In Search of the Missing Fundamental: by Richard K. Jones
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Significant Studies

Donald L. Sullivan (1996) tracked spectral lines for accuracy at each tuning lug of several professional timpani owned by retired Boston Pops timpanist, Everett Beale. In his study, he graphs the time histories of partial frequencies resulting from a single stroke on a 26″ Ludwig Professional timpani. He concluded that since the principal tone, mode (1,1) decays more rapidly than the other preferred modes, in order for timpani to produce a resonant sound with clear and focused pitch, the partials above the principal tone e.g. the fifth and the octave (modes (2,1) and (3,1) should decay slowly. 8

Lamberto Tronchin et al., (2004, 2005) studied the vibrating modes of two brands of timpani (Adams and Ludwig) and his findings corresponded very closely to those of Rossing and his colleagues with regard to which modes create the near harmonic ratios, (1,1), (2,1), (3,1), (4,1) and (5,1). The main focus of his studies was to further investigate the acoustic radiation of the various modes, specifically the intensity of this acoustic radiation as it applies to the directivity of the timpani sound which is important for architectural acoustics and auralization processes. 9

More recently, Helmut Fleischer and Hugo Fastl (2005, 2008) conducted a series of studies Vibroakustische Untersuchungen an Paukenfellen and Fell, Kessel und Gestell der Orchesterpauke, and Physikalische und gehörbezogene Analyse von Paukenklängen, confirming the findings of the earlier studies aforementioned plus adding much new data to the field as well. Of particular interest to this author are Fleischer and Fastl’s findings that: 10

1) It was found that the sound originates exclusively from the head and not from the kettle of the timpani. This finding is based on intensity measurements and numerical computations. Nevertheless, it has to be kept in mind that the kettle plays an important passive role. It acts on the acoustic radiation and on the fine tuning of the intervals of the heads vibration frequencies. As well experiments as computer simulations using Finite Elements and coupled Finite Elements/Boundary Elements have shown that the kettle is vibratory, but to a much less extent than the head. Further experiments have confirmed that the same holds for the stand and the remaining components of the instrument. The vibrations of these parts do not constructively contribute to the generation of the timpani sound. On the contrary, there are indications that they can downgrade the acoustic signal by shortening the sustain of partial tones. Within narrow frequency regions, the main tone, quint or octave happen to decay much faster than defined by the radiation resistance as the only damping mechanism. It is suspected that resonances of distinct parts of the instrument stand can convert vibration energy into heat which, in consequence, is no longer available to the generation of sound. It could be detected that the quint and octave decay irregularly fast when a resonance of the kettle edge is excited by the vibrating head.

2) The volume of the air enclosed influences the intervals of the partial tones, to an especially high extent the frequency of the 01 tone. To keep this inharmonic tone inaudible, the kettle should be small. With respect to the intervals of main tone, quint and octave, however, there is an optimum volume.

The first of these two findings runs counter to the belief of many professional timpanists that the frame of timpani should be massive and heavy in order to conduct energy and vibrations to the stage floor. This is believed to make the timpani project or radiate sound better. Structural integrity of the frame is however necessary for keeping the geometries of the instrument consistent, and mass and weight can certainly contribute to the physical stability of the drum. When the frame is stationary and does not flex under tension, the energy of the vibrating head can be projected out and away from the drum as sound energy rather than into the frame of the drum as physical vibrational energy, which is essentially heat. However, energy transferred from the head to the frame eliciting resonant frequencies from the mechanics of the instrument may be a desired color trait in a timpanist’s concept of his or her personal timpani sound.

The second reinforces the findings of Rossing’s et al. that the actual bowl shape has little or no effect on the sound of the instrument with respect to the near-harmonicity of the preferred modes, provided that the correct volume has been met. The scientific studies have focused the select group of partials known as the preferred modes, and not on all of the of the partials, which contribute to the concept of  from the timpanist’s perspective. Timpanists argue and debate incessantly about the shape and materials of timpani bowls and how they influence and affect the sound of a drum. How much do these inharmonic partials contribute to the overall timpani sound? It varies from instrument to instrument so it is difficult to quantify. Needless to say, more research on bowl shape vs. actual bowl volume as well as bowl material is needed.

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