In Search of the Missing Fundamental: by Richard K. Jones
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The Timpano Bowl

The function of the bowl in the acoustical performance of timpani has been a subject of contention and a matter of intense debate among scientists and musicians for many years (Rayliegh 1879; Richardson 1929; Kirby 1930; Wood 1962; Taylor 1964; Benade 1976; Rossing et al. 1982), and both musicians and scientists have advanced plausible theories without any real scientific justification (Wood 1962; Taylor 1964).42 The misinformation and misconceptions are still being promulgated by many performers and educators in texts, lexicons and method books today (Taylor 1964; Peters 1993; Leonard 2000; Beck 2013).43 44 45 46

Taylor PathErroneous information about bowl shape and the
path of the sound-wave by English timpanist Henry W. Taylor 43

 

There still remains a general belief among many timpanists that the shape of the bowl directs the path of the sound wave affecting the tonal characteristics of the drum. The shape of the bowl contributes to the harmonicity and color of the pitch only with respect to how the geometry of the bowl determines the volume of air the bowl can contain. Numerous scientific studies conducted by Thomas D. Rossing et al., as well as Helmut Fleischer, Hugo Fastl and associates have proven that the actual shape of a timpano bowl is quite unimportant in determining its intrinsic  sound. As long as the volume of air enclosed inside of the bowl is kept in the correct range for the diameter and mass of the head, cambered, hemispheric or parabolic shaped bowls, which have the same volume, will have the same effect with respect to how the drum produces its pitch. The correct volume of air for the diameter and tension/mass of the head helps to suppress the inharmonic fundamental (and its associated modes of vibration) allowing the more harmonic (pitch producing) modes to be heard. The volume of air enclosed in the bowl also acts as a restoring force trying to return the head to a stationary position. This enclosed volume of air has resonances of its own that can interact with modes of the vibrating membrane that have similar shapes. The size and shape of the bowl simply determine its volume. This volume of air and the motion of its associate resonant air modes fine tune the upper partials.

Another popular misconception about timpani is that the bowls serve as sound chambers or acoustic air cavity resonating chambers (Helmholtz resonator) like the body of a guitar or violin or a marimba resonator, which resonate or amplify the sound. They do not. Since the volume of air enclosed with in the bowl remains the same over the entire range of the drum, any true acoustic resonance would be limited to only a small range of the instrument; in fact, the frequencies of the various modes of enclosed air are much higher than that of the actual principal tone of the vibrating membrane so any acoustic resonance would affect the higher (less audible) partials only (Rossing).

The bowl is however, an important system modifier. The primary function of a timpano bowl is to act as a baffle, separating the top of the head from the bottom of the head so that the radiated energy from the top and bottom surfaces cannot interact and cancel each other. The presence of the bowl turns the drum into a monopole source.  Low frequencies from a monopole source radiate well in all directions. The radiation of the low frequency sound energy gives the impression that the bowl is amplifying or resonating the sound, hence the popular misconception that the bowl is resonating the sound of the vibrating head.

modal radiation
Modal radiation pattern mode 2,1 with a baffle 39

It is true that mechanical resonances from the bowl and frame exist, but they have been shown to not enhance the pitch to any significant degree (Fleischer & Fastl). If they do, it is completely serendipitous. In fact, these unintended hyper-resonances have been shown, more often than not, to actually detract from the sustain of the preferred modes. Be that as it may, one cannot deny the timpanist the pleasure of indulging in the beauty of sound produced by the various and sundry vibrations of his or her own instruments, no matter what they hear vibrating. It all adds to the mystique of the instrument.

The following chapters investigate popular beliefs and misconceptions about timpani bowls.

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