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A rainbow spans a continuous spectrum of colours - there are no "bands." The apparent discreteness is an artefact of the photopigments in the human eye and of the neural processing of our photoreceptor outputs in the brain. Because the peak response of human colour receptors varies from person to person, different individuals will see slightly different colours, and persons with colour blindness will see a smaller set of colours. However the seven colours listed below are thought to be representative of how humans everywhere, with normal colour vision, see the rainbow. The final colour in the rainbow is violet, not purple.
Newton originally (1672) named only five primary colours: red, yellow, green, blue and violet. Later he included orange and indigo, giving giving seven colours by analogy to the number of notes in a musical scale.