Modeling of Musical Instruments

  • Rolf Bader
  • Uwe Hansen

Signal processing techniques in acoustics address many concerns. Included are such things as wave propagation variables, amplitude considerations, spectral content, wavelength, and phase. Phase is primarily of concern when waves interact with each other, as well as with a medium, and the imposition of boundary conditions leads to normal mode vibrations. Such conditions are prevalent in all musical instruments, and thus relevant signal processing techniques are essential to both understanding and modeling the structure of musical instruments and the sound radiated.


Musical Instrument Initial Transient Back Plate Impulse Function Spectral Centroid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Backus, J.: Multiphonic tones in the woodwind instruments. J. Acoust. Soc. Am. 63, 591–599, 1978.CrossRefADSGoogle Scholar
  2. Bader, R.: Fractal correlation dimensions and discrete-pseudo-phase-plots of percussion instruments in relation to cultural world view. In: Ingenierias, Octubre-Diciembre 2002, Vol. V. No. 17, 1–11.Google Scholar
  3. Bader, R.: Physical model of a complete classical guitar body. Proc. Stockholm Musical Acoustics Conf. 2003, R. Bresin (ed.) Vol. 1,121–124, 2003.Google Scholar
  4. Bader, R.: Computational Mechanics of the Classical Guitar. Springer 2005.Google Scholar
  5. Bathe, K.-J.: Finite Element Procedures. Prentice Hall, 1996.Google Scholar
  6. Coltman, J.W.: Acoustics of the flute. Physics Today, 21, 11, 25–32, 1968.CrossRefGoogle Scholar
  7. Coltman, J.W.: Mouth resonance effects in the flute. J. Acoust. Soc. Am. 54, 417–420, 1973.CrossRefADSGoogle Scholar
  8. Durbin, P.A. & Pettersson, R.: Statistical Theory and Modeling for Turbulent Flows. Wiley, 2001.Google Scholar
  9. Elejabarrieta, M.J., Ezcurra, A. & Santamaria, C.: Coupled modes of the resonance box of the guitar. J. Acoust. Soc. Am. 111, 2283–2292, 2002.CrossRefADSGoogle Scholar
  10. Fletcher, N.H.: Bell clapper impact dynamics and the voicing of a carillon. J. Acoust. Soc. Am. 111, 1437–1444, 2002.CrossRefADSGoogle Scholar
  11. Fletcher, N.H. & Rossing, Th.D.: The Physics of Musical Instruments. Second Ed. Springer 1999.Google Scholar
  12. Fletcher, N.H., Strong, W.J. & Silk, R.K.: Acoustical characterization of flute head joints. J. Acoust. Soc. Am. 71, 1255–1260, 1982.CrossRefADSGoogle Scholar
  13. Gibiat, V.: Phase space representations of acoustical musical signals. J. Sound and Vibration, 123/3, 529–536, 1988.CrossRefADSMathSciNetGoogle Scholar
  14. Gibiat, V. & Castellengo, M.: Period doubling occurences in wind instruments musical performance. Acustica, 86, 746–754, 2000.Google Scholar
  15. Grey, J.M.: Multidimensional perceptual scaling of musical timbres. J. Acoust. Soc. Am. 61(5), 1977, 1270–1277, 1977.CrossRefADSGoogle Scholar
  16. Grey, J.M. & Moorer, J.A.: Perceptual evaluations of synthesized musical tones. J. Acoust. Soc. Am. 62(2), 454–462, 1977.CrossRefADSGoogle Scholar
  17. Haase, M., Widjajakusuma, J. & Bader, R.: Scaling laws and frequency decomposition from wavelet transform maxima lines and ridges. In: Emergent Nature, M.M. Novak, (ed.): World Scientific 2002,365–374.Google Scholar
  18. Hughes, J.R.: The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Dover Publications, 1987.Google Scholar
  19. Keefe, D.H. & Laden, B.: Correlation dimension of woodwind multiphonic tones. J. Acoust. Soc. Am. 90(4), 1754–1765, 1991.CrossRefADSGoogle Scholar
  20. Kolmogovov, A.N.: The local structure of turbulence in incompressible viscous fluid for vary large Reynolds number. Doklady Akademi Nauk SSSR, 30, 301–305, 1941.ADSGoogle Scholar
  21. Krumhansl, C.L.: Why is musical timbre so hard to understand? In: Structure and Perception of Electroacoustic Sound and Music. Nielzn, S. & Olsson, O. (ed.). Amsterdam 1989, 43–53, 1989.Google Scholar
  22. Luce, D. & Clark, M.: Durations of attack transients of nonpercussive orchestral instruments. J. Audio Eng. Soc. 13, 194–199, 1965.Google Scholar
  23. Meyer, J.: Verbesserung der Klangqualitt von Gitarren aufgrund systematischer Untersuchungen ihres Schwingungsverhaltens Improvement of the sound quality of guitars by systematic investigations of its vibrating behaviour. Physikalisch-Technische Bundesanstalt Braunschweig, Forschungsvorhaben Nr. 4490, 1980.Google Scholar
  24. Miller, J.R. & Carterette, E.C.: Perceptual space for musical structures. J. Acoust. Soc. Am. 58(3), 711–720, 1975.CrossRefADSGoogle Scholar
  25. Richardson, B.E. & Roberts, G.W.: The adjustment of mode frequencies in guitars: A study by means of holographic interferometry and finite element analysis. In: Proc. Stockholm Musical Acoustics Conf. 1983, 285–302, 1985.Google Scholar
  26. Saad, Yousef: Iterative Methods for Sparse Linear Systems, Cambridge University Press, 2003.Google Scholar
  27. Taylor, Ch.: Sound. In: The New Groove Dictionary of Music and Musicians, S. Sadie (ed.). Second ed. 23, 759–776, 2001.Google Scholar
  28. Wriggers, P.: Computational Contact Mechanics. Wiley, 2002.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Rolf Bader
    • 1
  • Uwe Hansen
    • 2
  1. 1.Institute of Musicology University of HamburgHamburgGermany
  2. 2.Department of PhysicsIndiana State UniversityTerre HauteUSA

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