We address the production of musical tones by a simple musical instrument of the Brazilian tradition: the berimbau-de-barriga. The vibration physics of the string and of the air mass inside the gourd are reviewed. Straightforward measurements of an actual berimbau, which illustrate the basic physical phenomena, are performed using a PC-based “soundcard oscilloscope.” The inharmonicity of the string and the role of the gourd are discussed in the context of known results in the psychoacoustics of pitch definition.
References
1.
Kay
Shaffer
, O berimbau-de-barriga e seus toques [The Berimbau and Its Rhythms]
(Ministério da Educação e Cultura
, Rio de Janeiro
, 1976
).2.
Eric
Galm
, The Berimbau: Soul of Brasilian Music
(University Press of Mississippi
, Jackson
, 2010
).3.
Richard P.
Graham
and N. Scott
Robinson
, see “Berimbau
” in Continuum Encyclopedia of Popular Music of the World, Volume 2: Performance and Production
, edited by John
Shepherd
, David
Horn
, Dave
Laing
, Paul
Oliver
, and Peter
Wicke
(Continuum
, New York
, 2003
), pp. 345
–349
(an unedited version is also available at <http://www.nscottrobinson.com/berimbau.php>).4.
C.
Zeitnitz
, the Soundcard Oscilloscope program may be found at <http://www.zeitnitz.de/Christian/scope?mid=2>.5.
Thomas D.
Rossing
and Neville H.
Fletcher
, Principles of Vibration and Sound
, 2nd ed. (Springer-Verlag
, New York
, 2004
).6.
Robert W.
Young
, “Inharmonicity of plain wire piano strings
,” J. Acoust. Soc. Am.
24
, 267
–273
(1952
).7.
Harvey
Fletcher
, “Normal vibration frequencies of a stiff piano string
,” J. Acoust. Soc. Am.
36
, 203
–209
(1964
).8.
Harvey
Fletcher
, E. Donnell
Blackam
, and Richard
Stratton
, “Quality of piano tones
,” J. Acoust. Soc. Am.
34
, 749
–761
(1962
).9.
Hanna
Järvelain
, Vesa
Välimäki
, and Matti
Karjalainen
, “Audibility of the timbral effects of inharmonicity in stringed instrument tones
,” Acoust. Res. Lett. Online
2
, 79
–84
(2001
).10.
Shin Hui Lin
Chin
and Jonathan
Berger
, “Analysis of pitch perception of inharmonicity in pipa strings using response surface methodology
,” J. New Mus. Res.
39
, 63
–73
(2010
).11.
Alejandra
Kandus
, Friedrich Wolfgang
Gutmann
, and Caio Mário Castro de
Carvalho
, “A física das oscilações mecânicas em instrumentos musicais: exemplo do berimbau
,” Rev. Brasil. Fís.
28
, 427
–433
(2006
).12.
Joe
Wolfe
, Helmholtz resonance, <www.phys.unsw.edu.au/jw/Helmholtz.html>. This is a rather comprehensive webpage on the Helmholtz resonator, included in the Musical Acoustics webpages of the University of New South Wales, Australia.13.
John William
Strutt
and Baron
Rayleigh
, The Theory of Sound
, Vol. II
, 2nd ed. (Macmillan
, 7, 1929
), Sec. 307 and Appendix A.14.
Harold
Levine
and Julian
Schwinger
, “On the radiation of sound from an unflanged circular pipe
,” Phys. Rev.
73
, 383
–406
(1948
).15.
CRC Handbook of Chemistry and Physics
, 78th ed., edited by David R.
Lide
(CRC Press
, Boca Raton, Florida
, 2008
).16.
Juan G.
Roederer
, Physics and Psychophysics of Music
, 4th ed. (Springer-Verlag
, New York
, 2008
).17.
Alexander J.
Ellis
and Alfred J.
Hipkins
, “Tonometrical observations on some existing non-harmonic musical scales
,” Proc. Roy. Soc. London
37
, 368
–385
(1884
).18.
E.
Zwicker
, G.
Flottorp
, and S. S.
Stevens
, “Critical band width in loudness summation
,” J. Acoust. Soc. Am.
29
, 548
–557
(1957
).19.
Christophe
Micheyl
and Andrew J.
Oxenham
, “Pitch harmonicity and concurrent sound segregation: Psychoacoustical and neurophysiological findings
,” Hearing Res.
266
, 36
–51
(2010
).20.
Alain de
Cheveigné
, “Harmonic fusion and pitch of mistuned partials
,” J. Acoust. Soc. Am.
102
, 1083
–1087
(1997
).21.
Pablo
Castellanos-Macín
and Julius O.
Smith
, “Towards a physical model of the berimbau: Obtaining the modal synthesis of the cabaza
,” J. Acoust. Soc. Am.
134
, 4243
(2013
).22.
Florian
Gomez
, Victor
Saase
, Nikolaus
Buchheim
, and Ruedi
Stoop
, “How the ear tunes in to sounds: A physics approach
,” Phys. Rev. Appl.
1
, 014003-1–7
(2014
).23.
Stefan
Martignoli
and Ruedi
Stoop
, “Local cochlear correlations of perceived pitch
,” Phys. Rev. Lett.
105
, 048101-1–4
(2010
).24.
Yu. V.
Ushakov
, A. A.
Dubkov
, and B.
Spagnolo
, “Regularity of spike trains and harmony perception in a model of the auditory system
,” Phys. Rev. Lett.
107
, 108103-1–4
(2011
).25.
Julyan H. E.
Cartwright
, Diego L.
González
, and Oreste
Piro
, “Nonlinear dynamics of the perceived pitch of complex sounds
,” Phys. Rev. Lett.
82
, 5389
–5392
(1999
).26.
R.
Plomp
, “Pitch of complex tones
,” J. Acoust. Soc. Am.
41
, 1526
–1533
(1967
).27.
Roelof J.
Ritsma
, “Frequencies dominant in the perception of the pitch of complex sounds
,” J. Acoust. Soc. Am.
42
, 191
–198
(1967
).28.
F. A.
Bilsen
, “On the influence of the number and phase of harmonics on the perceptibility of the pitch of complex signals
,” Acustica
28
, 60
–65
(1973
); available at http://www.ingentaconnect.com/content/dav/aaua/1973/00000028/00000001/art00011.29.
A. J. M.
Houtsma
and J.
Smurzynski
, “Pitch identification and discrimination for complex tones with many harmonics
,” J. Acoust. Soc. Am.
87
, 304
–310
(1990
).30.
Ray
Meddis
and Michael J.
Hewitt
, “Virtual pitch and phase sensitivity of a computer model of the auditory periphery. I: Pitch identification
,” J. Acoust. Soc. Am.
89
, 2866
–2882
(1991
).© 2014 American Association of Physics Teachers.
2014
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