An analogous color harmony is one that features colors that are similar. These are colors that are close to one another on the color wheel. The two most common analogous harmonies are warm colors (red, orange and yellow) and cool colors (blue, violet and green). However, a color harmony of red orange and violet would be analogous, as would one that is green, blue and yellow. Here is a painting by El Greco that features green and blue, two cool colors.
An analogous harmony would best correlate to music that featured similar timbres such as a string section or a brass section, as those families have very similar colors.