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In this system, the new day begins at sunset. When the reference of a birth was, for example, "two hours into the day", this meant two hours after sunset. This means a birth date of August 12 would, by modern reckoning, be considered to be August 11.
The year also began not on January 1 but rather on March 25, which is why some dates have an apparent one-year discrepancy. For example, a birth date of March 10, 1552 in Florentine reckoning translates to March 10, 1553 in modern reckoning. This was not unusual; the French year began on Easter day until 1564, the Venetian year on March 1 until 1522, and the English year on March 25 until 1752 (see beginning of the year).
Italy was one of the few nations to immediately convert from the Julian calendar to the Gregorian: October 4, 1582 was followed by October 15, 1582 (Gregorian).