Multiphase winding structures provide induction machines with favorable fault tolerant characteristics. Medium voltage drives have also benefited from the favorable application characteristics of multiphase machines, as well as advances in semiconductor technology. Although high voltage and current device technology has advanced significantly, device switching losses remains as one of the main design limitations in medium voltage drives. This limits the converter's switching frequency, causing degradation in the connected machine's performance due to an increase in torque ripple. This paper investigates the performance of various multiphase induction machines when fed from a quasi-square wave inverter. The inverter topology switches at the fundamental frequency to limit inverter losses, a highly desirable feature in medium voltage applications. Four multiphase induction machines with three, five, seven and eleven phases are designed and used in the comparison study. Finite element analysis is used to determine their parameters. The investigation aims to provide a clear understanding of optimal machine-converter matching criteria based on minimum torque ripple and maximum torque gain.