The compound adjective "ten-day" is a transparent formation from two native English roots of Germanic origin. The numeral "ten" descends from the Proto-Indo-European root déḱm̥t, a fundamental and stable numeral across many language families. The word "day" originates from a root meaning "to burn" or "be hot," reflecting the sunlit portion of the diurnal cycle. Combined in modern English using a hyphen, the morphemes retain their core meanings, creating a straightforward descriptive term for anything relating to a decade-long period, whether describing duration or frequency. The logic is purely arithmetic, specifying a quantity of the temporal unit.

Structure: ten (number) + day (unit of time) - ten: From Old English tēn, tīen, from Proto-Germanic tehun, from Proto-Indo-European déḱm̥t. Functions as a cardinal number. - day: From Old English dæg, from Proto-Germanic dagaz, from Proto-Indo-European dʰegʷʰ- ("to burn, be hot"). Functions as a noun denoting a 24-hour period.