October (Roman month) did not number days of a month sequentially from the 1st through the last day. Instead, they counted back from the three fixed points of the month: the Nones (5th or 7th), the Ides (13th or 15th), and the Kalends (1st) of the following month. The Nones of October was the 7th, and the Ides was the 15th. The last day of October was the "pridie Kalendas Novembris," "day before the Kalends of November". Roman counting was inclusive; October 9 was "ante diem VII Idūs Octobris", "the 7th day before the Ides of October," usually abbreviated "a.d. VII Id. Oct."
Month on the initial approximation that 2 lunations last 59 days: a 30-day full month followed by a 29-day hollow month — but this is only roughly accurate, and eventually needs correction by using larger cycles, or the equivalent of leap days. Additionally, the synodic month does not fit easily into the year, which makes accurate, rule-based lunisolar calendars complicated. The most common solution to this problem is the Metonic cycle, which takes advantage of the fact that 235 lunations are approximately 19 tropical years (which add up to not quite 6940 days). However, a Metonic calendar will drift against the