There are two fundamental systems in use to describe primary colours; Additive and Subtractive.
The first, Additive, is used to describe the three primaries where combinations of them will produce all the colours in the visible spectrum and where the three primary colours themselves, when mixed equally, will produce white light. This is the greatest hint of all as to where these colours are found - they are the colours of transmitted light. The primary colours are Red, Green and Blue (RGB) and they relate particularly to light, digital cameras and displays. This is illustrated in the figure below.
Subtractive colours are so called, because when the three primaries used in this system are mixed together in equal parts, they produce Black. A good way to remember this is that if you remove all light, then there is nothing left and "nothing" is typically associated with Black. In digital terms, Black has the value 0 and White is represented by 255.
Subtractive colours are Cyan, Magenta and Yellow (CMY), as used in printing, or Red, Yellow and Blue (RYB) which are used in painting and in art theory. In a later section of this part of TAOP, the colour wheel used will be that based on the painters primaries, RYB and their complementary opposites, which are green violet and orange. In printing, these colours are also referred to as CMYK, where K stands for black, or originally "Key Plate". The Key Plate, in printing, was that which was used to provide or enhance detail and contrast and was usually impressed in black ink
The way subtractive colours mix is shown in the illustration below.
The figures used above have both been obtained from Wikipedia and have been released into the public domain by their author.
Complementary and harmonious colours.
First of all a simple definition of primary colours, based on that given in the course text. Primary colours are those which cannot be further broken down into other colours.
I have already used the term "complementary", so probably best to describe here what is meant by this. Such colours are those which are located opposite to primaries in the colour wheel. So with the RYB model, green is complementary to red, violet to yellow and orange to blue. Where such colours appear in a photograph, they create maximum contrast (should I be using this word here as it could be misunderstood) and can create greatest impact.
Harmonious colours are those which are located alongside each other. Why so called? That is because there is some harmony between them; I've seen reference to such colours giving a sense of calm and peace, though this does not really equate with the way we see colours, with oranges and reds providing striking and vibrant images, warm looking, whereas blues and greens are cool and therefore frequently regarded as restful. Less saturated harmonious colours, regardless of whether they are "hot" or "cool" produce images which are restful.