A new design of a plane mirror Fabry-Perot interferometer with the mirror blanks freely supported by horizontal rings is described. Special attention is paid to the surface flatness and dielectric coatings of the mirrors. It is shown that any two piezoelectrically scanned Fabry-Perot interferometers can be synchronized in tandem operation using simple optics and standard electronic driving and stabilization equipment. Applications of the tandem system to Brillouin scattering are given. The observation of Brillouin spectra of supported thin plastic films and of a clamped metal surface is reported.