Prior to yesterday's painting workshop in Albany, I did two sample pieces of the painting I was to use for my demonstration reference.
The first was done using burnt sienna as my "red", yellow ochre as my "yellow" and French ultramarine as my "blue".
The second was done using cadmium scarlet as my "red", cadmium yellow deep as my "yellow" and French ultramarine, again, as my "blue".
The third was my demonstration piece and was done using permanent crimson as my "red", cadmium yellow deep as my "yellow" and French ultramarine as my "blue".
The results are shown below.
The first painting, using earth colours for the red and yellow, has a strong tonal feel to it where the colour is barely relevant, while the third painting, using a cool red to make saturated shadows, has a richer colourist feel to it. One is quietly cool while the other feels like a warm summer's morning.
The centre painting has muted shadows resulting from the combination of a warm, "orangey", scarlet with the purply blue, but shows wonderfully warm highlights in the dune shrubbery and in the sand in the immediate foreground. In fact, until I painted those highlighted areas, the second painting differed very little from the first and it took some effort to get a bit of colour into the foreground shadow area.
I like them all though each one carries a different feeling. Ultimately, were I to do the same scene as a full studio piece, I would likely use a combination of all the colours listed so that my shadow areas are as rich as they can be, without compromising the highlight areas and vice versa. Cadmium scarlet is a rich, warm red and makes very bright oranges when mixed with a similarly warm yellow. Permanent crimson, on the other hand, is a cool, bluish red and makes wonderfully saturated purple shadows when mixed with a reddish blue like ultramarine. Earth colours like burnt sienna and yellow ochre will always make muted (greyed, desaturated) colours in any mixes they particpate in.
Using a three-colour palette is a great way to do quick paintings with little fuss. You can either choose three random colours from your reds, yellows and blues and see what results you get, or choose the three colours that will give you the most desirable result in a selected area.