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Colour theory is concerned with the psychological affect of colour choice. Colours can have an emotional impact that transcend the initial reaction. This can be helpful to know in design for campaigns, signs, interior design and in art for how for example a painting conveys its emotion through colour.
What is it?
Colour theory is how colours complement, contrast and relate to each other and how they have an impact on the viewer.
Why is it useful?
Everyone has a different perception of colour. However, in general colours are purported to have certain meanings and affect whether that is conditioned or somehow inherent. Colours effect mood, action, perception. They are perceived in the world in various forms, associated with things (e.g. blue for boy, pink for girl, red for danger). In fact colour is a product of the mind not out there in the world, so colour is a very psychological phenomena.
How do I use it?
Colours can be chosen based on the impact that is desired.