Particularly, these types of colours:
|c60 m60 y0 k0; c60 m80 y0 k0; c50 m90 y0 k0; c40 m100 y0 k0|
Purple is actually a tricky colour to show on screen.
For paint, I would consider dioxazine violet to be a very typical purple (mauve too, to a certain extent).
However, in ancient times, purple was a bit different.
It could vary too, but was closer to this:
|r102 g2 b60 (approx c52 m99 y81 k7)|
I've just added this to my palette. I have others that would work well too - but only the last one was in my original 'purple' chart:
|c22 m100 y40 k46; c15 m100 y40 k35; c20 m100 y30 k15|