I have spoken of all colours as of full intensity and purity, but we have to deal also with other conditions. All colours may be darkened by black, when _shades_ are produced; or reduced by white, when _tints_ are produced. Besides these alterations in intensity, a portion of one colour may be added to another. Thus, if a small portion of blue be mingled with red, the red becomes a crimson or blue-red; or if a small portion of yellow be added to the red, the latter becomes a scarlet or yellow-red. In like manner, when yellow is in excess in a green, we have a yellow-green; or when blue is in excess, a blue-green; and so with the other colours. Such alterations produce _hues_ of colour.
We now come to the subtleties of harmony. Thus, if we have a yellow-red or scarlet--a red with yellow in it--the green that will harmonise with it will be a blue-green; or if we have a blue-red or crimson--a red with blue in it--the green that will harmonise with it will be a yellow-green. This is obvious, for the following reasons:--Let us suppose a red represented by the equivalent number, five, with one part of blue added to it, thus causing it to be a blue-red or crimson. Were the red pure, there should be eleven parts of green as a complement to the five of red, of which green eight parts would be blue and three yellow; but the blue-red occurs in six parts, one of which is blue--there are, then, but seven parts of blue remaining in the equivalent quantity to combine with the three of yellow, one being already used; hence the green formed is a yellow-green, one of the equivalents of blue necessary to the formation of a true green being already in combination with the red, and thus absent from the green.
The same reasoning will apply to the scarlet-red and blue-green, and, indeed, to all similar cases; but to take the case of the crimson-red and yellow-green, as just given, and carry it a stage further, we might add two parts (out of the eight) of blue to the red, and make it more blue, and then form the complementary green of six parts of blue and three of yellow, and thus make it more yellow. Or we may go further still, and add to the red six of the eight parts of blue, when the admixture would appear as a red-purple rather than as a blue-red, in which case the complementary green--or, rather, green-yellow--would consist of two parts of blue and three of yellow. These facts are diagrammatically expressed in the following:--