"I want purple buttercream." Those are words I dread hearing, not because I don't like the color purple, it's a perfectly fine color, it's just that I dread making purple buttercream. It's such a finicky color and I can never seem to get a "good" purple using just violet or purple gel colors. And, then there's the issue of it fading (you can find out more about that here).
So, what to do to get a pretty, perfectly purple buttercream? Something I've found that helps is using milk (see the fading issue above) rather than water and starting with a mix of blue and PINK gel colors. Yes, we were taught in school that blue and red make purple, but in this case the red tends to be to dark giving you a gray-ish tone. The pink keeps it brighter, giving you a better purple! Once you have a nice purple using the mix of blue and pink, you can add additional purple or violet gel to help deepen the color if necessary.
So, remember when it comes to buttercream - blue and pink make purple!