The compound "stair-step" is a modern English tautological construction, where two near-synonyms are combined for emphasis or to create a specific technical nuance. Both components, "stair" and "step," descend from a common Proto-Indo-European root \stebh-, meaning "to post, stem, or place firmly on." This root gave rise to concepts of support and placing the foot. In Old English, the meanings diverged slightly: "stair" evolved to denote a connected series (a flight), while "step" referred to the single act or unit of movement. The compound, first attested in the 19th century, logically fuses these related concepts to vividly describe anything—from architectural features to data patterns on a graph—that ascends or descends in a discrete, incremental manner reminiscent of a staircase. It is a transparent metaphor built from two ancient, stable Germanic words.

Structure: stair (a step in a series) + step (a single movement made by lifting the foot) - stair: From Old English stǣger (a flight of steps, staircase), from Proto-Germanic staigri- (climbing, ascent). Functions as the primary noun, indicating the series or flight. - step: From Old English stæpe, stepe, steppan (to step), from Proto-Germanic stap-. Functions as a reinforcing noun, emphasizing the individual unit within the series.