There are just as many whites as there are reds or greens.
Choose whites with the same care. For cool colors, choose a cool white from Vicente Wolf's Color Diaries to add crisp contrast. For warm colors, choose a warm white to make it less severe.
Vicente Wolf
Designer
As a day moves from morning to night, white can shift from bright and cool to softer and warmer.
Inspired by Lisbon
Cool White Colors
The artistic cobblestones of Lisbon are made from architectural rubble after the quake of 1775. It illustrates how whites should always be intentional. Don't use white paint color as a default because you can't choose a color. It will look unfinished. White paint colors can be elegant, art-gallery, complex and relaxed.
See White Paint Colors