Skip to main content

Part of the book series: Springer Handbooks ((SHB))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Baines: Woodwind Instruments and Their History (Dover, New York 1991)

    Google Scholar 

  2. H. Helmholtz: On the Sensation of Tone (Dover, New York 1954)

    Google Scholar 

  3. J.W. Strutt (Lord Rayleigh): The Theory of Sound (Dover, New York 1945)

    Google Scholar 

  4. H. Bouasse: Instruments a Vent (Librairie Delagrave, Paris 1929/30)

    Google Scholar 

  5. J. Backus: The Acoustical Foundation of Music (Norton, New York 1969)

    Google Scholar 

  6. C.J. Nederveen: Acoustical Aspects of Woodwind Instruments (Northern Illinois Univ. Press, DeKalb 1998)

    Google Scholar 

  7. M. Campbell, C. Greated: The Musician’s Guide to Acoustics (Schirmer Book, New York 1987)

    Google Scholar 

  8. N.H. Fletcher, T. Rossing: The Physics of Musical Instruments, 2nd edn. (Springer, New York 1998)

    Book  Google Scholar 

  9. A. Hirschberg, J. Kergomard, G. Weinreich: Mechanics of Musical Instruments (Springer, Wien 1995)

    MATH  Google Scholar 

  10. L. Henrique: Acustica Musical, 2nd edn. (Fundacao Calouste Gulbenkian, Lisboa 2007)

    Google Scholar 

  11. A. Chaigne, J. Kergomard: Acoustics of Musical Instruments (Springer, New York 2016)

    Book  Google Scholar 

  12. B. Fabre, J. Gilbert, A. Hirschberg, X. Pelorson: Aeroacoustics of musical instruments, Ann. Rev. Fluid Mech. 44, 1–25 (2012)

    Article  MathSciNet  Google Scholar 

  13. P. Taillard, J. Kergomard, F. Laloe: Iterated maps for clarinet-like systems, Nonlinear Dyn 62, 253–271 (2010)

    Article  MathSciNet  Google Scholar 

  14. R. Bader: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology (Springer, Berlin, Heidelberg 2013)

    Book  Google Scholar 

  15. M. Campbell: Brass instruments as we know them today, Acta Acust. United Acust. 90(4), 600–610 (2004)

    Google Scholar 

  16. T. Boehm: The Flute and Flute-Playing (Dover, New York 1964)

    Google Scholar 

  17. J.W. Coltman: Resonance and sounding frequencies of the flute, J. Acoust. Soc. Am. 40, 99–107 (1966)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. M.E. McIntyre, R.T. Schumacher, J. Woodhouse: On the oscillations of musical instruments, J. Acoust. Soc. Am. 74, 1325–1345 (1983)

    Article  Google Scholar 

  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. J.O. Smith III: Physical modeling synthesis update, Comput. Music J. 20, 44–56 (1996)

    Article  Google Scholar 

  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. 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. 1–10

    Google Scholar 

  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. 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. T.D. Rossing, F.R. Moore, P.A. Wheeler: The Science of Sound, 3rd edn. (Person, Harlow 2001)

    Google Scholar 

  37. M. Castellengo: Acoustical analysis of initial transients in flute like instruments, Acta Acust. United Acust. 85, 387–400 (1999)

    Google Scholar 

  38. A. Miklos, J. Angster: Properties of the sound of flue organ pipes, Acta Acust. United Acust. 86, 611–622 (2000)

    Google Scholar 

  39. A.H. Benade: Fundamentals of Musical Acoustics (Oxford University Press, Oxford 1976)

    Google Scholar 

  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)

    Article  Google Scholar 

  41. U. Ingard, H. Ising: Acoustic nonlinearity of an orifice, J. Acoust. Soc. Am. 42, 6–17 (1967)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  43. D. Noreland: An experimental study of temperature variations inside a clarinet. In: In: Proc. Stockh. Music Acoust. Conf (KTH, Stockholm 2013) pp. 446–450

    Google Scholar 

  44. T. Grothe: Experimental Investigation of Bassoon Acoustics, Ph.D. Thesis (Technische Universität Dresden, Dresden 2014)

    Google Scholar 

  45. A. Almeida, C. Vergez, R. Causse: Quasi-static non-linear characteristics of double-reed instruments, J. Acoust. Soc. Am. 121, 536–546 (2007)

    Article  Google Scholar 

  46. N. Grand, J. Gilbert, F. Laloe: Oscillation threshold of woodwind instruments, Acustica 83, 137–151 (1997)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  48. A.O. St Hilaire, T.A. Wilson, G.A. Beavers: Aerodynamic excitation of the harmonium reed, J. Fluid Mech. 49, 803–816 (1971)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  51. L. Millot, C. Baumann: A proposal for a minimalModel of free reeds, Acta Acust. United Acust. 93, 122–144 (2007)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  55. K. Ishizaka, M. Matsudaira: Fluid Mechanical Considerations of Vocal Cord Vibration (Speech Commun. Res. Lab., Santa Barbara 1972)

    Google Scholar 

  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. 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)

    Article  Google Scholar 

  58. A. Hirschberg, J. Gilbert, R. Msallam, A.P.J. Wijnands: Shock waves in trombones, J. Acoust. Soc. Am. 99, 1754–1758 (1996)

    Article  Google Scholar 

  59. J.W. Beauchamp: Analysis of simultaneous mouthpiece and output waveforms. In: 66th AES Conf., Los Angeles (1980)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  62. A. Powell: On the edge tone, J. Acoust. Soc. Am. 33, 395–409 (1961)

    Article  Google Scholar 

  63. J.W. Coltman: Sound radiation from the mouth of an organ pipe, J. Acoust. Soc. Am. 46, 477 (1969)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. J.W. Coltman: Effect of material on flute tone quality, J. Acoust. Soc. Am. 49, 520–523 (1971)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 19–39

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Benoit Fabre .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fabre, B., Gilbert, J., Hirschberg, A. (2018). Modeling of Wind Instruments. In: Bader, R. (eds) Springer Handbook of Systematic Musicology. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55004-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-55004-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-55002-1

  • Online ISBN: 978-3-662-55004-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics