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British Library MS Harley 2332
DailyMedieval has already addressed one piece of the dating confusion: the shift from the Julian to Gregorian calendars, when correcting the calendar year to match the astronomical calendar required dropping 10 days from October of 1582 in Italy, Poland, Spain, and Portugal (other countries followed suit later).
Dates could be recorded in other ways that make life difficult for modern historians.
The calendar year began on 1 January, but for several centuries in England the civil and ecclesiastical year began on 25 March. (Four days after the spring equinox on 21 March was long enough for the naked eye to be certain that days were growing longer than nights.) So Chaucer could celebrate 1 January 1360 at home, but the Exchequer records would call it 1 January 1359; as far as the Exchequer was concerned, 1359 didn't end until 24 March.
Regnal years were the practice of starting a calendar with the coronation of the king. Henry VIII came to the throne on 22 August 1485. Therefore, events and records dated in "1 Henry VIII" took place from 22 August 1485 until 21 August 1486.
Things weren't always that simple, though. Events could be described in official documents by their relationship to known anniversaries, such as saints' feast days. "Five days after Michaelmas" (29 September) would be 4 November. Of course, one of the major ecclesiastical feast days around which events revolved was easter, but Easter was a movable date, and so altered each year.
These issues and more make translating dates found in medieval documents tricky.