In Search of the Missing Fundamental: by Richard K. Jones
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The Vent-Hole

Contemporary studies on timpani acoustics have determined that the vent-hole found at the bottom of most timpano bowls has no direct influence on how the drum produces pitch. Some, however, believe that it does have an indirect influence on other aspects of how the instrument functions.

So, what is the function of the vent-hole? Why is it there? Does one size fit all?

Benade’s theory was that it had a strong influence on the sound through its damping of the air vibrations in the kettle; specifically, mode 0,1 the actual inharmonic fundamental. “The vent-hole prevents the frequency change phenomenon and gives rise instead to a very heavy damping of the mode (0,1), because of the viscous friction in the air as it is pumped in and out of the kettle by the vibration of the drumhead.”58

Rossing’s ( studies rebuked Benade’s theory and stated, “Closing the vent-hole with a rubber stopper has little or no effect on the decay time of (0,1) mode and lowers the modal frequency by a very small amount, typically 0.4%” Rossing felt that the function of vent-hole was simply to equalize the air pressure inside and outside of the bowl as the barometric pressure changes. Rossing also commented that it is also convenient for humidifier pads when using calf heads.59

More recently, the studies of Fastl and Fleischer’s have shown that when there is an open vent-hole in the bottom of the bowl, a Helmholtz resonance occurs at very low frequencies (10 Hz to 20 Hz). This resonance occurs only when the bowl has the open vent-hole. Fleischer and Fastl tested this theory with Dieter Dyk, who was then solo timpanist of the Tonhalle Orchestra Zurich. Dyk said he could not detect any audible difference in sound, however he did comment that the “zurückprallen” (rebound) had changed when the vent-hole was closed.60

While this resonance doesn’t impact the actual pitch of the drum, it can certainly impact the playability or the feel of the instrument, especially for the seasoned timpanist who is sensitive to the response of the head. The viscothermal characteristics (viscosity and thermal conduction-stiffness in this case) of the air inside of the bowl act as a natural restoring force, much like a spring pushing the head back into its normal position. This restoring force pertains to the motion of the concentric modes, which do not contribute to the pitch of the drum, but they do influence how the membrane vibrates. When some of the air is escaping through the vent-hole creating this resonance, it can’t be used as a restoring force, thus affecting how the head responds to the impact of the stick with each stroke.

Regarding what current drum builders are doing with the vent-hole, the Yamaha Corporation states “When the hole is smaller, the sound has a longer sustain; and when the hole is larger, the sound has a shorter sustain, with a lighter touch when played.”  This adheres to the theory that the internal air acts as a spring-like restoring force helping to keep the membrane in motion.

Yamaha Vent-hole

The timpani builder Wolfgang Hardtke also suggests that the vent-hole should be kept small. Other manufacturers, e.g. Hinger Touch-Tone, experimented with graduated vent-holes, decreasing the size of the hole as the diameter of the bowl decreased in size. Some timpani bowls, e.g. Rogers Accu-sonic, and many Viennese Schnellar style timpani do not have vent-holes at all, or extremely small vent-holes. The Schnellar tuning system uses a lift-plate at the bottom of the bowl, which raises and lowers the bowl from the bottom to change the tension on the membrane. Even a small hole in the lift-plate would affect the motion of the internal bowl air, albeit to a very small degree. One must bear in mind, however, that the internal volume of air for each manufacturer is different, which has a direct affect on how the membrane vibrates, and in turn affects the voice of the instrument. (see Bowl Volume and Air Loading)

Since air density is not a constant (see Environmental Considerations), and since air density has a direct influence on the viscothermal characteristics of the air contained within the bowl, any significant changes in the internal confined air will affect the air stiffness and the restoring force of the concentric modes to a measurable degree.  While not noticeable audibly, it can certainly alter the feel of the head to the experienced player.

As with the lack of consensus for a standard bowl shape, there is also no consensus for the size of the vent-hole, or if one is really needed at all. Since no two locations will have the same exact environmental conditions, it is difficult to quantify what size of vent-hole is appropriate in order to balance the viscothermal characteristics (viscosity and thermal conduction) of the internal bowl air with the physical response of the membrane, specifically the response of the concentric modes. Perhaps a solution to accommodate for different environmental conditions, is to devise an F-stop device for the vent hole, which is controlled by a cable attached alongside the master tuner.  Much like a throttle cable or a carburetor coke.  Pull out on the throttle when you want to close the vent hole completely or just keep more air in the bowl, push in when you want the air to escape. This device could be used to alter the motion of the internal air when environmental conditions changed, thus affecting the response of the head.