If you're interested in frequency shifting, Harald Bode was the leading engineer in this area. You can read a gentle introduction here: and if you look around there are some VST plugins that emulate the Bode designs.

I haven't tried using this for precision stuff - over a small range it might well improve intelligibility at the expense of only minor distortion. I tend to reach for it when I want to give sounds an extra weird dimension, it sounds somewhat orthogonal to the normal harmonic distributions we're familiar with.