Shorting rings are used to make motor movement more symmetrical, as you know. I have only seen evidence that this reduces even harmonics, i.e. 2nd, 4th, etc. Speaking only of harmonic distortion, are you saying that you believe odd harmonics are reduced too?

Other non-linearities are present in the system, to be sure. At high power levels in particular, there are many other matters than just push-pull flux symmetry. But push-pull symmetry is what the shorting ring is used for. Can you think of other benefits it may bring?

Wayne