Skip to main content

Musical Acoustics

  • Reference work entry
Springer Handbook of Acoustics

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

Abstract

This chapter provides an introduction to the physical and psycho-acoustic principles underlying the production and perception of the sounds of musical instruments. The first section introduces generic aspects of musical acoustics and the perception of musical sounds, followed by separate sections on string, wind and percussion instruments.

In all sections, we start by considering the vibrations of simple systems – like stretched strings, simple air columns, stretched membranes, thin plates and shells. We show that, for almost all musical instruments, the usual text-book description of such systems is strongly perturbed by material properties, geometrical factors and acoustical coupling between the drive mechanism, vibrating system and radiated sound.

For stringed, woodwind and brass instruments, we discuss excitation by the bow, reed and vibrating lips, which all involve strongly non-linear processes, even though the vibrations of the excited system usually remains well within the linear regime. However, the amplitudes of vibration of very strongly excited strings, air columns, thin plates and membranes can sometimes exceed the linear approximation limit, resulting in a number of interesting non-linear phenomena, often of significant musical importance.

Musical acoustics therefore provides an excellent introduction to the physics of both linear and non-linear acoustical systems, in a context of rather general interest to professional acousticians, teachers and students, at both school and college levels.

The subject continues its long tradition in advancing the frontiers of experimental, computational and theoretical acoustics, in an area of wide general appeal and contemporary relevance.

By discussing the theoretical models and experimental methods used to investigate the acoustics of many musical instruments, we have aimed to provide a useful background for professional acousticians, students and their teachers, for whom musical acoustics provides an exceedingly rich area for original research projects at all educational levels.

Because the subject is ultimately about the sounds produced by musical instruments, a large number of audio illustrations have been provided on a CD accompanying this volume, which can also be accessed by the electronic version of the Handbook on springerlink.com. The extensive list of references is intended as a useful starting point for entry to the current research literature, but makes no attempt to provide a comprehensive list of all important research.

This chapter highlights the acoustics of musical instruments. Other related topics, such as the human voice, the perception and psychology of sound, architectural acoustics, sound recording and reproduction, and many experimental, computational and analytic techniques are described in more detail elsewhere in this volume.

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 399.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

ADC:

analog-to-digital converter

FEA:

finite-element analysis

FFT:

fast Fourier transform

PC:

phase conjugation

PIV:

particle image velocimetry

SPL:

sound pressure level

References

  1. T. Levenson: Measure for Measure: How Music and Science together have explored the Universe (Oxford Univ. Press, Oxford 1997)

    Google Scholar 

  2. S. Hawkins (Ed.): On the Shoulders of Giants (Running, Philadelphia 2002)

    Google Scholar 

  3. Lord Rayleigh: The Theory of Sound: I and II (1896), 2nd edn. (Dover, New York 1945), Reprint

    Google Scholar 

  4. S. Hawkins: The Universe in a Nutshell (Bantam, London 2001)

    Google Scholar 

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

    MATH  Google Scholar 

  6. T.D. Rossing, F.R. Moore, P.A. Wheeler: The Science of Sound, 3rd edn. (Addison Wesley, San Francisco 2002)

    Google Scholar 

  7. D.M. Campbell, A. Myers, C.A. Greated: Musical Instruments: History, Technology and Performance of Instruments of Western Music (Oxford Univ. Press, Oxford 2006)

    Google Scholar 

  8. G. Bissinger: Contemporary generalised normal mode violin acoustics  Acustica 90, 590–599 (2004)

    Google Scholar 

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

    ADS  Google Scholar 

  10. T.J.W. Hill, B.E. Richardson, S.J. Richardson: Modal Radiation from Classical Guitars: Experimental Measurements and Theoretical Predictions. Proc SMAC 03 (KTH, Stockholm 2003) pp. 129–132

    Google Scholar 

  11. L. Cremer: The Physics of the Violin, section 11.2 (MIT Press, Mass 1984)

    Google Scholar 

  12. B. Britten: Serenade for Tenor, Horn and Strings (Hawkes Son, London 1944)

    Google Scholar 

  13. J.M. Barbour: Tuning and Temperament (Michigan State College Press, East Lansing 1953)

    Google Scholar 

  14. National Instruments: Windowing: Optimizing FFTs Using Windowing Functions (National Instruments, Austin 2006), http://zone.ni.com/devzone/conceptd.nsf/

    Google Scholar 

  15. M.-P. Verge, A. Hirschberg: Turbulence noise in flue instruments. In: Proc. Int. Symp. Mus. Acoust., SMAC 95 (IRCAM, Paris 1995) pp. 94–99

    Google Scholar 

  16. M.E. McIntyre, R.T. Schumacher, J. Woodhouse: Aperiodicity in bowed-string motion: On the differential slipping mechanism  Acustica 49, 13–32 (1981)

    Google Scholar 

  17. J. Meyer: Zur klanglichen wirkung des streicher-vibratos, Acustica 76, 283–291 (1992)

    Google Scholar 

  18. C.E. Gough: Measurement, modelling and synthesis of violin vibrato sounds  Acta Acustica 91, 229–240 (2005)

    Google Scholar 

  19. E.I. Prame: Measurement of the vibrato rate of ten singers  J. Acoust. Soc. Am. 96, 1979–1984 (1994)

    ADS  Google Scholar 

  20. J. Gilbert, L. Simon, J. Terroir: Vibrato in single reed instruments, SMAC 03 (Royal Swedish Academy of Music, Stockholm 2003) pp. 271–273

    Google Scholar 

  21. D.W. Robinson, R.S. Dadson: A re-determination of the equal-loudness relations for pure tones  Brit. J. Appl. Phys. 7, 166–181 (1956)

    ADS  Google Scholar 

  22. H.A. Fletcher, W.A. Munson: Loudness, its definition, measurement and calculation  J. Acoust. Soc. Am. 9, 82–108 (1933)

    Google Scholar 

  23. B. Patterson: Musical dynamics  Sci. Am. 231(5), 78–95 (1974)

    Google Scholar 

  24. B.C.J. Moore: Psychology of Hearing (Academic, London 1997)

    Google Scholar 

  25. A.J.M. Houtsma, T.D. Rossing, W.M. Wagenaars: Auditory Demonstrations, Phillips compact disc 1126-061 (Acoust. Soc. Am., Sewickley 1989)

    Google Scholar 

  26. C.M. Hutchins (Ed.): Musical Acoustics, Part I (Violin Family Components) and II (Violin Family Functions) Benchmark papers in Acoustics, Nos. 5 and 6 (Dowden Hutchinson, Ross, Stroudsburg 1975,1976)

    Google Scholar 

  27. C. Hutchins, V. Benade (Eds.): Research Papers in Violin Acoustics 1975-1993, Vols. 1 and 2, (Acoust. Soc. Am., Melville 1997)

    Google Scholar 

  28. CAS Newsletters (1994-1987), CAS Journals (1988-2004), www.catgutacoustical.org

    Google Scholar 

  29. L. Cremer: The Physics of the Violin (MIT Press, Cambridge 1984)

    Google Scholar 

  30. R. Midgley: Musical Instruments of the World (Paddington, New York 1978)

    Google Scholar 

  31. A. Baines: European and American Musical Instruments (Chancellor, London 1983)

    Google Scholar 

  32. G.G. Stokes: On the communication of vibrations from a vibrating body to a surrounding gas (Philos. Trans., London 1868)

    Google Scholar 

  33. C.E. Gough: The resonant response of a violin G-string and the excitation of the wolf-note  Acustica 44(2), 673–684 (1980)

    MathSciNet  Google Scholar 

  34. H.F. Helmholtz: The Sensation of Tone (1877), translated by A.J. Ellis (Dover, New York 1954)

    Google Scholar 

  35. C.V. Raman: On the mechanical theory of the vibrations of bowed strings and of musical instruments of then violin family, with experimental verification of the results: Part 1  Indian Assoc. Cultivation Sci. Bull. 15, 1–158 (1918)

    Google Scholar 

  36. J.C. Schelling: The bowed string and player  J. Acoust. Soc. Am. 9, 91–98 (1973)

    Google Scholar 

  37. S. Thwaites, N.H. Fletcher: Some notes on the clavichord  J. Acoust. Soc. Am. 69, 1476–1483 (1981)

    ADS  Google Scholar 

  38. D.E. Hall: Piano string excitation in the case of a small hammer mass  J. Acoust. Soc. Am. 79, 141–147 (1986)

    ADS  Google Scholar 

  39. D.E. Hall: Piano string excitation II: General solution for a hard narrow hammer  J. Acoust. Soc. Am. 81, 535–546 (1987)

    ADS  Google Scholar 

  40. D.E. Hall: Piano string excitation III: General solution for a soft narrow hammer  J. Acoust. Soc. Am. 81, 547–555 (1987)

    ADS  Google Scholar 

  41. D.E. Hall: Piano string excitation IV: Non-linear modelling  J. Acoust. Soc. Am. 92, 95–105 (1992)

    ADS  Google Scholar 

  42. P.M. Morse, K.U. Ingard: Theoretical Acoustics (McGraw-Hill, New York 1968), Reprinted by Princeton Univ. Press, Princeton 1986

    Google Scholar 

  43. H. Fletcher: Normal vibration frequencies of a stiff piano string  J. Acoust. Soc. Am. 36, 203–209 (1964)

    ADS  Google Scholar 

  44. E.L. Kent: Influence of irregular patterns in the inharmonicity of piano-tone partials upon tuning practice  Das Musikinstrument 31, 1008–1013 (1982),

    Google Scholar 

  45. N.C. Pickering: The Bowed String (Bowed Instruments, Southampton 1991)

    Google Scholar 

  46. N.C. Pickering: Physical Properties of Violin Strings  J. Catgut Soc. 44, 6–8 (1985), paper 21 in ref [15.42]

    Google Scholar 

  47. C. Vallette: The mechanics of vibrating strings. In: Mechanics of musical instruments, ed. by A. Hirschberg, J. Kergomard, G. Weinreich (Springer, Berlin, New York 1995) pp. 115–183

    Google Scholar 

  48. K. Legge, N.H. Fletcher: Nonlinear generation of missing modes on a vibrating string  J. Acoust. Soc. Am. 76, 5–12 (1984)

    ADS  Google Scholar 

  49. C.E. Gough: The nonlinear free vibration of a damped elastic string  J. Acoust. Soc. Am. 75, 1770–1776 (1984)

    ADS  Google Scholar 

  50. J. Miles: Resonant non-planar motion of a stretched string  J. Acoust. Soc. Am. 75, 1505–1510 (1984)

    ADS  MathSciNet  Google Scholar 

  51. R.J. Hanson, J.M. Anderson, H.K. Macomber: Measurement of nonlinear effects in a driven vibrating wire  J. Acoust. Soc. Am. 96, 1549–1556 (1994)

    ADS  Google Scholar 

  52. R.J. Hanson, H.K. Macomber, A.C. Morrison, M.A. Boucher: Primarily nonlinear effects observed in a driven asymmetrical vibrating wire  J. Acoust. Soc. Am. 117, 400–412 (2005)

    ADS  Google Scholar 

  53. J.A. Elliot: Intrinsic nonlinear effects in vibrating strings  Am. J. Phys. 48, 478–480 (1980)

    ADS  Google Scholar 

  54. J. Woodhouse, P.M. Galluzzo: The bowed string as we know it today  Acustica 90, 579–590 (2004)

    Google Scholar 

  55. F.A. Saunders: Recent work on violins  J. Acoust. Soc. Am. 25, 491–498 (1953)

    ADS  Google Scholar 

  56. J.C. Schelling: The bowed string and the player  J. Acoust. Soc. Am. 53, 26–41 (1973)

    ADS  Google Scholar 

  57. J.C. Schelling: The physics of the bowed string. In: The Physics of Music, ed. by C. Hutchins, Scientific American (W.H. Freeman Co., San Fransisco 1978)

    Google Scholar 

  58. R.T. Schumacher: Measurements of some parameters of bowing  J. Acoust. Soc. Am. 96, 1985–1998 (1994)

    ADS  Google Scholar 

  59. F.G. Friedlander: On the oscillation of the bowed string  Proc. Cambridge Phil. Soc. 49, 516–530 (1953)

    MATH  MathSciNet  ADS  Google Scholar 

  60. M.E. McIntyre, J. Woodhouse: On the fundamentals of bowed string dynamics  Acustica 43, 93–108 (1979)

    MATH  Google Scholar 

  61. J. Woodhouse: On the playability of violins, Part II: Minimum bow force and transients  Acustica 78, 137–153 (1993)

    Google Scholar 

  62. M.E. McIntyre, R.T. Schumacher, J. Woodhouse: Aperiodicity in bowed-string motion: On the differential slipping mechanism  Acustica 49, 13–32 (1981)

    Google Scholar 

  63. R.T. Schumacher: Oscillations of bowed strings  J. Acoust. Soc. Am. 43, 109–120 (1979)

    MATH  Google Scholar 

  64. K. Guettler: On the creation of the Helmholtz motion in bowed strings  Acustica 88, 2002 (2002)

    Google Scholar 

  65. P.M. Galluzzo: On the Playability of stringed instruments, PhD Thesis (Cambridge University, Cambridge 2003)

    Google Scholar 

  66. J.H. Smith, J. Woodhouse: The tribology of rosin  J. Mech. Phys. Solids 48, 1633–1681 (2000)

    MATH  ADS  Google Scholar 

  67. W. Reinicke: Dissertation, Institute for Technical Acoustics (Technical University of Berlin, Berlin 1973)

    Google Scholar 

  68. J. Woodhouse, R.T. Schumacher, S. Garoff: Reconstruction of bowing point friction force in a bowed string  J. Acoust. Soc. Am. 108, 357–368 (2000)

    ADS  Google Scholar 

  69. J.H. Smith: Stick-slip vibration and its constitutive laws, PhD thesis (Cambridge University, Cambridge 1990)

    Google Scholar 

  70. J. Woodhouse: Bowed string simulation using a thermal friction model  Acustica 89, 355–368 (2003)

    Google Scholar 

  71. W. Reinicke, L. Cremer: Application of holographic interferometry to the bodies of sting instruments  J. Acoust. Soc. Am. 48, 988–992 (1970)

    ADS  Google Scholar 

  72. J. Woodhouse: data kindly provided for this chapter

    Google Scholar 

  73. H. Dünnewald: Ein erweitertes Verfahren zur objektiven Bestimmung der Klangqualität von Violinen, Acustica 71, 269–276 (1990), reprinted in English as Deduction of objective quality parameters on old and new violins, J. Catgut Acoust. Soc. 2nd Ser. 1(7) 1-5 (1991), included in Hutchins [15.27, Vol 1]

    Google Scholar 

  74. E.V. Jansson: Admittance measurements of 25 high quality violins  Acta Acustica 83, 337–341 (1997)

    Google Scholar 

  75. E.V. Jansson: Violin frequency response - bridge mobility and bridge feet distance  Appl. Acoust. 65, 1197–1205 (2004)

    Google Scholar 

  76. J. Woodhouse: On the "bridge hill" of the violin  Acustica 91, 155–165 (2005)

    Google Scholar 

  77. J.A. Moral, E.V. Jansson: Eigenmodes, input admittance and the function of the violin  Acustica 50, 329–337 (1982)

    Google Scholar 

  78. M. Hacklinger: Violin timbre and bridge frequency response  Acustica 39, 324–330 (1978)

    Google Scholar 

  79. D. Gill: The Book of the Violin, ed. by D. Gill (Phaedon, Oxford 1984) p. 11, Prologue

    Google Scholar 

  80. C.E. Gough: The theory of string resonances on musical instruments  Acustica 49, 124–141 (1981)

    Google Scholar 

  81. J. Woodhouse: On the synthesis of guitar plucks  Acustica 89, 928–944 (2003)

    Google Scholar 

  82. J. Woodhouse: Plucked guitar transients: comparison of measurements and synthesis  Acustica 89, 945–965 (2003)

    Google Scholar 

  83. G. Weinreich: Coupled piano strings  J. Acoust. Soc. Am. 62, 1474–1484 (1977)

    ADS  Google Scholar 

  84. C.G.B. Baker, C.M. Thair, C.E. Gough: A photo-detector for measuring resonances of violin strings  Acustica 44, 70 (1980)

    Google Scholar 

  85. F. Savart: Mémoires sur le construction des Instruments à Cordes et à Archet (Deterville, Paris 1819), See also the brief summary and references to modern translations of Savartʼs research in Hutchins 15.26 Part 1, page 8

    Google Scholar 

  86. M.E. McIntyre, J. Woodhouse: On measuring the elastic and damping of orthotropic sheet materials  Acta. Metall. 36, 1397–1416 (1988)

    Google Scholar 

  87. M.D. Waller: Vibrations of free rectangular plates  Proc. Phys. Soc. London B 62, 277–285 (1949)

    ADS  Google Scholar 

  88. A.W. Leissa: Vibration of Plates (NASA SP-160, Washington 1993), Reprinted by Acoust. Soc. Am., Woodbury 1993

    Google Scholar 

  89. C. Hutchins: The Acoustics of Violin Plates  Sci. Am. 1, 71–186 (1981)

    Google Scholar 

  90. B.E. Richardson, G.W. Roberts: The adjustment of mode frequencies in guitars: a study by means of holographic interferometry and finite element analysis. SMAC 83 (Royal Swedish Academy of Music, Stockholm 1985) pp. 285–302

    Google Scholar 

  91. C. Hutchins: A rationale for BI-TRI octave plate tuning  Catgut Acoust. Soc. J. 1(8), 36–39 (1991), Series II

    Google Scholar 

  92. E. Reissner: On axi-symmetrical vibrations of shallow spherical shells  Q. Appl. Math. 13, 279–290 (1955)

    MATH  MathSciNet  Google Scholar 

  93. K.D. Marshall: Modal analysis of a violin  J. Acoust. Soc. Am. 77(2), 695–709 (1985)

    ADS  Google Scholar 

  94. G. Bissinger: Contemporary generalised normal mode violin acoustics  Acustica 90, 590–599 (2004)

    Google Scholar 

  95. N.J.-J. Fang, O.E. Rodgers: Violin soundpost elastic vibration  Catgut Acoust. Soc. J. 2(1), 39–40 (1992)

    Google Scholar 

  96. G.A. Knott: A modal Analysis of the Violin using MSC.NASTRAM and PATRAN. MSc Thesis (Naval Postgraduate School, Monterey 1987), Reproduced in Hutchins/Benade 15.27

    Google Scholar 

  97. J.P. Beldie: Dissertation (Technical University of Berlin, Berlin 1975), as described in Cremer 15.29 Sect. 10.4-5

    Google Scholar 

  98. J. Meyer: Die Abstimmung der Grundresonanzen von Guitarren, Das Musikinstrument 23, 179–186 (1974), English translation in J. Guitar Acoustics No.5, 19 (1982)

    Google Scholar 

  99. Q. Christensen: Qualitative models for low frequency guitar function  J. Guitar Acoust. 6, 10–25 (1982)

    Google Scholar 

  100. T.D. Rossing, J. Popp, D. Polstein: Acoustical Response of Guitars. SMAC 83 (Royal Swedish Academy of Music, Stockholm 1985) pp. 311–332

    Google Scholar 

  101. E.V. Jansson: On higher air modes in the violin  Catgut Acoust. Soc. Newsletter 19, 13–15 (1973), Reprinted in Musical Acoustics, Part 2, ed. C.M.Hutchins (Dowden, Hutchinson & Ross, Stroudsberg 1976)

    Google Scholar 

  102. G. Derveaux, A. Chaigne, P. Joly, J. Bécache: Time-domain simulation of guitar: Model and method  J. Acoust. Soc. Am. 114, 3368–3383 (2003)

    ADS  Google Scholar 

  103. G. Roberts, G. Finite: Element analysis of the violin, PhD Thesis (Cardiff University, Cardiff 1986), extract reproduced in Hutchins and Benade 15.27, pp.575-590

    Google Scholar 

  104. B.E. Richardson, G.W. Roberts: The adjustment of mode frequencies in guitars: A study by means of holographic and finite element analysis. Proc. SMAC. 83 (Royal Swedish Academy of Music, Stockholm 1985) pp. 285–302

    Google Scholar 

  105. G. Derveaux, A. Chaigne, P. Joly, J. Bécache: Numerical simulation of the acoustic guitar (INRIA, Rocquencourt 2003), from http://www.inria.fr/multimedia/Videotheque-fra.html

    Google Scholar 

  106. G. Bissinger: A unified materials-normal mode approach to violin acoustics  Acustica 91, 214–228 (2005)

    Google Scholar 

  107. M. Schleske: On making "tonal copies" of a violin  J. Catgut Acoust. Soc. 3(2), 18–28 (1996)

    Google Scholar 

  108. L.S. Morset: A low-cost pc-based tool for violin acoustics measurements, ISMA 2001 (Fondazione Scuola Di San Giorgio, Venice 2001) pp. 627–630

    Google Scholar 

  109. H.O. Saldner, N.-E. Molin, E.V. Jansson: Vibrational modes of the violin forced via the bridge and action of the soundpost  J. Acoust. Soc. Am. 100, 1168–1177 (1996)

    ADS  Google Scholar 

  110. E.V. Jansson, N.-E. Molin, H. Sundin: Resonances of a violin body studied by hologram interferometry and acoustical methods  Phys. Scipta 2, 243–256 (1970)

    ADS  Google Scholar 

  111. N.-E. Molin, A.O. Wählin, E.V. Jansson: Transient response of the violin  J. Acoust. Soc. Am. 88, 2479–2481 (1990)

    ADS  Google Scholar 

  112. N.-E. Molin, A.O. Wählin, E.V. Jansson: Transient response of the violin revisited  J. Acoust. Soc. Am. 90, 2192–2195 (1991)

    ADS  Google Scholar 

  113. J. Curtin: Innovation in violin making, Proc. Int. Symp. Musical Acoustics  CSA-CAS 1, 11–16 (1998)

    Google Scholar 

  114. J. Meyer: Directivity of the bowed string instruments and its effect on orchestral sound in concert halls  J. Acoust. Soc. Am. 51, 1994–2009 (1972)

    ADS  Google Scholar 

  115. G. Weinreich, E.B. Arnold: Method for measuring acoustic fields  J. Acoust. Soc. Am. 68, 404–411 (1982)

    ADS  Google Scholar 

  116. G. Weinreich: Sound hole sum rule and dipole moment of the violin  J. Acoust. Soc. Am. 77, 710–718 (1985)

    ADS  Google Scholar 

  117. T.J.W. Hill, B.E. Richardson, S.J. Richardson: Acoustical parameters for the characterisation of the classical guitar  Acustica 89, 335–348 (2003)

    Google Scholar 

  118. G. Bissinger, A. Gregorian: Relating normal mode properties of violins to overall quality signature modes  Catgut Acoust. Soc. J. 4(8), 37–45 (2003)

    Google Scholar 

  119. E.V. Jansson: Admittance measurements of 25 high quality violins  Acustica 83, 337–341 (1997)

    Google Scholar 

  120. G. Weinreich: Directional tone colour  J. Acoust. Soc. Am. 101, 2338–2346 (1997)

    ADS  Google Scholar 

  121. J. Meyer: Zur klangichen Wirkung des Streicher-Vibratos, Acustica 76, 283–291 (1992)

    Google Scholar 

  122. H. Fletcher, L.C. Sanders: Quality of violin vibrato tones  J. Acoust. Soc. Am. 41, 1534–1544 (1967)

    ADS  Google Scholar 

  123. M.V. Matthews, K. Kohut: Electronic simulation of violin resonances  J. Acoust. Soc. Am. 53, 1620–1626 (1973)

    ADS  Google Scholar 

  124. J. Nagyvary: Modern science and the classical violin  Chem. Intel. 2, 24–31 (1996)

    Google Scholar 

  125. L. Burckle, H. Grissino-Mayer: Stradivari, violins, tree rings and the Maunder minimum  Dendrichronologia 21, 41–45 (2003)

    Google Scholar 

  126. C.M. Hutchins: A 30-year experiment in the acoustical and musical development of violin family instruments  J. Acoust. Soc. Am. 92, 639–650 (1992),

    ADS  Google Scholar 

  127. H.L.F. Helmholtz: On the Sensations of Tone, 4th edn. (Dover, New York 1954), trans. by A.J. Ellis

    Google Scholar 

  128. H. Bouasse: Instruments á Vent (Delagrave, Paris 1929)

    Google Scholar 

  129. M. Campbell, C. Greated: The Musicians Guide to Acoustics (Oxford Univ. Press, Oxford 1987)

    Google Scholar 

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

    Google Scholar 

  131. A. Hirschberg, J. Kergomard, G. Weinreich: Mechanics of Musical Instruments (Springer, Berlin, New York 1995)

    MATH  Google Scholar 

  132. J. Backus: The Acoustical Foundations of Music, 2nd edn. (Norton, New York 1977)

    Google Scholar 

  133. A.H. Benade: Fundamentals of Musical Acoustics (Oxford Univ. Press, Oxford 1975)

    Google Scholar 

  134. D.M. Campbell (Ed.): Special Issue on Musical Wind Instruments Acoustics  Acustica 86(4), 599–755 (2000)

    Google Scholar 

  135. P.M. Moorse, K.U. Ingard: Theoretical Acoustics (McGraw–Hill, New York 1968), reprinted by Princeton Univ. Press, Princeton (1986)

    Google Scholar 

  136. L.L. Beranek: Acoustics (McGraw Hill, New York 1954) pp. 91–115, reprinted by Acoust. Soc. Am. (1986)

    Google Scholar 

  137. H. Levine, L. Schwinger: On the radiation of sound from an unflanged pipe  Phys. Rev. 73, 383–406 (1948)

    MATH  ADS  MathSciNet  Google Scholar 

  138. R.D. Ayers, L.J. Eliason, D. Mahrgereth: The conical bore in musical acoustics  Am. J. Phys. 53, 528–527 (1985)

    ADS  Google Scholar 

  139. H.F. Olson: Acoustic Engineering (Van Nostrand-Reinhold, Princeton 1957) pp. 88–123

    Google Scholar 

  140. L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders: Fundamentals of Acoustics (Wiley, New York 1982), Fig. 14.19

    Google Scholar 

  141. A.G. Webster: Acoustical impedance, and the theory of horns and the phonograph  Proc. Nat. Acad. Sci. (US) 5, 275–282 (1919)

    ADS  Google Scholar 

  142. C.J. Nederveen: Acoustical Aspects of Woodwind Instruments (Knuf, Amsterdam 1969) p. 60

    Google Scholar 

  143. D.H. Keefe, A.H. Benade: Wave propagation in strongly curved ducts  J. Acoust. Soc. Am. 74, 320–332 (1983)

    ADS  Google Scholar 

  144. R. Caussé, J. Kergomard, X. Luxton: Input impedance of brass instruments – Comparison between experiment and numerical models  J. Acoust. Soc. Am. 75, 241–254 (1984)

    ADS  Google Scholar 

  145. N.H. Fletcher, R.K. Silk, L.M. Douglas: Acoustic admittance of air-driven reed generators  Acustica 50, 155–159 (1982)

    Google Scholar 

  146. A. Almeida, C. Verges, R. Caussé: Quasistatic nonlinear characteristics of double-reed instruments  J. Acoust. Soc. Am. 121, 536–546 (2007)

    ADS  Google Scholar 

  147. S. Ollivier, J.-P. Dalmont: Experimental investigation of clarinet reed operation, SMAC 03 (Royal Swedish Academy of Music, Stockholm 2003) pp. 283–289

    Google Scholar 

  148. J.-P. Dalmont, J. Gilbert, S. Ollivier: Nonlinear characteristics of single-reed instruments: Quasi-static flow and reed opening measurements  J. Acoust. Soc. Am. 114, 2253–2262 (2003)

    ADS  Google Scholar 

  149. J. Backus, C.J. Nederveen: Acoustical Aspects of Woodwind Instruments (Knuf, Amsterdam 1969) pp. 28–37

    Google Scholar 

  150. S. Ollivier, J.-P. Dalmont: Experimental investigation of clarinet reed operation, Proc. SMAC 03 (Royal Swedish Academy of Music, Stockholm 2003) pp. 283–289

    Google Scholar 

  151. A.P.J. Wijnands, A. Hirschberg: Effect of pipeneck downstream of a double reed. In: Proc. Int. Symp. Musical Acoustics (IRCAM, Paris 1995) pp. 148–151

    Google Scholar 

  152. N.H. Fletcher: Excitation mechanisms in woodwind and brass instruments  Acustica 43, 63–72 (1979), erratum Acustica 50, 155-159 (1982)

    Google Scholar 

  153. P.D. Koopman, C.D. Hanzelka, J.P. Cottingham: Frequency and amplitude of vibration of reeds from American reed organs as a function of pressure  J. Acoust. Soc. Am. 99, 2506 (1996)

    ADS  Google Scholar 

  154. J.-P. Dalmont, J. Gilbert, J. Kergomard: Reed instruments, from small to large amplitude periodic oscillations and the Helmholtz motion analogy  Acustica 86, 671–684 (2000)

    Google Scholar 

  155. J. Backus: Vibrations of the reed and air column of the clarinet  J. Acoust. Soc. Am. 33, 806–809 (1961)

    ADS  Google Scholar 

  156. N.H. Fletcher: Nonlinear theory of musical wind instruments  Appl. Acoust. 30, 85–115 (1990)

    Google Scholar 

  157. R.T. Schumacher: Self-sustained oscillations of a clarinet; an integral equation approach  Acustica 40, 298–309 (1978)

    MATH  MathSciNet  Google Scholar 

  158. R.T. Schumacher: Ab initio calculations of the oscillations of a clarinet  Acustica 48, 71–85 (1981)

    Google Scholar 

  159. J. Gilbert, J. Kergomard, E. Ngoya: Calculation of steady state oscillations of a clarinet using the harmonic balance technique  J. Acoust. Soc. Am. 86, 35–41 (1989)

    ADS  Google Scholar 

  160. D.M. Campbell: Nonlinear dynamics of musical reed and brass wind instruments  Contemp. Phys. 40, 415–431 (1999)

    ADS  Google Scholar 

  161. N. Gand, J. Gilbert, F. Lalöe: Oscillation threshold of wood-wind instruments  Acta Acustica 1, 137–151 (1997)

    Google Scholar 

  162. J.-P. Dalmont, J. Kergomard: Elementary model and experiments for the Helmholtz motion of single reed wind instruments. In: Proc. Int. Symp. Mus. Acoust. (IRCAM, Paris 1995) pp. 115–120

    Google Scholar 

  163. A.H. Benade: Air column reed and playerʼs windway interaction in musical instruments. In: Vocal Fold Physiology, Biomechanics, Acoustics and Phonatory Control, ed. by I.R. Titze, R.C. Scherer (Denver Centre for the Performing Arts, Denver 1985) pp. 425–452

    Google Scholar 

  164. G.P. Scavone: Modelling vocal tract influence in reed wind instruments, Proc. SMAC 03 (Royal Swedish Academy of Music, Stockholm 2003) pp. 291–294

    Google Scholar 

  165. N.H. Fletcher: Mode locking in non-linearly excited inharmonic musical oscillators  J. Acoust. Soc. Am. 64, 1566–1569 (1978)

    ADS  Google Scholar 

  166. D. Ayers: Basic tests for models of the lip reed, ISMA 2001 (Fondazione Scuola Di San Giorgio, Venice 2001) pp. 83–86

    Google Scholar 

  167. S.J. Elliot, J.M. Bowsher: Regeneration in brass wind instruments  J. Sound Vibrat. 83, 181–207 (1982)

    ADS  Google Scholar 

  168. F.C. Chen, G. Weinreich: Nature of the lip-reed  J. Acoust. Soc. Am. 99, 1227–1233 (1996)

    ADS  Google Scholar 

  169. S. Adachi, M. Sato: Trumpet sound simulation using a two-dimensional lip vibration model  J. Acoust. Soc. Am. 99, 1200–1209 (1996)

    ADS  Google Scholar 

  170. I.R. Titze: The physics of small-amplitude oscillation of the vocal folds  J. Acoust. Soc. Am. 83, 1536–1552 (1988)

    ADS  Google Scholar 

  171. D.C. Copley, W.J. Strong: A stroboscopic study of lip vibrations in a trombone  J. Acoust. Soc. Am. 99, 1219–1226 (1996)

    ADS  Google Scholar 

  172. S. Yoshikawa, Y. Muto: Brass playerʼs skill and the associated li-p wave propagation, ISMA 2001 (Fondazione Scuola Di San Giorgio, Venice 2002) pp. 91–949

    Google Scholar 

  173. J. Gilbert, S. Ponthus, J.F. Petoit: Artificial buzzing lips and brass instruments: experimental results  J. Acoust. Soc. Am. 104, 1627–1632m (1998)

    ADS  Google Scholar 

  174. J. Cullen, J.A. Gilbert, D.M. Campbell: Brass instruments: linear stability analysis and experiments with an artificial mouth  Acustica 86, 704–724 (2000)

    Google Scholar 

  175. N.H. Fletcher: Nonlinear theory of musical wind instruments  Appl. Acoust. 30, 85–115 (1990)

    Google Scholar 

  176. T.H. Long: The performance of cup-mouthpiece instruments  J. Acoust. Soc. Am. 19, 892–901 (1947)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  179. R.D. Ayers: Impulse responses for feedback to the driver of a musical wind instrument  J. Acoust. Soc. Am. 100, 1190–1198 (1996)

    ADS  Google Scholar 

  180. B. Fabre, A. Hirschberg: Physical modelling of flue instruments: a review of lumped models  Acustica 86, 599–610 (2000)

    Google Scholar 

  181. N.H. Fletcher: Sound production in organ pipes  J. Acoust. Soc. Am. 60, 926–936 (1976)

    ADS  MathSciNet  Google Scholar 

  182. P. Savic: On acoustically effective vortex motions in gaseous jets  Philos. Mag. 32, 287–252 (1941)

    Google Scholar 

  183. J.W. Coltman: Jet drive mechanism in edge tones and organ pipes  J. Acoust. Soc. Am. 60, 723–733 (1976)

    ADS  Google Scholar 

  184. S. Adachi: CFD analysis of air jet deflection- comparison with Nolleʼs measurements, SMAC 03 (Royal Swedish Academy of Music, Stockholm 2003) pp. 313–319

    Google Scholar 

  185. A.W. Nolle, Sinuous instability of a planar air jet: Propagation parameters and acoustic excitation  J. Acoust. Soc. Am. 103, 3690–3705 (1998)

    ADS  Google Scholar 

  186. L. Cremer, H. Ising: Die selbsterregten Schwingungen von Orgelpfeifen, Acustica 19, 143–153 (1967)

    Google Scholar 

  187. J.W. Coltman: Sounding mechanism of the flute and organ pipe  J. Acoust. Soc. Am. 44, 983–992 (1968)

    ADS  Google Scholar 

  188. M. Raffel, C. Willert, J. Kompenhans: Particle Image Velocimetry - A Practical Guide (Springer, Berlin, Heidelberg 1998)

    Google Scholar 

  189. C. Ségoufin, B. Fabre, M.P. Verge, A. Hirschberg, A.P.J. Wijnands: Experimental study of the influence of mouth geometry on sound production in recorder-like instruments: windway length and chamfers  Acta Acustica 86, 649–661 (2000)

    Google Scholar 

  190. S. Thwaites, N.H. Fletcher: Wave propagation on turbulent jets  Acustica 45, 175–179 (1980)

    Google Scholar 

  191. S. Thwaites, N.H. Fletcher: Wave propagation of turbulent jets: II  Acustica 51, 44–49 (1982)

    Google Scholar 

  192. B. Fabre, A. Hirschberg: From sound synthesis to instrument making: an overview of recent researches on woodwinds, SMAC 03 (Royal Swedish Academy of Music, Stockholm 2003) pp. 239–242

    Google Scholar 

  193. N.H. Fletcher: Jet-drive mechanism in organ pipes  J. Acoust. Soc. Am. 60, 481–483 (1976)

    ADS  MathSciNet  Google Scholar 

  194. S.A. Elder: On the mechanism of sound production in organ pipes  J. Acoust. Soc. Am. 54, 1554–1564 (1973)

    ADS  Google Scholar 

  195. R.C. Chanaud: Aerodynamic whistles  Sci. Am. 222(1), 40–46 (1970)

    Google Scholar 

  196. T.A. Wilson, G.S. Beavers, M.A. DeCoster, D.K. Holger, M.D. Regenfuss: Experiments on the fluid mechanics of whistling  J. Acoust. Soc. Am. 50, 366–372 (1971)

    ADS  Google Scholar 

  197. D.K. Holger, T. Wilson, G. Beavers: Fluid mechanics of the edge-tone  J. Acoust. Soc. Am. 62, 1116–1128 (1977)

    ADS  Google Scholar 

  198. S. Yoshikawa: Jet wave amplification in organ pipes  J. Acoust. Soc. Am. 103, 2706–2717 (1998)

    ADS  Google Scholar 

  199. B. Fabre, A. Hirschberg, A.P.J. Wijnands: Vortex shedding in steady oscillations of a flue organ pipe  Acustica - Acta Acustica 82, 877–883 (1996)

    Google Scholar 

  200. A. Baines: European and American Musical Instruments (Chancellor, London 1983)

    Google Scholar 

  201. T.D. Rossing: Science of Percussion Instruments (World Scientific, Singapore 2000)

    Google Scholar 

  202. J. Blades: Percussion Instruments and Their History (Faber, Faber, London 1974)

    Google Scholar 

  203. P. Boulez: Notations I-IV (Universal Edition, Vienna 1945, 78, 84)

    Google Scholar 

  204. M. Bertsch: Vibration patterns and sound analysis of the Viennese timpani. ISMA 2001 (Fondazione Scuola Di San Giorgio, Venice 2001)

    Google Scholar 

  205. C.V. Raman: The Indian Musical Drum, Proc. Indian Acad. Sci. A1 179 (1934). In: Reprinted in Musical Acoustics Selected Reprints, ed. by T.D. Rossing (Am. Assoc. Phys. Teach., College Park 1988)

    Google Scholar 

  206. T.D. Rossing, W.A. Sykes: Acoustics of indian drums  Percuss. Notes 19(3), 58 (1982)

    Google Scholar 

  207. B.S. Ramakrishna, M.M. Sondhi: Vibrations of indian musical drums regarded as composite membranes  J. Acoust. Soc. Am. 26, 523 (1954)

    ADS  Google Scholar 

  208. S. De: Experimental study of the vibrational characteristics of a loaded kettledrum  Acustica 40, 206 (1978)

    Google Scholar 

  209. H. Zhao: Acoustics of Snare Drums: An Experimental Study of the Modes of Vibration, Mode Coupling and Sound Radiation Pattern, M.S. thesis (Northern Illinois Univ., DeKalb 1990)

    Google Scholar 

  210. C.V. Raman: On some Indian stringed instruments  Proc. Indian Assoc. Adv. Sci. 7, 29–33 (1922)

    Google Scholar 

  211. T.D. Rossing, I. Bork, H. Zhao, D. Fystrom: Acoustics of snare drums  J. Acoust. Soc. Am. 92, 84–94 (1992)

    ADS  Google Scholar 

  212. T.D. Rossing: Acoustics of percussion instruments: Part I  Phys. Teacher 14, 546–556 (1976)

    ADS  Google Scholar 

  213. T.D. Rossing: Chladniʼs law for vibrating plates  Am. J. Phys. 50, 271–274 (1982)

    ADS  Google Scholar 

  214. N.H. Fletcher: Nonlinear frequency shifts in quasi-spherical-cap shells: Pitch glide in Chinese Gongs  J. Acoust. Soc. Am. 78, 2069 (1985)

    ADS  Google Scholar 

  215. P.L. Grossman, B. Koplik, Y.-Y. Yu: Nonlinear vibration of shallow spherical shells  J. Appl. Mech. 36, 451–458 (1969)

    MATH  Google Scholar 

  216. K.A. Legge, N.H. Fletcher: Non-linear mode coupling in symmetrically kinked bars  J. Sound Vib. 118, 23–34 (1987)

    ADS  Google Scholar 

  217. S. Schedin, P.O. Gren, T.D. Rossing: Transient wave response of a cymbal using double pulsed TV holography  J. Acoust. Soc. Am. 103, 1217–1220 (1998)

    ADS  Google Scholar 

  218. R. Perrin, T. Charnley, H. Banu, T.D. Rossing: Chladniʼs law and the modern English church bell  J. Sound Vib. 102, 11–19 (1985)

    ADS  Google Scholar 

  219. R. Perrin, T. Charnley, J. de Pont: Normal modes of the modern English church bell  J. Sound Vib. 102, 28048 (1983)

    Google Scholar 

  220. T.D. Rossing, R. Perrin: Vibration of bells  Appl. Acoust. 20, 41–70 (1988)

    Google Scholar 

  221. R. Perrin, T. Charnley, J. de Pont: Normal modes of the modern English church bell  J. Sound Vibr. 102, 28048 (1983)

    Google Scholar 

  222. T.D. Rossing, D.S. Hampton, B.E. Richardson, H.J. Sathoff: Vibrational modes of Chinese two-tone bells  J. Acoust. Soc. Am. 83, 369–373 (1988)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Colin Gough Prof. .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Science+Business Media, LLC New York

About this entry

Cite this entry

Gough, C. (2007). Musical Acoustics. In: Rossing, T. (eds) Springer Handbook of Acoustics. Springer Handbooks. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30425-0_15

Download citation

Publish with us

Policies and ethics