Terce, Sext and None exist because the ancient Mediterranean day was already divided for everyone. Roman timekeeping split daylight into twelve hours and announced the third, sixth and ninth publicly; business, courts and markets ran on those bells, so prayer at those moments cost nothing to schedule and stamped the whole day with remembrance.
The Christian manuals of the third century made the divisions theological, attaching to each hour an event of the passion or of the church's birth, and the monastic movement then bound the custom into rule: Benedict prescribes the three little hours with their psalms and orders the community to break work for them, wherever its members happen to be labouring. The subsequent history of the little hours is a quiet negotiation with busyness. Cathedral clergy aggregated them; the breviary allowed them to be said privately in a few minutes; and the 1971 reform, recognising that few outside monasteries would pray all three, provided that one midday hour suffices for those not bound to the full cycle, with Terce, Sext and None kept distinct in communities that maintain them.
The Byzantine Horologion preserves all the little hours with their own psalms and troparia, prayed chiefly in monasteries and in Lent. The deeper legacy is the idea itself, that the working day should be interrupted for prayer at fixed points, an idea Islam's five daily prayers embody with comparable rigour and which returns in every modern rule of life that sets a midday pause: the little hours are the ancestral form of the sanctified workday.