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Harmonic Analysis of Mallet Percussion By Max Candocia

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Goals Basic understanding of sound waves and mallet percussion Understand harmonic analysis Understand difference in sounds of different mallets and striking location

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Marimba Photo courtesy of vichitex.com Vibraphone Photo courtesy of woodbrass.com Recording: Vermont Counterpoint, Nathaniel Bartlett Recording: La Fille Aux Cheveux de Lin, Ozone Percussion Ensemble

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Xylophone Photo courtesy of onlinerock.com Recording: Fantasy on Japanese Wood Prints

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Sine: Sawtooth: Sound Waves Vibrating medium (ie. Air, water, ground) Longitudinal Harmonics Sinusoidal Components Images courtesy of Wikipedia

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Qualities of Harmonics Frequency Cycles per second (Hertz); determines pitch Amplitude Power of wave; determines loudness Phase Location of harmonic relative to other harmonics Photo courtesy of Wikipedia Photo courtesy of physics.cornell.edu Photo courtesy of 3phasepower.org

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Harmonic Analysis Harmonics of Kelon xylophone struck in center with hard rubber mallet

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Vibraphone Harmonics Dry: Wet: InstrumentMalletLocation# HarmonicsH1 dBH2 dBH3 dBH4 dBH5 dB VibraphoneBlackDry56190.8133 VibraphoneBlackWet2161.1 VibraphoneRedDry3223.51.5 VibraphoneRedWet11 VibraphoneWhiteDry4160.590.6 VibraphoneWhiteWet2251.5

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Xylophone Harmonics InstrumentMalletLocation# HarmonicsH1 FreqH2 FreqH3 FreqH4 FreqH5 Freq XylophoneHard RubberCenter4886.9175026705100 XylophoneHard RubberEdge4886.9176026705150 XylophoneHard RubberNode3886.852670.55155 XylophoneNatural RubberCenter3886.917502670 XylophoneNatural RubberEdge3886.9517602670 XylophoneNatural RubberNode5887175921672670.55150 XylophonePlasticCenter4886.9175026705100 XylophonePlasticEdge4886.95176026705170 XylophonePlasticNode3886.852670.55200

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On the Node

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Marimba Harmonics InstrumentMalletLocation# HarmonicsH1 FreqH2 FreqH3 FreqH4 Freq MarimbaBlackCenter3221.5665990 MarimbaBlackEdge4221.46658852240 MarimbaBlackNode3221.5885.52210 MarimbaRedCenter2221.6664 MarimbaRedEdge3221.4664885.5 MarimbaRedNode2221.5885

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Using a Stick on Marimba InstrumentMalletLocation# HarmonicsH1 FreqH2 FreqH3 FreqH4 FreqH5 FreqH6 Freq MarimbaStickCenter4222210022102400 MarimbaStickEdge3221.58852205 MarimbaStickNode6221855.32064221039004460

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Conclusion Sounds made of harmonics Relative phase has no apparent pattern in mallet percussion Vibraphone very simple sound when wet, more complicated when dry Soft mallets on marimba and vibes induce sounds with less harmonics Xylophone has different sounds depending on striking location Harder mallets on marimba produce trends in harmonics similar to xylophone

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Thanks to: Professor Steve Errede Adam Watts Dan Carson 3M Richard Feynman playing conga; photo courtesy of physics.miami.edu