You are all seriously too nice
The purple and blue ... erm... the purple is a mica, straight out of the bag, and it's fairly true to colour; it's about a shade lighter than what it looks like as a mica which makes sense, considering soap is white(ish). I don't have a clue what the name is and I'm not near it atm, but it's a pretty standard deep purple mica.
The blue is another story. I can't give a good answer there. It's a pre-mixed shade that I made up out of about six different blues, and then I threw in a lot of blue pigment from a neon sampler pack. It's probably 50/50 mica mix/pigment.
Next rainbow I think I'm going to straight up colour with neons to see how that turns out -- neons are fun! I'd also love to do a rainbow soap that's very muted pastels. Rainbows are beautiful!
UPDATE on the soap itself --> this morning it's looking a bit different, more... cohesive, if that makes sense. It looks a bit more translucent, like a fully gelled soap, so I think the gooey oily stuff has resorbed and this might turn into an okay soap. I'm going to try to post an updated picture later, maybe a before/after if there's a significant difference.