The acoustic radiating membrane (1) is for assembly in a music box or a striking watch. The membrane is made with at least one area of asymmetrical shape, formed in the material of the membrane or with at least one area of asymmetrical shape having a different thickness from the general thickness of the membrane. It preferably includes two asymmetrical areas of elliptical shape (2, 3) which are partly superposed and have a different thickness from each other. The two ellipses (2, 3), preferably hollowed out of the membrane, are off-centre in relation to each other.