Acoustics of the marimba
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Acoustics of the Marimba. Heather Hill Advised by Professor Steven Errede. Yamaha YM-5100A. Striking Areas. Center Off-Center Edge. Frequency Ratios for Sculpted Marimba Bars. Bork’s Data 1. My Analysis.

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Acoustics of the Marimba

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Acoustics of the marimba

Acoustics of the Marimba

Heather Hill

Advised by Professor Steven Errede

Yamaha YM-5100A


Striking areas

Striking Areas

  • Center

  • Off-Center

  • Edge


Frequency ratios for sculpted marimba bars

Frequency Ratios for Sculpted Marimba Bars

Bork’s Data1

My Analysis

1Bork, Ingolf. “Practical Tuning of Xylophone Bars and Resonators,” Appl. Acoust. J. Acoust. 46, 103-127 (1995).


Frequency and time decay

Frequency and Time Decay

The reverberation time for each harmonic is inversely proportional to the frequency.2

2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.


Frequency and time decay1

Frequency and Time Decay

The reverberation time for each harmonic is inversely proportional to the frequency.2

2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.


Exponential time decays for c 2

Exponential Time Decays for C2


Exponential time decays for c n bars

Exponential Time Decays for Cn Bars


Calculating eta

Calculating Eta

Using Cremer’s Equation,2 I solved for η.

2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.


Average eta values for c n bars

Average Eta Values for Cn Bars


Summary

Summary

  • The harmonics present in a sculpted marimba bar are f1, f4, f10, and f20.

  • The exponential time decay constants τnare inversely proportional to the frequency

  • The mean absorptivity of rosewood is <η> = 0.45% ± 0.09%

  • The methodology we have developed can be used to analyze the decay times of other musical instruments, room acoustics, etc.

Acknowledgements:

I thank Professor Steven Errede for a wonderful summer and for all of his advice and support. I also thank John Nichols for his additional guidance.

The NSF Grant PHY-1062690 supports the REU program at UIUC.


Inharmonicity

Inharmonicity


Tuning evolution

Tuning Evolution


Resonator effect on harmonics

Resonator Effect on Harmonics


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