The lower section of each cone has tabs cut, just like a welsh seam - but these are flared out to meet the inside of the cone below to make the joints. Because I like to do so I am riveting each tab also. As the lower diameter on each come is bigger than the top diameter of the preceding cone it fits like a cork. This gives you the flexibility to change the angles to make the curves - if you wish. Put the cones together, rotate to the correct angle and then mark where the seam line will be so you can cut and trim the tabs. After that it is just a case of flaring the tabs out and soldering them.
I am building two halves which will then be joined at the mid point through the opening in the base. This was going to be a 6" triclamp but it is much heavier than I anticipated, so instead this is going to be a flange type joint that will be soldered as the last opperation in the build.

If you wished to build a multi profile swan neck you would start at the narrow end. That way each joint is being made with access through the wide opening of each cone - just solder them together one at a time with each cone probably only a few inches long