Modeling of Wind Instruments

  • Benoit FabreEmail author
  • Joël Gilbert
  • Avraham Hirschberg
Part of the Springer Handbooks book series (SHB)


Wind instruments driven by a constant pressure air reservoir produce a steady oscillation and associated sound waves. This self-sustained oscillation can be explained in terms of a lumped element feedback loop composed of an exciter, such as a reed-valve or an unstable jet, coupled to an acoustical air column resonator, usually a pipe. In this chapter this simplified model is used to classify wind instruments. Five prototype wind instruments are selected: the clarinet , the oboe , the harmonica , the trombone and the modern transverse flute . The elements of this feedback loop are described for each instrument. In simplified models the player is reduced to the role of a pressure reservoir. The player's control, also called the embouchure is however essential. This aspect is discussed briefly for each instrument.


  1. 7.1
    A. Baines: Woodwind Instruments and Their History (Dover, New York 1991)Google Scholar
  2. 7.2
    H. Helmholtz: On the Sensation of Tone (Dover, New York 1954)Google Scholar
  3. 7.3
    J.W. Strutt (Lord Rayleigh): The Theory of Sound (Dover, New York 1945)Google Scholar
  4. 7.4
    H. Bouasse: Instruments a Vent (Librairie Delagrave, Paris 1929/30)Google Scholar
  5. 7.5
    J. Backus: The Acoustical Foundation of Music (Norton, New York 1969)Google Scholar
  6. 7.6
    C.J. Nederveen: Acoustical Aspects of Woodwind Instruments (Northern Illinois Univ. Press, DeKalb 1998)Google Scholar
  7. 7.7
    M. Campbell, C. Greated: The Musician’s Guide to Acoustics (Schirmer Book, New York 1987)Google Scholar
  8. 7.8
    N.H. Fletcher, T. Rossing: The Physics of Musical Instruments, 2nd edn. (Springer, New York 1998)CrossRefGoogle Scholar
  9. 7.9
    A. Hirschberg, J. Kergomard, G. Weinreich: Mechanics of Musical Instruments (Springer, Wien 1995)zbMATHGoogle Scholar
  10. 7.10
    L. Henrique: Acustica Musical, 2nd edn. (Fundacao Calouste Gulbenkian, Lisboa 2007)Google Scholar
  11. 7.11
    A. Chaigne, J. Kergomard: Acoustics of Musical Instruments (Springer, New York 2016)CrossRefGoogle Scholar
  12. 7.12
    B. Fabre, J. Gilbert, A. Hirschberg, X. Pelorson: Aeroacoustics of musical instruments, Ann. Rev. Fluid Mech. 44, 1–25 (2012)MathSciNetCrossRefGoogle Scholar
  13. 7.13
    P. Taillard, J. Kergomard, F. Laloe: Iterated maps for clarinet-like systems, Nonlinear Dyn 62, 253–271 (2010)MathSciNetCrossRefGoogle Scholar
  14. 7.14
    R. Bader: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology (Springer, Berlin, Heidelberg 2013)CrossRefGoogle Scholar
  15. 7.15
    M. Campbell: Brass instruments as we know them today, Acta Acust. United Acust. 90(4), 600–610 (2004)Google Scholar
  16. 7.16
    T. Boehm: The Flute and Flute-Playing (Dover, New York 1964)Google Scholar
  17. 7.17
    J.W. Coltman: Resonance and sounding frequencies of the flute, J. Acoust. Soc. Am. 40, 99–107 (1966)CrossRefGoogle Scholar
  18. 7.18
    J.P. Dalmont, C.J. Nederveen, V. Dubos, S. Olivier, V. Méserette, E. te Sligte: Experimental determination of the equivalent circuit of an open side hole: Linear and non-linear behavior, Acta Acust. United Acust. 88, 567–575 (2002)Google Scholar
  19. 7.19
    J.P. Dalmont, J. Gilbert, S. Olivier: Non-linear characteristics of single reed instruments: Quasi-static volume flow and reed opening measurements, J. Acoust. Soc. Am. 114, 2253–2262 (2003)CrossRefGoogle Scholar
  20. 7.20
    A. da Silva, G. Scavone, M. van Walstijn: Numerical simulations of fluid-structure interaction in single-reed mouthpieces, J. Acoust. Soc. Am. 122, 1798–1810 (2007)CrossRefGoogle Scholar
  21. 7.21
    V. Lorenzoni, D. Ragni: Experimental investigation of the flow inside a saxophone mouthpiece by particle image velocimetry, J. Acoust. Soc. Am. 131, 716–721 (2012)CrossRefGoogle Scholar
  22. 7.22
    M. Deverge, X. Pelorson, C. Vilain, P.Y. Lagrée, F. Chentouf, J. Willems, A. Hirschberg: Influence of collision on the flow through in-vitro rigid models of the vocal folds, J. Acoust. Soc. Am. 114, 3354–3362 (2003)CrossRefGoogle Scholar
  23. 7.23
    P. Guillemain: Some roles of the vocal tract in clarinet breath attacks: Natural sounds analysis and model-based synthesis, J. Acoust. Soc. Am. 121, 2396–2406 (2007)CrossRefGoogle Scholar
  24. 7.24
    G.P. Scavone, A. Lefebvre, A.R. da Silva: Measurement of vocal-tract influence during saxophone performance, J. Acoust. Soc. Am. 123, 2391–2400 (2008)CrossRefGoogle Scholar
  25. 7.25
    J. Chen, J. Smith, J. Wolfe: Pitch bending and glissandi on the clarinet: Roles of the vocal tract and partial tone hole closure, J. Acoust. Soc. Am. 126, 1511–1520 (2009)CrossRefGoogle Scholar
  26. 7.26
    J. Kergomard, X. Meynial: Systèmes micro-intervalles pour les instruments de musique à vent a trous lateraux, J. Acoust. 1, 255–270 (1988)Google Scholar
  27. 7.27
    J. Gilbert, J. Kergomard, E. Ngoya: Calculation of the steady-state oscillation of a clarinet using the harmonic balance technique, J. Acoust. Soc. Am. 86, 35–41 (1989)CrossRefGoogle Scholar
  28. 7.28
    J. Kergomard, S. Olivier, J. Gilbert: Calculation of the spectrum of the self-sustained oscillators using a variable truncation method: Application to cylindrical reed instruments, Acustica 86, 685–703 (2000)Google Scholar
  29. 7.29
    M.E. McIntyre, R.T. Schumacher, J. Woodhouse: On the oscillations of musical instruments, J. Acoust. Soc. Am. 74, 1325–1345 (1983)CrossRefGoogle Scholar
  30. 7.30
    E. Ducasse: Modélisation d’instruments de musique pour la synthèse sonore: Application aux instruments à vent, Sup. J. Phys. Colloq. Phys. 51-C2, 837–840 (1990)Google Scholar
  31. 7.31
    J.O. Smith III: Physical modeling synthesis update, Comput. Music J. 20, 44–56 (1996)CrossRefGoogle Scholar
  32. 7.32
    V. Välimäki: Discrete-time modeling of acoustic tubes using fractional delay filters, Ph.D. Thesis (Helsinki University of Technology, Helsinki 1995)Google Scholar
  33. 7.33
    C. Vergez, P. Tisserand: The BRASS project, from physical models to virtual musical instruments. In: CMMR Third Int. Symp. Play. Issues (Computer Music Modelling and Retrivial) (2005) pp. 1–10Google Scholar
  34. 7.34
    P. Guillemain, J. Kergomard, T. Voinier: Real-time synthesis of wind instruments using nonlinear physical models, J. Acoust. Soc. Am. 105, 444–455 (2005)Google Scholar
  35. 7.35
    E. Mandaras, V. Gibiat, C. Besnainou, N. Grand: Caractérisation mécanique des anches simples d’instruments à vent, Suppl. J. Phys. III 4-C5, 633–636 (1994)Google Scholar
  36. 7.36
    T.D. Rossing, F.R. Moore, P.A. Wheeler: The Science of Sound, 3rd edn. (Person, Harlow 2001)Google Scholar
  37. 7.37
    M. Castellengo: Acoustical analysis of initial transients in flute like instruments, Acta Acust. United Acust. 85, 387–400 (1999)Google Scholar
  38. 7.38
    A. Miklos, J. Angster: Properties of the sound of flue organ pipes, Acta Acust. United Acust. 86, 611–622 (2000)Google Scholar
  39. 7.39
    A.H. Benade: Fundamentals of Musical Acoustics (Oxford University Press, Oxford 1976)Google Scholar
  40. 7.40
    E. Moers, J. Kergomard: On the cutoff frequency of clarinet-like instruments. Geometrical versus acoustical regularity, Acta Acust. United Acust. 97, 984–996 (2011)CrossRefGoogle Scholar
  41. 7.41
    U. Ingard, H. Ising: Acoustic nonlinearity of an orifice, J. Acoust. Soc. Am. 42, 6–17 (1967)CrossRefGoogle Scholar
  42. 7.42
    J. Buick, M. Atig, D. Skulina, M. Campbell, J.P. Dalmont, J. Gilbert: Investigation of Non-Linear Acoustic Losses at the Open End of a Tube, J. Acoust. Soc. Am. 129, 1261–1272 (2011)CrossRefGoogle Scholar
  43. 7.43
    D. Noreland: An experimental study of temperature variations inside a clarinet. In: In: Proc. Stockh. Music Acoust. Conf (KTH, Stockholm 2013) pp. 446–450Google Scholar
  44. 7.44
    T. Grothe: Experimental Investigation of Bassoon Acoustics, Ph.D. Thesis (Technische Universität Dresden, Dresden 2014)Google Scholar
  45. 7.45
    A. Almeida, C. Vergez, R. Causse: Quasi-static non-linear characteristics of double-reed instruments, J. Acoust. Soc. Am. 121, 536–546 (2007)CrossRefGoogle Scholar
  46. 7.46
    N. Grand, J. Gilbert, F. Laloe: Oscillation threshold of woodwind instruments, Acustica 83, 137–151 (1997)zbMATHGoogle Scholar
  47. 7.47
    J.P. Dalmont, B. Gazengel, J. Gilbert, J. Kergomard: Some aspects of tuning and clean intonation in reed instruments, Appl. Acoust. 46, 19–60 (1995)CrossRefGoogle Scholar
  48. 7.48
    A.O. St Hilaire, T.A. Wilson, G.A. Beavers: Aerodynamic excitation of the harmonium reed, J. Fluid Mech. 49, 803–816 (1971)CrossRefGoogle Scholar
  49. 7.49
    D. Ricot, R. Caussé, N. Misdrariis: Aerodynamic excitation and sound production of blown-closed free reeds without acoustic coupling: The example of the accordion reed, J. Acoust. Soc. Am. 117, 826–841 (2005)CrossRefGoogle Scholar
  50. 7.50
    A.Z. Tarnopolsky, N.H. Fletcher, J.C.S. Lai: Oscillating reed valves: An experimental study, J. Acoust. Soc. Am. 108, 400–406 (2000)CrossRefGoogle Scholar
  51. 7.51
    L. Millot, C. Baumann: A proposal for a minimalModel of free reeds, Acta Acust. United Acust. 93, 122–144 (2007)Google Scholar
  52. 7.52
    R. Causse, J. Kergomard, X. Lurton: Input impedance of brass musical instruments – Comparison between experiment and numerical models, J. Acoust. Soc. Am. 75, 241–254 (1984)CrossRefGoogle Scholar
  53. 7.53
    J.M. Chen, J. Smith, J. Wolfe: Do trumpet players tune resonances of the vocal tract?, J. Acoust. Soc. Am. 131, 722–727 (2012)CrossRefGoogle Scholar
  54. 7.54
    V. Freour, G.P. Scavone: Acoustical interaction between vibrating lips, downstream air column, and upstream airways in trombone performance, J. Acoust. Soc. Am. 134, 3887–3898 (2013)CrossRefGoogle Scholar
  55. 7.55
    K. Ishizaka, M. Matsudaira: Fluid Mechanical Considerations of Vocal Cord Vibration (Speech Commun. Res. Lab., Santa Barbara 1972)Google Scholar
  56. 7.56
    J. Cullen, J. Gilbert, M. Campbell: Brass instruments linear stability analysis and experiments with an artificial mouth, Acta Acust. United Acust. 86, 704–724 (2000)Google Scholar
  57. 7.57
    M. Newton, D.M. Campbell, J. Gilbert: Mechanical response measurements of real and artificial brass players lips, J. Acoust. Soc. Am. 123, EL14–EL20 (2008)CrossRefGoogle Scholar
  58. 7.58
    A. Hirschberg, J. Gilbert, R. Msallam, A.P.J. Wijnands: Shock waves in trombones, J. Acoust. Soc. Am. 99, 1754–1758 (1996)CrossRefGoogle Scholar
  59. 7.59
    J.W. Beauchamp: Analysis of simultaneous mouthpiece and output waveforms. In: 66th AES Conf., Los Angeles (1980)Google Scholar
  60. 7.60
    A. Myers, R.W. Pyle Jr., J. Gilbert, D.M. Campbell, J.P. Chick, S. Logie: Effects of nonlinear sound propagation on the characteritic timbres of brass insruments, J. Acoust. Soc. Am. 131, 678–688 (2012)CrossRefGoogle Scholar
  61. 7.61
    L. Norman, J. Chick, D.M. Campbell, A. Myers, J. Gilbert: Player control of ‘brassiness’ at intermediate dynamic levels in brass instruments, Acta Acust. United Acust. 96, 614–738 (2010)CrossRefGoogle Scholar
  62. 7.62
    A. Powell: On the edge tone, J. Acoust. Soc. Am. 33, 395–409 (1961)CrossRefGoogle Scholar
  63. 7.63
    J.W. Coltman: Sound radiation from the mouth of an organ pipe, J. Acoust. Soc. Am. 46, 477 (1969)CrossRefGoogle Scholar
  64. 7.64
    M.P. Verge, A. Hirschberg, R. Caussé: Sound production in recorderlike instruments. II A simulation model, J. Acoust. Soc. Am. 101, 2925–2939 (1997)CrossRefGoogle Scholar
  65. 7.65
    S. Dequand, J.F.H. Willems, M. Leroux, R. Vullings, M. van Weert, C. Thieulot: Simplified models of flute instruments: Influence of mouth geometry on the sound source, J. Acoust. Soc. Am. 113, 1724–1735 (2003)CrossRefGoogle Scholar
  66. 7.66
    J. Wolfe, J. Smith, J. Tann, N.H. Fletcher: Acoustic impedance spectra of classical and modern flutes, J. Sound Vib. 243, 127–144 (2001)CrossRefGoogle Scholar
  67. 7.67
    M.S. Howe: Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute, J. Fluid Mech. 71, 625–673 (1975)MathSciNetCrossRefGoogle Scholar
  68. 7.68
    R. Auvray, A. Emoult, B. Fabre, P.Y. Lagrée: Time-domain simulation of flute-like instruments: Comparison of jet-drive and discrete-vortex models, J. Acoust. Soc. Am. 136, 389–400 (2014)CrossRefGoogle Scholar
  69. 7.69
    B. Fabre, A. Hirschberg, A.P.J. Wijnands: Vortex shedding in steady oscillation of a flue organ pipe, Acta Acust. United Acust. 82, 863–877 (1996)Google Scholar
  70. 7.70
    J.W. Coltman: Effect of material on flute tone quality, J. Acoust. Soc. Am. 49, 520–523 (1971)CrossRefGoogle Scholar
  71. 7.71
    G. Paal, J. Angster, W. Garen, A. Miklos: A combined LDA and flow-vizualization on flue organ pipes, Exp. Fluids 40, 825–835 (2006)CrossRefGoogle Scholar
  72. 7.72
    R. Chaffin, A. Lemieux: Musical excellence strategies and techniques to enhance performance. In: General Perceptives on Achieving Musical Excellence, ed. by A. Williamon (Oxford University Press, Oxford 2004) pp. 19–39Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2018

Authors and Affiliations

  • Benoit Fabre
    • 1
    Email author
  • Joël Gilbert
    • 2
  • Avraham Hirschberg
    • 3
  1. 1.LAM – Institut d’AlembertSorbonne Universités, UPMC Univ Paris 06ParisFrance
  2. 2.Laboratoire d’AcoustiqueUniversité du Maine – CNRSLe MansFrance
  3. 3.VeldhovenNetherlands

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