Fixed midday prayer is one of the points where the great traditions visibly rhyme. The Christian Sext, the Jewish Mincha in its earliest permissible window, and the Islamic Dhuhr all set worship at or after the sun's zenith, each with its own reasoning, and the family resemblance is no accident: all descend from a world that told time by the sun and understood the day's turning point as a religious moment.
Within Christianity the hour's fortunes have tracked the office's general history. The medieval West prayed Sext in choir and chapter; the breviary made it a few private minutes; and the 1971 Liturgy of the Hours, facing the reality of modern schedules, created a single Midday Prayer that may be prayed as Terce, Sext or None according to the actual time, keeping the threefold division for communities that maintain it. The Byzantine Horologion keeps the Sixth Hour with its psalms and its troparion of the crucifixion, prayed in monasteries daily and in parishes chiefly in Lent, when the hours are read publicly.
The Anglican tradition, having folded the little hours into Morning and Evening Prayer at the Reformation, recovered a midday office in its modern books, and contemporary ecumenical communities, Taize most visibly, have made short midday prayer one of their signatures. The persistence is telling: of all the hours, midday is the one the working world can most nearly keep, a fact the tradition grasped eighteen centuries ago and modern rules of life keep rediscovering.