Harmonious elements in a painting are those that are similar or related in some way. They are vital because they create interest in those areas which may be devoid of activity whilst at the same time act in unifying the composition.. Harmonious shapes may be ellipses (ovals), circles, square, rectangles etc. and harmonious sizes ate those close together.
Straight and slightly curved lines are in harmony as well as close tonal values.
Unlike contrast, harmony involves subtle, gentle changes in order to achieve added interest. One of the best ways to achieve harmony is to restrict your colour palette, by mixing the tones that you need from your basic colour range to create an overall unified effect. (cf Colour Harmony).