The Science and Craft of Bell-Plate Gongs

Bell-plate gongs are unique percussion instruments that bridge the gap between traditional church bells and flat gongs. Unlike a standard metal sheet that produces a dull “clunk,” a properly engineered bell plate produces a long, pure, and resonant tone. This phenomenon is achieved by manipulating the geometry of the plate to control its vibrational modes.

1. The Geometry of Resonance

The secret to a ringing bell plate lies in its specific proportions. Research from Harvard University suggests that while various sizes work, the ratio of dimensions is critical. A standard bell-plate design often follows a specific polygonal shape with a “tang” (a handle-like protrusion).

• Standard Ratios: The ratio of the length (a) to the width (b) is typically between 1.5 to 1.6.
• Thickness: Thickness (c) relates to the length (a) in a ratio of approximately 1:6 or 1:7 for optimal sustain.

2. Calculating Ringing Frequency

The fundamental frequency (pitch) of a bell plate is determined by its material properties and dimensions. According to the Acoustics research at UNSW, for thin plates, the frequency follows this general relationship:

This means if I double the thickness, I double the frequency (one octave higher). However, if I double the overall size (length and width), the frequency drops to one-quarter of its original value. In practice, tuning is often refined by me removing small amounts of metal from the edges or back to lower the pitch.

3. Determining Hole Locations (Nodal Points)

To allow a plate to ring freely, it must be suspended at its nodal points—areas where the plate does not vibrate. If I drill a hole in an “antinode” (a high-vibration area), the mounting hardware will dampen the sound immediately.

I use Chladni Patterns to find these spots. By pouring fine sand on a vibrating plate, the sand naturally settles on the nodes. In a standard bell-plate shape, the nodal lines of the (0,2) vibration mode converge at the tang. This is why my bell plates can be held by the handle and still ring; the handle is effectively “vibration-neutral.”

4. Refrain and Harmonic Calculations

A “musical” bell plate isn’t just one frequency; it’s a cluster of harmonized overtones. A high-quality plate is often tuned to include a fundamental, an octave, and sometimes a fifth. The relationship between these partials is what defines the “bell” timbre.

The “refrain” or sustain duration is highly sensitive to the edges. Removing even 5mm of material can drastically shorten the ring time. I use use the FFT (Fast Fourier Transform) to analyze these overtones, ensuring the secondary frequencies are integer multiples (or close to them) of the fundamental to avoid “beating” or dissonance.

5. Material Selection

While bronze is traditional for bells, bell plates are frequently made from 6061-T6 Aluminum or Stainless Steel. I favour Aluminum because it is easy to cut, has high internal damping, and produces a clear, bright tone at a 1/16″ to 1/8″ thickness, although I do work with cold-rolled steel.