While the single-molecule conductance properties of pi-conjugated and sigma-conjugated systems have been well-studied, little is known regarding the conductance properties of mixed sigma-pi backbone wires and the factors that control their transport properties. Here we utilize a scanning tunneling microscope-based break-junction technique to study a series of molecular wires with pi-sigma-pi backbone structures, where the pi-moiety is an electrode-binding thioanisole ring and the sigma-moiety is a triatomic alpha-beta-alpha chain composed of C, Si, or Ge atoms. We find that the sequence and composition of group 14 atoms in the alpha-beta-alpha chain dictates whether electronic communication between the aryl rings is enhanced or suppressed. Placing heavy atoms at the alpha-position decreases conductance, whereas placing them at the beta-position increases conductance: for example, the C-Ge-C sequence is over 20 times more conductive than the Ge-C-Ge sequence. Density functional theory calculations reveal that these conductance trends arise from periodic trends (i.e., atomic size, polarizability, and electronegativity) that differ from C to Si to Ge. The periodic trends that control molecular conductance here are the same ones that give rise to the alpha and beta silicon effects from physical organic chemistry. These findings outline a new molecular design concept for tuning conductance in single-molecule electrical devices.