> * A purple-inclined red (crimson) and an orange-inclined red (scarlet)

> * A green-inclined yellow (practically speaking, "spring green") and an orange-inclined yellow ("yellow")

> * A purple-inclined blue (ultramarine) and a green-inclined blue (cerulean)

> * White to make light tones (don't worry about black)

This is excellent advice for a painter, though I would not exclude black.

The six color you describe are, in essence, a warm/cool pairing of the three primaries. When I painted in color I used:

Cadmium red/alizarin crimson, lemon yellow/cadmium yellow, cobalt blue/Prussian blue