Chladni figures

On the left is a square plate with sand on it, vibrating as a simplified model. Drag the point across the grid on the right to change the note (m, n): the sand jumps up and comes down where the plate stays still, along the nodal lines. In this model, points on one dashed arc share m² + n² and sound the same note, and so do (m, n) and its mirror (n, m); slide Mix of the pair α and the two blend in other proportions, so the note stays while the lines shift. When m = n there is only one mode, and the slider does nothing. The plate is held at its centre, so the modes that swing hardest there, with m and n both even, are left out and their points stay empty.