Compared to nonmodular machines, modular topologies become increasingly attractive due to their simplified manufacture process, better fault-tolerant capability, and potentially reduced material consumption. In order to maintain or even enhance the machine performance while achieving high fault-tolerant capability, novel modular, single-layer winding switched reluctance machines (SRMs) with different pole numbers are proposed, which are supplied by rectangular wave current with different conduction angles. The influences of the pole number and flux gap width between E-core segmented stators on the electromagnetic performance have been investigated in terms of self- and mutual inductances, electromagnetic torque, copper loss, iron loss, and radial force. It has been found that the modular structures with higher rotor pole numbers than stator slot numbers (12-slot/14-pole and 12-slot/16-pole SRMs) can maintain and even improve the average torque due to the nature of self and mutual inductances. In addition, the torque ripples for modular machines are significantly reduced (below 50%), so do the iron loss and radial force, leading to higher efficiency albeit with potentially lower vibration and acoustic noise. Two prototypes with 12-slot/8-pole and 12-slot/14-pole combinations have been built with both nonmodular and modular structures to validate the predictions in terms of inductances and static torques.