One of the reasons bright red stands out in gardens is that it's the highest contrast to green. Pure red flowers jump out at you even from a great distance, sometimes making a garden seem smaller because your eye makes the leap from near to far in a nanosecond. Blue has the opposite effect, as your eye has to spend some time trying to see it in the distance. Conventional wisdom had it that sticking white flowers in the midst of clashing colors tones them down, helping out with the disharmony. In fact, white often does the opposite by calling attention to itself.
Bright white can also make other colors look dull or muddy.
Landscape architect Richard Arentz suggests looking carefully at individual flowers or leaves for clues about what combinations might work. Such signs of harmony are telling you that you might want to replicate the same color combination in your garden. You can do the same thing with leaves. In hostas alone there are multiple possibilities for echoes. If you want to do a more serious study of color, the most useful device I've found is called Rainbow Color Selector, a wheel that points the user to contrasts and felicitous blends.