The complimentary color scheme uses two colors directly opposite each other on the color wheel. The two colors are harmonious but create a lot of contrast when used in interiors.
If you choose for example blue as your base color then orange is the compliment. To reduce the intense contrast, use shades and tints of the complimentary color to create a more relaxing room.
Here is a sofa with a neutral base that demonstrates the use of tints and shades.
Use the complimentary color scheme to create contrast and excited in a room with accessories. Use tints on larger pieces to create a softer overall feel.