‘Primary’ colours
‘Primary’ colours are commonly defined as a limited set of colours (most often three), which when combined using various mixing processes, can produce all other colours. However, this definition and indeed the underlying concept of ‘primaries’ is an oversimplification of how colour behaves, and has resulted in a number of unfortunate misconceptions and points of confusion about colour. It is in fact physically impossible to mix all colours from a limited set of three - in any medium, or via any mixing process - even if black and white are added, or cyan, magenta and yellow colorants are used.
The well known ‘primary’ sets for coloured media - cyan, magenta and yellow for colorants like inks or paints, and red, green and blue for sources of light - form the optimal set of three, and mix to the widest range of colours for the subtractive and additive mixing processes respectively. Red, yellow and blue are the historical set of primaries for painters, and mix to a more limited range of colours compared to cyan, magenta and yellow. For painters, there is no practical reason to limit a set of paints to three. However in commercial applications, there may be financial considerations for using a limited set of ‘primaries’.
In some cases, it may be possible to mix all hues from a set of three, but not all colours. The physical act of mixing coloured media diminishes the vividness or chroma of the mixed colour.
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See the expanded discussion on Not all colours from primaries.