We report on the realization of high-Q/V photonic crystal cavities in thin silicon membranes, with resonances around 1.55 μm wavelength. The cavity designs are based on a recently proposed photonic crystal implementation of the Aubry-André-Harper bichromatic potential, defined from the superposition of two one-dimensional lattices with a non-integer ratio between their periodicity constants. In photonic crystal nanocavities, this confinement mechanism is such that optimized figures of merit can be straightforwardly achieved, in particular an ultra-high-Q factor and diffraction-limited mode volume. Several silicon membrane photonic crystal nanocavities have been realized with measured Q-factors in the 1 × 106 range, as evidenced by resonant scattering. The generality of the proposed designs and their easy implementation and scalability make these results particularly interesting for realizing highly performing photonic nanocavities on different material platforms and operational wavelengths.