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Timbre comes from the overtones stacked on a fundamental, and those overtones come from the shape of the space the instrument vibrates in. I thought it would be cool to make a small web demo that lets you hear what instruments in different dimensions sound like.
At 1D you get the harmonic series. At 2D you get the ragged ladder of a drumhead. By 4D or 5D so many modes crowd into the first couple of octaves that the tone turns into a gong or a wash. The app also supports changing the shape of the instrument between an N-dimensional box (edges and corners) and an N-dimensional ball (round, no corners).
The live demo is embedded below. Headphones recommended.