Different lunar calendars start the month at a different part of the moon’s cycle, and as long as it is consistent it doesn’t really matter. It is generally believed that in the Bible, the Israelites started the new day at sunset, while the new month in the Hebrew calendar is said to have started when the new crescent moon was
visible at sunset.
The length of the lunar cycle from one new moon to the next is 29.530589 days, so months would normally alternate between 29 and 30 days, although over about 3 years one extra day will slip in.
On that basis, an ordinary 12-month year will have only 354 days, 11 days shorter than our common year. If such a calendar is used, the seasons will move later in the year
by 11 days each year. After 3 years, seasons will have moved by a month, and after 9 years, the calendar would be saying it was time for spring to start when summer had already started. After only 17 years, the calendar would suggest that it was summer when it was actually the middle of winter.
This simply cannot work and so in the Hebrew lunar calendar still used today, mostly for religious purposes
(https://en.wikipedia.org/wiki/Hebrew_calendar), a “leap month” is added every two or three years to bring the calendar and the seasons together again. There is no mention of this in the Bible, but it is hard to imagine any other method if months are to be based on lunar cycles.
When Israel was about to leave Egypt, God instructed them that the Passover was to occur in the first month of the year (Exodus 12:2) and that the Passover was
to be followed by the feast of first fruits where the new fruit of spring was to be offered to God (Leviticus 23:4-21). In later times, these two feasts were linked in a fixed way and the name “the Day of Pentecost”, meaning “the 50th day” was used.
Why does this matter? Well, to keep the Passover in spring, adjustment was necessary, and adding extra months seems to be the only possible answer. It is suggested that an extra
month was added at the end of the year where necessary (i.e. two twelfth months - Adar I and Adar II), based either on weather conditions or on a repeated cycle of years.
So where does all this fit into the Bible?
Let’s start by saying what we do not find in the Bible:
- No thirteenth month is mentioned anywhere.
- No months are mentioned with 58-60 days.
- No mention is made of repeating a month while still calling it by the same name.
What we do find in the Bible are little items of evidence which are interesting, but don’t allow us to draw many conclusions.
The largest day number in a
month mentioned in the Bible is the 27th day of a month (Genesis 8:14, 2 Kings 25:27). This fits with the idea of 29/30 day months.
In some places, when giving a date, Ezekiel specifies the number of the year and day but not the month (Ezekiel 26:1; 32:17 (Note that the ESV adds “the twelfth month” in the latter passage, along with a note that the Hebrew lacks these words)). Could these refer to a leap or intercalary month?
There is no way of knowing.