This paper uses modal analysis to investigate the effect of manipulating drumhead tension on the modal frequency ratios of a cylindrical drum with two drumheads. This analysis evaluates a drum’s free vibration after excitation. It is shown that the frequency of the (01) mode of the drum is the same on both heads, whereas the frequency of each (11) mode has a decreased dependence on that of the opposite drumhead. This allows manipulation of the ratios for the (11) modes of the batter and resonant heads with respect to the overall (01) mode. This manipulation is shown to allow a range of tunings such that the (11) mode of the batter head can be tuned to a ratio of 1.5× that of the (01) mode.
REFERENCES
1.
T. D.
Rossing
, Science of Percussion Instruments
(World Scientific
, Singapore
, 2005
), pp. 1
–46
.2.
T. D.
Rossing
and N. H.
Fletcher
, Principles of Vibration and Sound
(Springer
, New York
, 2004
), pp. 69
–70
.3.
D.
Russell
(2006
), “Vibrational modes of a circular membrane
,” http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html (last viewed August 2010).4.
T. D.
Rossing
, I.
Bork
, H.
Zhao
, and D.
Fystrom
, “Acoustics of snare drums
,” J. Acoust. Soc. Am.
, 92
, 84
–94
(1992
). 5.
C.
Mei
, “Free vibrations of circular membranes under arbitrary tension by the finite-element method
,” J. Acoust. Soc. Am.
46
, 693
–700
(1969
). 6.
R.
Worland
, “Normal modes of a musical drumhead under non-uniform tension
,” J. Acoust. Soc. Am.
127
, 525
–533
(2010
). 7.
L.
Rhaouti
, A.
Chaignea
, and P.
Joly
, “Time-domain modeling and numerical simulation of a kettledrum
,” J. Acoust. Soc. Am.
105
, 3545
–3562
(1999
). 8.
E.
Toulson
, C.
Crigny
, P.
Robinson
, and P.
Richardson
, “The perception and importance of drum tuning in live performance and music production
,” Proceedings of the Fourth Art of Record Production Conference
, Lowell, MA, 2008
.9.
T. D.
Rossing
, “Acoustics of percussion instruments: Recent progress
,” Acoust. Sci. & Tech.
22
, 177
–188
(2001
). 10.
H.
Suzuki
and Y.
Hwang
, “Coupling between two membranes of a Japanese drum
,” Acoust. Sci. & Tech.
29
, 215
–220
(2008
). 11.
N.
Fletcher
, and T. D.
Rossing
, The Physics of Musical Instruments
, 2nd ed. (Springer Science+Business Media, Inc.
, New York
, 1998
), Vol. 2
, pp. 591
–599
.12.
J.
Montagu
, Timpani & Percussion
(Yale University Press
, New Haven, CT
, 2002
), p. 120
.13.
J.
Blades
, Percussion Instruments and Their History
(The Bold Strummer, Ltd.
, Westport, CT
, 1992
), p. 370
.14.
Rhythm Magazine, “
So you want to sound like Steve Perkins
,” (Future Publishing, Bath, UK, 2004
), Vol. 105
, p. 72
.15.
A.
Budofsky
, “Brian Chase
,” Modern Drummer
(Modern Drummer Publications
, Cedar Grove, NJ
, 2009
), pp. 48
–62
.16.
J.
Boxall
, “Fever to sell
,” Rhythm Magazine
(Future Publishing
, Bath, UK
, 2004
), Vol. 99
, pp. 51
–52
.17.
B.
Gatzen
, Drum Tuning (Sound and Design. Simplified)
(Alfred Publishing Co., Inc.
, Van Nuys, CA
, 2006
), DVD.18.
G.
Nicholls
, The Drum Handbook
(Backbeat Books
, San Francisco, CA
, 2003
), pp. 120
–134
.19.
P. G. M.
Richardson
, and E. R.
Toulson
, “Clearing the drumhead by acoustic analysis method
,” Proceedings of the Institute on Acoustics, Reproduced Sound Conference
, Cardiff, Wales, UK, 2010
.20.
The MathWorks, Natick, MA, “
FFT—discrete Fourier transform
,” http://www.mathworks.com/help/techdoc/ref/fft.html (Last viewed October 18, 2010
).21.
M.
Weeks
, Digital Signal Processing Using MATLAB and Wavelets
, 2nd ed. (Jones and Bartlett
, Sudbury, MA
, 2010
), p. 213
.22.
D. L.
Sullivan
, “Accurate frequency tracking of timpani spectral lines
,” J. Acoust. Soc. Am.
, 101
, 530
–538
(1997
). © 2012 Acoustical Society of America.
2012
Acoustical Society of America
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