Harmonic Analysis of Mallet Percussion By Max Candocia

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

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

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

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

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

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

Vibraphone Harmonics Dry: Wet: Harmonics and Frequencies of Vibraphone Struck with Mallets 4500 4000 Frequency (Hz) 3500 VBD 3000 VBW 2500 VRD 2000 VRW 1500 VWD 1000 VWW 500 0 Harmonic 1 Instrument Vibraphone Vibraphone Mallet Black Red White Harmonic 2 Location Dry Wet Harmonic 3 # Harmonics H 1 d. B 5 2 3 1 4 2 H 2 d. B 6 16 22 1 16 25 Harmonic 4 H 3 d. B 19 1. 1 3. 5 0. 5 1. 5 Harmonic 5 H 4 d. B H 5 d. B 0. 8 13 1. 5 9 0. 6 3

Xylophone Harmonics Instrument Xylophone Xylophone Xylophone Mallet Location Hard Rubber Center Hard Rubber Edge Hard Rubber Node Natural Rubber Center Natural Rubber Edge Natural Rubber Node Plastic Center Plastic Edge Plastic Node # Harmonics H 1 Freq H 2 Freq H 3 Freq 4 886. 9 1750 4 886. 9 1760 3 886. 85 2670. 5 3 886. 9 1750 3 886. 95 1760 5 887 1759 4 886. 9 1750 4 886. 95 1760 3 886. 85 2670. 5 H 4 Freq H 5 Freq 2670 5100 2670 5150 5155 2670 2167 2670. 5 5150 2670 5100 2670 5170 5200

On the Node

Marimba Harmonics Instrument Marimba Marimba Mallet Black Red Red Location Center Edge Node # Harmonics H 1 Freq 3 4 3 2 H 2 Freq 221. 5 221. 4 221. 5 221. 6 221. 4 221. 5 H 3 Freq H 4 Freq 665 990 665 885 2240 885. 5 2210 664 885. 5 885

Using a Stick on Marimba Instrument Marimba Mallet Stick Location Center Edge Node # Harmonics H 1 Freq H 2 Freq H 3 Freq 4 222 2100 3 221. 5 885 6 221 855. 3 H 4 Freq H 5 Freq 2210 2400 2205 2064 2210 H 6 Freq 3900 4460

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

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