision 001. Concorso Internazionale di Composizione Elettronica “Pierre Schaeffer”. SIAE (1997)Google Scholar
  6. 6.
    Escudero, J.G.: Time and Frequency Structures within Selfsimilar Aperiodic Geometries. In: Feichtinger, H.G., Doerfler, M. (eds.) Diderot Forum on Mathematics and Music. Oesterreichische Computer Gesellschaft Series, Viena, vol. 133, pp. 145–152 (1999)Google Scholar
  7. 7.
    Escudero, J.G.: Continuous and Discrete Fourier Spectra of Aperiodic Sequences for SoundModeling. In: Rocchesso, D., Signoretto, M. (eds.) Proceedings Digital Audio Effects Workshop DAFX 2000.Universitádegli Studi di Verona, pp. 265–268 (2000)Google Scholar
  8. 8.
    Escudero, J.G.: ET0L-Systems for Composite Dodecagonal Quasicrystal Patterns. International Journal of Modern Physics B 15, 1165–1175 (2001)CrossRefGoogle Scholar
  9. 9.
    Escudero, J.G.: A construction of inflation rules for Pisot octagonal tilings. International Journal of Modern Physics B 15, 2925–2931 (2003)CrossRefGoogle Scholar
  10. 10.
    Escudero, J.G.: Fibonacci Sequences and the Multiperiodicity of the Variable Star UW Herculis. Chinese Journal of Astronomy and Astrophysics 3, 235–240 (2003)CrossRefGoogle Scholar
  11. 11.
    Godrèche, C., Luck, J.M.: Indexing the diffraction spectrum of a non-Pisot self-similar structure. Physical Review B 45, 176 (1992)CrossRefGoogle Scholar
  12. 12.
    Hollander, M., Solomyak, B.: Two-symbol Pisot substitutions have pure discrete spectrum. Ergodic Theory and Dynamical Systems 23, 533–540 (2003)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Pinheiro, F., et al.: Oscillations in the PMS Delta Scuti star V346 Ori. Astronomy and Astrophysics 399, 271–274 (2003)CrossRefGoogle Scholar
  14. 14.
    Roads, C.: Microsound. The MIT Press, Cambridge (2001)Google Scholar
  15. 15.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)MATHGoogle Scholar
  16. 16.
    Stockhausen, K.: ...wie die Zeit vergeht.. Texte zur elektronischen und instrumentalen Musik. Bd.1. Dumont Buchverlag, Koeln (1963)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Juan García Escudero
    • 1
  1. 1.Facultad de CienciasUniversidad de OviedoOviedoSpain

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