'half-step' originates from the combination of 'half,' meaning 'one of two equal parts,' and 'step,' meaning 'a movement made by lifting the foot and setting it down in a new position.'

'Half-step' evolved from the Old English 'healf' and 'stæpe,' eventually becoming the modern English word 'half-step.'

Initially, it referred to a small movement, but over time it evolved to include the musical interval meaning.