We propose to synthesize a new class of single-walled nanotubular compounds (SWNCs) and investigate the interplay between their structural and electronic properties using ab initio density functional calculations. SWNCs are composed of cyclacenes of variable diameter interconnected by various linker compounds. Cyclacenes map directly onto and can be viewed as the shortest segments of (n,0) zigzag carbon nanotubes. We focus on cyclacenes with n=6–12 fused benzene rings interconnected by biphenyl, tetrazine, or acetylene linkers. Depending upon the nature and the orientation of the linkers, we find it possible to change the systems from narrow-gap to wide-gap semiconductors, and to modulate the band dispersion, suggesting the possibility of band gap engineering.