Opposite colors on the color wheel are the complementary colors: Reds complement is green; blues complement is orange and yellows complement is purple. They are also harmonious as they complement each other. Now, some other harmonious colors are the ones on the color wheel that are close together, such as: Red, red-orange and orange to carry it farther, you could add yellow-orange and yellow to those. You can select any that appeal to you and just go to either side and you have harmony.
