In Search of the Missing Fundamental: by Richard K. Jones
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Historical Influence

Epilogue:

Technically, very little has changed in the frame design of the suspended bowl timpani since Einbigler’s innovation. The modern Dresden style drum retains all the same essential characteristics of the instruments Einbigler created with the exception of the modern pedal tuning mechanism, closer machining tolerances and better production of heads.

Do modern timpani bowls and frames that follow the Einbigler design add resonance and enhance the pitch of the instrument?

Modern timpani are variable pitched instruments that have many elements that have potential resonance. With respect to being actual resonant frequencies, the frequencies generated by the bowl, frame, tensioning rods etc., will seldom correlate to the near-harmonic frequency spectra produced by the head. Contrary to popular belief, the energy output from the vibrating bowl (and frame/parts) doesn’t add all that much to the actual sound output of the instrument. In the frequency range of the preferred modes (65 Hz- 520 Hz), at most, it is less than 1% in terms of actual output level. Most of the SPL (sound pressure level) energy output (<1 dB) from the bowl/frame occurs in the 1K -2K frequency range, which adds a small amount of collateral color to the sound, but it doesn’t support the preferred modes, which are the modes of vibration that give the timpano its sense of pitch.

The Fleischer & Fastl studies have shown that there can be as much as 16% of the overall energy being transferred to the bowl, frame and external parts producing what they call parasitic pitch.  This energy can no longer be used by the vibrating head and in fact, all of these unintended resonances have been shown, more often than not, to actually detract from the sustain of the preferred modes rather than enhance or support them. If any do, it is completely arbitrary and is something that cannot be controlled. They may not contribute constructively to the pitch being produced, but they do contribute to the overall sound of the instrument to a small degree. 36

Timpani bowls, the modes of air inside of the bowl, the frame parts, tensioning rods etc., all have resonant frequencies of their own, which can and do interact to some degree with the frequencies of the vibrating head, but these do not necessarily contribute constructively to the pitch of the vibrating head. The frequencies produced by the vibrations of the mechanical parts are by nature inharmonic and create parasitic pitch, which attaches itself to the spectrum being produced by the vibrating head. The frequencies they produce generally will not enhance or reinforce the actual pitch being produced by the vibrating head; instead they detract from the actual pitch being produced by the vibrating head causing destructive interference, shortening the length of sustain of the head and often mask the strength of the principal tone. At best, these extra vibrations only add collateral color to the sound of the instrument and are not true resonant frequencies of the vibrating membrane.

One of the important things that the bowl, and the material it is made from, can and does influence, is the amount of mechanical energy loss. Energy created by the vibrating head and the displaced internal air mass is lost through the bowl walls to a certain degree. Once this mechanical energy is lost, it is no longer available for use by the vibrating head. How the bowl reacts to this mechanical energy in turn influences how the head will vibrate contributing to its resonance and sustain, which is often misinterpreted and misunderstood as being resonance generated by the vibrations being emitted from the bowl. To date, most professional timpanists prefer suspended, hand-hammered copper artisan  bowls on their timpani. The section Why copper? investigates this phenomenon.

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 and personality of the instrument.

3) Chapter 3 References and Document Links

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