Abstract: A method for designing a bell, comprising defining a shape of a body wall of the bell in a general form of a frustum that is open at both ends, and determining an optimal size and location of a stiffening element to be added to said bell for increasing a frequency ratio of a second mode of vibration of the bell relative to one or more other modes of vibration to be tuned in the bell. Also, a method of producing a bell, and a bell so produced.

Abstract: A bell is described having the first at least three or more frequencies substantially in harmonic sequence. A method for designing such a bell is also disclosed. An optimization procedure is described wherein an initial bell shape is modified until the first at least three or more frequencies are substantially in an harmonic sequence. An asymmetric bell is also described wherein a meridonal cross-section of the side portion is substantially geometrically similar to a cross-section having: 1) an outer line formed by fitting an arc of a circle to the three described points of the nodes and an inner line formed by fitting a line to the described points of the nodes; or 2) having an outer line formed by joining a straight line to the two described points of the nodes and an inner line formed by fitting a line to the described points of the nodes.