Eigendrum

gist

Basel Ashraf’s Eigendrum turns any closed shape into a playable virtual drum. It triangulates the outline, solves the finite-element eigenvalue problem for its vibration modes, and synthesizes the resulting frequencies in the browser. Strike position changes which modes are excited, while formula-defined and isospectral shapes make the mathematics audible. The tool works as both a musical instrument and an interactive explanation of spectral geometry.

ideas

• Shape becomes timbre. The outline fixes the vibration modes and frequency ratios, so changing the geometry changes the sound.
• A strike selects a mixture. Each mode responds according to how much it moves where the mallet lands; a nodal line cannot excite that mode.
• Known spectra test the solver. Circle and rectangle results match closed-form values to better than one tenth of a percent.
• Isospectral shapes separate outline from spectrum. The two Kac drums have different boundaries but identical frequency sets.
• The instrument stays local and shareable. Computation and audio run in the browser, while formula-defined shapes travel in the URL.