This paper aims to investigate the semantic perceptual space of synthetic tactile textures rendered via an ultrasonic based haptic tablet and the parameters influencing this space. Through a closed card sorting task, 30 participants had to explore 32 tactile-only textures and describe each texture using adjectives. A factorial analysis of mixed data was conducted. Results suggest a 2 dimensional space with tactile textures belonging to a continuum of rough to smooth adjectives. Influence of waveform and amplitude is shown to play an important role in perceiving a texture as smooth or rough, and spatial period is a possible modulator of different degrees of roughness or smoothness. Finally, we discuss how these findings can be used by designers on tactile feedback devices.