The optical Vernier effect provides magnification of the sensing capabilities of an interferometer, allowing unprecedented sensitivities and resolutions to be achieved. Just like a calliper uses two different scales to achieve higher resolution measurements, the optical Vernier effect is based on the overlap between the responses of two interferometers with slightly detuned interference signals. Here we present in detail, as a novel approach, the generation of optical harmonics of the Vernier effect with Fabry-Perot interferometers, where the two interferometers can have very different frequencies in the interferometric pattern. We demonstrate not only a considerable enhancement, but also a better control of the sensitivity magnification factor, which scales up with the order of the harmonics, breaking the limits of the conventional Vernier effect as used today. In addition, this novel concept opens also new ways of dimensioning the sensing structures, together with improved fabrication tolerances.