# Pre-registered prediction: Gordon–Webb–Wolpert drums, tabletop build

Written 2026-10-25, before any physical measurement. The sha256 of this file is recorded on the results page; edit nothing below after measuring, add results in a separate file.

## Geometry
Two polygons, each made of 7 right-isosceles half-squares with leg L = 70 mm (area 3.5 L^2 = 171.5 cm^2, perimeter (6+3*sqrt2) L = 717.0 mm for both).
Drum 1 vertices (units of L): (0,0) (0,1) (2,3) (2,2) (3,2) (2,1) (1,1) (1,0)
Drum 2 vertices (units of L): (1,0) (0,1) (0,2) (2,2) (2,3) (3,2) (2,1) (1,1)
Cut files: D1_frame, D2_frame, D1_lid, D2_lid, base (.svg and .dxf, mm, 270 x 270 plates).

## Build A, air cavity (primary test; rigid walls give Neumann conditions)
Stack per drum: base, two 3 mm acrylic frames (cavity height 6 mm), lid with two 4 mm ports. Glue or clamp airtight.
Drive a small speaker at the speaker port with a 300 to 4000 Hz sine sweep (or white noise), record at the mic port, take the spectrum, note the air temperature T.
Ports in drum coordinates: drum 1 speaker [1.542, 1.833], mic [0.833, 1.458]; drum 2 speaker [1.917, 1.75], mic [0.833, 1.625] (chosen so every one of the first 12 modes couples).

Predicted resonances at 20 C (c = 343 m/s), both cavities identical: 717, 1403, 1604, 2127, 2450, 2576, 2872, 3274, 3465, 3713 Hz.
Scale by c(T)/343 with c(T) = 331.3*sqrt(1+T/273.15).

PASS if, for each of the first 8 resonances found in both cavities, the two cavities agree within 0.5 %, and each lies within 3 % of the temperature-corrected prediction.
FAIL (of the build, not the theorem) if any of the first 8 matched pairs differ by more than 1.5 %. Likely causes, in order: leaks, port perturbation, kerf asymmetry, warped acrylic.

## Build B, stretched membrane (fun test; not a clean one)
Sandwich a drumhead film or balloon latex between two frames of the same drum. Tap, record, take the spectrum.
Absolute pitch depends on tension, so only ratios f_n/f_1 are predicted, identical for both drums:
1.000, 1.200, 1.428, 1.605, 1.690, 1.905, 2.043, 2.132, 2.205, 2.268
Expectation, stated honestly: air loading on a light membrane depends on the mode shape, and the two drums' modes have different shapes, so the low modes will drift from the ideal ratios by several percent and not by the same amount on both drums. Predict agreement between drums within 3 % for modes 3 to 8, worse for modes 1 and 2. A heavier, tighter membrane should improve it.

## Control, the cut-out tiles (predicted to FAIL)
The pieces that drop out of the frame cut are the same two shapes as free plates. Isospectrality does not carry over to plates: odd and even reflection, which the transplantation proof uses, does not preserve clamped or free plate boundary conditions. Computed for clamped plates: matched modes differ by 1 to 15 % (first 12). Free plates were not computed.
Prediction: tapping the two dropouts gives spectra whose first 8 matched peaks differ by more than 2 % for at least 3 of them.

## Timbre prediction (all builds)
Same set of frequencies, different loudness of each peak, and the loudness pattern depends on where you strike. The drums play the same notes, not the same sound.