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Rigidity, in both material and design, can help substitute for mass in controlling resonances. Mass and rigidity are balanced and traded off in every aspect of arm design, from the choice of materials through the shape of the arm tube to the choice of headshell material and design, arm bearings, and every other detail.
For example, to minimize mass while maximizing rigidity, the arm tube may be built with a thin wall for low mass but a large diameter for high rigidity. A low-mass arm with a small diameter would easily flex when excited by external vibrations, moving the cartridge body all over the place. The small diameter would also make it difficult to provide rigid coupling to the headshell. It's essential that not only the tube be rigid and dead but also the headshell and the coupling between the two. Most arms fail miserably at this.
The more rigid the arm, the higher the resonant frequency and the higher the Q or sharpness of the resonance. Rigid arms must be care fully damped. To check for adequate damping, sharply tap the tube with your fingernail or other small sharp object and listen closely. The sound should be a dull thunk, like a spoon dropped in a jug of whipped cream, with no lingering after-ring.