I started a similar thread on the DoubleGun forum and it was correctly pointed out that, in my inadequate effort to keep things simple, I only created more confusion
I've never found the word 'scroll' or 'leaves' in the mid to late 1800s Belgian and British descriptions of methodology or pattern nomenclature.
Alternees is obviously French. Steve Culver already told me neither a c. late 1800s nor modern blacksmith would approve

Dr Gaddy used the scroll or whorl words, and I do think they are appropriate descriptive terms
That said, the 'scroll' that we see in the pattern is made up of the 2 halves of adjacent rods hammer welded. The rod would have at least twice the numbers I stated for the 1/2 scroll.
You can count the alternees pretty easily in this image, and can see how the 'outside' alternee joins the adjacent scroll. I count 12 and possibly 13 iron alternee, for a total of 24 or 26. The rod is between the two 'zipper' (wavy) welds.
'English Two Stripe' and the lower barrel quite clearly shows the zipper (wavy) weld which is down the middle of a scroll but is the weld of adjacent rods, and the straight weld where the edges of the ribband are 'jumped' or butt welded. I count 24 alternees.
These are a Two Iron 'Horse-shoe' pattern. One can clearly see that the leaves between the zipper welds are connected ie. part of the same rod