Click on the picture and zoom in, these two parts were printed with the exact same setting in Slic3r except 1. The one on the left was sliced with the setting "External perimeters first" checked and the one on the right was printed with it unchecked (default)
The on on the right is also very wavy and bumpy as some of the layers are bulged out further than others while the one on the left is nice and smooth. And they are just the opposite on the inside, The right one is very even and smooth on the inside while the left one is very wavy and bumpy.
Attached in the STL if anyone wants to see what results they get. (I scaled it down a bit but I get the same results without scaling it.) I have it set to 4 perimeters and no infill and no top layers. I haven't tried printing with less layers yet to see if that has an effect on it. I'm not sure what is causing the banding issue yet either.