1. The ancient Hebrew 'calendar' (though there is no Hebrew equivalent of this term) divided the year (shana)—in a fashion similar to the Chinese—into 12 months (yerah, 'moons') of 29/30 days each. This left a difference of 11 days between the solar and the lunar year. The Hebrew calendar made up for this by intercalating an extra sixth or twelth year over a 19-year cycle.
The year begins in Mar/Apr and the names of the twelve months are (pre-exilic names in brackets):
1. Nisan (Abib) - Mar/Apr.
2. Iyyar (Ziv) - Apr/May.
3. Sivan - May/Jun.
4. Tammuz - Jun/Jul.
5. Ab - Jul/Aug.
6. Elul - Aug/Sept.
7. Tishri (Ethanim) - Sept/Oct.
8. Marchesvan (Bul) - Oct/Nov.
9. Chislev - Nov/Dec.
10. Tebeth - Dec/Jan.
11. Shebat - Jan/Feb.
12. Adar - Feb/Mar.
See what happens in an OT year ☰
2. In NT times the Julian calendar (named after Julius Caesar who adopted it from the Egyptians) would presumably have been followed though there are no incidences in the NT when a particular month was specified. The names of the months of the Julian calendar are essentially what we use today: January, February, etc. The Julian calendar faced the same problem of the extra days accumulated by the Hebrew lunar one since a solar year was actually not exactly 365 days. Since there is no intercalation in the Julian calendar, it had accumulated an extra 10 days by 1582. Reforms by Pope Gregory XIII—hence our calendar is called a Gregorian one—solved this problem by ordering that 4 October of that year should be followed by 15 October. It took many centuries before the solution was adopted universally, Russian and China among the last to do so (1919 and 1949 respectively).
To read about what this means for dating the birth of Jesus ☰
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