Acoustic Coupling of Drumset Cymbals

1
Acoustic Coupling of Drumset Cymbals

• Edmund Spencer, Paul Wheeler,
• Srinidhi Kaveri, Tushar Andriyas, Brian
• Beardall.
• Electrical and Computer Engineering Dept., Utah
  State
• University, Logan, Utah.
• ASA Meeting, Salt Lake City, 5th June 2007.

2
Summary

• Introduction and Motivation
• Measurement Set-up
• Time data and analysis
• Spectral Data
• Time-Frequency (spectrogram) plots
• Conclusions and future work
• References

3
Motivation

• Investigate cymbal behaviour, interaction with
  other cymbals.
• Cymbals are usually placed close to each other on
  a drumset.
• -Relative placement may affect sound.
• Many cymbals are in proximity in a drum store.
• -Interaction may affect sound.

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Cymbal Characteristics

• Similar to circular plates (non-harmonic radial
  modes).
• Modified form of Chladnis law
• plt2 for cymbals.
• Larger, thicker, heavier cymbals more complex.
• Chose 10 and 12 small, thin, light splash
  cymbals for this study.

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Experimental Setup

• 10 splash cymbal and 12 splash cymbal selected
• Measurements made with Audio-Technica ATM31a
  condenser microphone
• Recordings made using Marantz PMD 670 at 44.1
  kS/sec.
• Spectra-Plus, Audacity and Matlab used for
  analysis.

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Experimental Setup II

• Maximized proximity and area of overlap.
• No tilt in either cymbal.
• Cymbals struck at the edge with the shoulder of
  drumstick by drummer.
• Avoided hitting too hard since wobbling produces
  beats.

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Photograph of Setup Diagonal View
Front View
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Vibration of a cymbal in slow-motion (120 times
slower)(Source University of Salford Website)
www.acoustics.salford.ac.uk
9
Time series plot for 3 hits of 10 cymbal 20 s
apart
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Time series plot for 3 hits of 12 cymbal 20 s
apart
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Time series plot for 3 hits of 12 cymbal in
presence of 10 cymbal 20 s apart
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10 cymbal spectrum (1st hit)
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Spectrum plots for 10 only (3 hits)
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12 cymbal spectrum (1st hit)
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Spectrum plots for 12 only
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Spectrum of 12 cymbal when struck in presence of
10 cymbal (1st hit)
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Spectrum of 12 struck in presence of 10
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12 cymbal only spectrogram
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12 struck in presence of 10 spectrogram
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Observations

• Interaction between 10 and 12 splash cymbals
  has been observed.
• Decay time for the 12 slightly shorter when 10
  is present.
• Relative amplitude between the lowest two modes
  changed.
• Frequencies at which beats occurred were
  different.

21
Future Work

• Numerical modeling of cymbals.
• Analysis of the interaction at higher
  frequencies.
• Interaction between cymbals of substantially
  different sizes.
• More realistic setup.

22
References

• Neville H. Fletcher and Thomas D. Rossing, The
  Physics of Musical Instruments,Springer-Verlag,
  1991.
• Kinsler et al, Fundamentals of Acoustics, Wiley,
  2000.
• Charles A. Culver, Musical Acoustics, Fourth
  Edition, Mc Graw-Hill Book Co., 1956.
• Thomas D. Rossing and N. H. Fletcher, Nonlinear
  vibrations in plates and gongs, J. Acoust. Soc.
  Am., Jan. 1983.
• Thomas D. Rossing, Chladni's law for vibrating
  plates, Am. J. Phys. 50(3), Mar. 1982.
• Antoine Chaigne, Cyril Touze, Olivier Thomas,
• Nonlinear vibrations and chaos in gongs and
• cymbals, Acoust. Sci. Tech. 26, 5 (2005).
• R. Perrin et al, Normal Modes of an 18 Inch
  Crash Cymbal, Proceedings Inst. Acoustics, 2006.