Generally one of the colors has a little touch of its adjacent harmonizing colors in it (i.e. with the Blue/Magenta pair, Magenta is made up of Red and Blue). The term harmonize sounds nice, pleasant. But some harmonizing colors may appear washed out (yellow/green) or too dark and similar (blue/purple) to work well together unless a third harmonizing (or a contrasting) color is added to the mix. Using a tint or shade of one of a pair or trio of harmonizing colors can improve the way they work together.
Although harmonizing and complementary sound like they should be similar, they are not. Note the spelling of complementary (not complimentary). Complementary colors have a greater degree of separation from one another on the color wheel (opposite sides) than harmonizing colors.
