Musical Saw

Above, the blade from the side, its handle held between the knees and its tip in the fingers, bent into an S (drawn four times deeper than it is). Below, the blade from above, tapering from heel to toe, with the trapped mode glowing where the curvature turns over: two stripes along the blade, moving in opposite senses, with still lines between them. Bowed, the bow crosses the smooth edge; struck, the mallet lands on the face.

Along the blade, from the handle (left) to the tip: the lowest frequency a wave with the note's shape across the blade can have at each place (the band edge, the line), which the curvature raises on either side of the inflection, and the note (across). Where the note lies under the line the wave cannot run, only fade; it is caught in the dip between, and its shape (filled) sits there. A loose bend makes the dip shallow and the mode spreads to the hands; a J has no dip at all.