My name is Janice, and I'm a Purple-holic.
Purple is a mix of Red and Blue, but not every mix makes a lovely vibrant purple - some mixes of red and blue make a nasty brown sludge. The secret is in the red and blue you choose. There are many different red paints and many different blues. To get purple you need to choose the right red and the right blue.
There is a whole spectrum of reds - crimson, indian, cherry etc, from reds that are closer to orange (hot reds) to reds that are closer to purple (cool reds). The same is true of blues - blues that tend towards green ( cool blues) and blues that tend towards purple ( warm blues).
To mix a great purple you need a warm blue and a cool red. The great thing is that once you get the right pair of colours, you have a whole new spectrum of colours depending on how much of each colour you put in the mix. You can also add white to make paler tones or black for darker shades.
Try it with your favourite colours - I made up a swatch for each colour combination so when ever I want a particular hue, I know exactly what to mix.