My guess on mounting the iron band is that the lower section of the spout originally had a bead ring where the band now sits. It was shaved down to have flat sides with a slight taper toward the top, leaving its bottom diameter slightly larger (perhaps about the same as the ring above)...to force the cracked segment together as the ring was seated all the way down. The bead just above it, which appears to be slightly larger than the iron ring and the crux of the problem, has several small flat spots on its surface. They could be dings, but perhaps they were "ironed" into the bead when the ring was forced over it. I'm betting the lower spout segment was heated in oil/lard to slightly soften its surface and make it slippery, then the ring was simply forced down over it...perhaps pushed evenly with another ring or tube to avoid excessive pressure on one side or the other...or perhaps "walked" down. I don't believe there is really much difference between the diameter of the "troublesome" bead above and the inside diameter of the iron ring itself. The only important area of diameter difference would be the bottom of the tapered area where the was ring finally forced/seated, to hold that section of the spout tightly together. There are no signs of burning or scorching from a hot ring...of course, it's possible such discoloration could have worn off. Ah, the little mysteries of these neat old horns! Shelby Gallien