Natural gratings explored by a finger generate vibratory patterns. These vibrations contain a wide range of frequencies, which include the fundamental spatial frequency of the grating and other (higher) harmonics. In this study, it was proposed to investigate how the fundamental and harmonic frequencies contribute to the perception of a virtual grating presented in the form of spatial pattern of friction force. Using multidimensional scaling methods, we established that the first overtone was the main characteristic used by the participants to identify gratings. When asked to rate the pleasantness to the touch, participants' preferences were for gratings with low spatial frequencies and low amplitudes. These results suggest new ways of creating meaningful, pleasant human-computer interactions in the context of surface-haptic displays.