Acoust. Sci. & Tech. 25, 6 (2004) INVITED REVIEW Acoustics of percussion instruments: An update Thomas D. Rossing, Junehee Yoo and Andrew Morrison Physics Department, Northern Illinois University, DeKalb, IL 60115, USA Abstract: Methods for studying the modes of vibration and sound radiation from percussion instruments are reviewed. Recent studies on the acoustics of marimbas, cymbals, gongs, tamtams, lithophones, steelpans, and bells are described. Vibrational modes and sound radiation from the HANG, a new steel percussion instrument are presented. Keywords: Percussion, Marimbas, Cymbals, Gongs, Tamtams, Lithophones, Steelpans, bells, HANG PACS number: 43.75.Kk, 43.40.Dx [DOI: 10.1250/ast.25.406] frequency (eigenfrequency). It should be possible to excite 1. INTRODUCTION a normal mode of vibration at any point in a structure that Percussion instruments are an important part of every is not a node and to observe motion at any other point that musical culture. Although there has been less research on is not a node. It is a characteristic only of the structure the acoustics of percussion instruments, as compared to itself, independent of the way it is excited or observed. In wind or string instruments, quite a number of scientists practice, it is difficult to avoid small distortions of the continue to study these instruments. normal modes due to interaction with the exciter, the In 2001 we published a review paper on the acoustics sensor, and especially the supports. of percussion instruments in this journal [1]. It is the Normal modes shapes are unique for a structure, purpose of this paper to continue the discussion of whereas the deflection of a structure at a particular percussion instruments, and to summarize some research frequency, called its operating deflection shape (ODS), done in recent years. may result from the excitation of more than one normal mode [2]. Normal mode testing has traditionally been done 2. METHODS FOR STUDYING using sinusoidal excitation, either mechanical or acoustical. PERCUSSION INSTRUMENTS Detection of motion may be accomplished by attaching Recent studies of the acoustics of percussion instru- small accelerometers, although optical and acoustical ments have included: 1) theoretical studies of modes of methods are less obtrusive. Modal testing with impact vibration; 2) experimental studies of modes of vibration; 3) excitation, which became popular in the 1970s, offers a sound radiation studies; 4) physical modeling; 5) studies of fast, convenient way to determine the normal modes of a nonlinear behavior. structure. In this technique, an accelerometer is generally attached to one point on the structure, and a hammer with a 2.1. Finite Element and Boundary Element Methods load cell is used to impact the structure at carefully For all but the simplest vibrator shapes, it is difficult to determined positions. Estimates of modal parameters are calculate vibrational modes analytically. Fortunately, there obtained by applying some type of curve fitting program. are powerful numerical methods that can be carried out Experimentally, all modal testing is done by measuring quite nicely by use of digital computers. These generally operating deflection shapes and then interpreting them in a are described as finite element methods or boundary specific manner to define mode shapes [2]. Strictly speak- element methods. ing, some type of curve-fitting program should be used to determine the normal modes from the observed ODSs, 2.2. Experimental Studies of Modes of Vibration even when an instrument is excited at a single frequency. When a percussion instrument is excited by striking (or In practice, however, if the mode overlap is small, the bowing or plucking), it vibrates in a rather complicated single-frequency ODSs provide a pretty good approxima- way. The motion can be conveniently described in terms of tion to the normal modes. normal modes of vibration. A normal mode of vibration 2.2.1. Scanning with a microphone or an accelerometer represents the motion of a linear system at a normal Probably the simplest method for determining ODSs 406 T. D. ROSSING et al.: ACOUSTICS OF PERCUSSION INSTRUMENTS (and hence normal modes) is to excite the structure at 2.2.3. Experimental modal testing single frequency with either a sinusoidal force or a Modal testing may be done with sinusoidal, random, sinusoidal sound field, and to scan the structure with an pseudorandom, or impulsive excitation. In the case of accelerometer or else to scan the near-field sound with a sinusoidal excitation, the force may be applied at a single small microphone [3]. With practice, it is possible to point or at several locations. The response may be determine mode shapes rather accurately by this method. measured mechanically (with accelerometers or velocity 2.2.2. Holographic interferometry sensors), optically, or indirectly by observing the radiated Holographic interferometry offers by far the best spatial sound field. resolution of operating deflection shapes (and hence of In modal testing with impact excitation, an acceler- normal modes). Whereas experimental modal testing and ometer is typically attached to the instrument at some key various procedures for mechanical, acoustical, or optical point, and the instrument is tapped at a number of points on scanning may look at the motion at hundreds (or even a grid with a hammer having a force transducer (load cell). thousands) of points, optical holography looks at almost an Each force and acceleration waveform is Fourier trans- unlimited number of points. formed and a transfer function Hij is calculated. Several Recording holograms on photographic plates or film (as different algorithms may be used to extract the mode in most of the holographic interferograms in [1]) tends to shape and modal parameters from the measured transfer be rather time consuming since each mode of vibration functions [5]. must be recorded and viewed separately. TV holography, on the other hand, is a fast, convenient way to record ODSs 2.3. Radiated Sound Field and to determine the normal modes [4]. The best way to describe sound radiation from complex An optical system for TV holography is shown in Fig. 1. sources such as percussion instruments is by mapping the A beam splitter BS divides the laser light to produce a sound intensity field. Sound intensity is the rate at which reference beam and an object beam. The reference beam sound energy flows outward from various points on the reaches the CCD camera via an optical fiber, while the instrument. The sound intensity field represents the object beam is reflected by mirror PM so that it illuminates direction and the magnitude of the sound intensity at every the object to be studied. Reflected light from the object point in the space around the source. reaches the CCD camera, where it interferes with the A single microphone measures the sound pressure at a reference beam to produce the holographic image. The point, but not the direction of the sound energy flow. In speckle-averaging mechanism SAM alters the illumination order to determine the sound intensity it is necessary to angle in small steps in order to reduce laser speckle noise in compare the signals from two identical microphones the interferograms. spaced a small distance apart. The resulting pressure Generally holographic interferograms show only var- gradient can be used to determine sound intensity. When iations in amplitude. It is possible, however, to recover this is done at a large number of locations, a map of the phase information by modulating the phase of the reference sound intensity field results [6]. beam by moving mirror PM at the driving frequency. This is a useful technique for observing motion of very small 2.4. Physical Modeling amplitude or resolving normal modes of vibration which Synthesizing sounds by physical modeling has attracted are very close in frequency. a great deal of interest in recent years. The basic notion of physical modeling is to write equations that describe how particular sets of physical objects vibrate and then to solve those equations in order to synthesize the resulting sound. Percussion instruments have proven particularly difficult to model completely enough to be able to synthesize their sounds entirely based on a physical model. Physical modeling is complicated by their nonlinear behavior and by the strong role which transients play in their sound. 3. MARIMBAS In most of the World, the term marimba denotes a deep-toned instrument with tuned bars and resonator tubes that evolved from the early Latin American instrument. 1 The marimba typically includes 3 to 4 2 octaves of tuned Fig. 1 Optical system for TV holography. bars of rosewood or synthetic material with a deep arch cut 407 Acoust. Sci. & Tech. 25, 6 (2004) in the underside to tune the overtones. The first overtone, not be excited to any great extent. On the other hand, if the which is radiated by the second bending mode, is normally bars are struck away from the center, deliberately or not, tuned to the 4th harmonic of the fundamental in the first 3 the torsional modes could contribute to the timbre. 1 to 3 2 octaves, after which the interval decreases [1]. Applying finite element methods to marimba and Some companies now make large 5-octave concert xylophone bars showed that a small curvature in the bars marimbas which cover the range C2 to C7. In two such has very little effect on the relative frequencies of the instruments, the second bending mode is accurately tuned vibrational modes [8]. Henrique and Antunes have used 1 to the 4th harmonic in the first 3 2 octaves. The third finite element methods both to optimize the shape of bending mode is tuned to the 10th harmonic in the first 2 marimba and xylophone bars and to model the sound. They octaves, after which the interval decreases. The fourth employ a physical modeling approach that addresses the mode varies from the 20th harmonic in the lowest bars to spatial aspects of the problem and is suitable for both non- about the 6th harmonic in the highest bars [7].