I did use Catherine Wheel joins to very small picots, to keep the lines of the spiral shape smooth. Debbie Arnold of DS9Designs has prepared excellent directions for how to do the Catherine Wheel join - scroll down to the bottom of her page to find the link to her well-illustrated pdf file. I think there are more instructions for this technique prepared by other tatters, this just happens to be one link I had handy.
Something that confused me when I was learning this join was, "Which thread do I pull first?!" It's the thread that's coming from the chain! Pull till it "pops" through. Then a "hump" appears. Next pull the "hump"! That's when the first half of a double stitch appears, and then the rest is easy.Anyway, I am thrilled with the effect given by the multicolored HDT in the spiral shape!
I finished the bracelet with tatted rings and chains in a coordinating solid, strung with pink beads to pick up the pink in the multicolored thread. By the way, I am currently working on dyeing more of this colorway I call "Vibrato", along with some of the solid blue as well.