The present invention relates to horizontal frame tensile structures (“HFTS”) of the kind employing corner elements to interconnect beams and posts. The corner elements of the invention comprise 1) two arms that engage the ends of adjacent beams, and 2) a leg that engages the top of a post. The arms are splayed so as to produce canted corner angles. Optionally, or additionally, the leg angle of the corner element is canted. Canting the corner angle and/or the leg angle causes the beams to bow upwards and/or outwards, thereby effectively increasing the angle in the horizontal plane between adjacent beams. This bow in the beams is reduced or eliminated when the membrane is attached to the frame, thereby providing straight beams and an aesthetically pleasing profile and introducing beneficial increased tension into the frame.