The first day of the month is still 'Monday', or 'Wednesday' in English, no matter what 'day of the month' it is, correct? Well it is exactly the same in the Jewish lunar calendar - this might be the 'tenth of Cheshvan' but it is still 'Thursday' (or 'fifth day' in the Hebrew naming of weekdays). It's the fifth day (for instance) of the WEEK, no matter what the DATE may be.

The only day with a 'real name' is Shabbat. Every other day is named in order leading up to Shabbat - First Day, Second Day, etc. Weeks pay little attention to monthly dates.

The Jewish calendar is lunar-solar: each month begins on a new moon, but we add 'leap days' (actually, an entire MONTH) regularly in order to keep the DATED holy days in their proper seasons - thus Passover is always in Spring (and always on the 14th day of the month of Nisan) and the High Holy Days are always in the autumn.

You could think of it this way also - weeks are continuously revolving, but months begin and end and start the 'clock' over.

The leap month is inserted prior to Nisan, in the spring, approximately every third year (nine times in 17 years), pushing the dates back 29-30 days - a purely lunar calendar falls behind the solar (seasonal) year 11 days annually.

What??

I don't like to be confrontational, but yes indeed the Jewish calendar definitely IS a 'lunar calendar'. Every month begins on the new moon. The 14th/15th of each month is the full moon. Each month is 29 or 30 days long....the cycle of the moon.

It's a lunar calendar.

However, it isn't a 'purely' lunar calendar.

The seasons of the year are driven by the solar cycle - the time it takes the earth to move around the sun. The Jewish LUNAR calendar adds a month seven times in nineteen years, on a regular cyclel, to keep the months (which are lunar) in their appropriate SEASONS - spring months like Nisan in the spring, Fall months like Tishri in the fall.

Since a 'lunar year' falls behind a solar year by 11 days (about) annually, we add a thirty day month every two to three years (it varies through the nineteen year cycle), in between winter and spring - it's called 'Adar II' because it comes after Adar.

Our new year begins in the fall with the first of the month of Tishri, which is the holiday of Rosh Hashana.

Days of the week are irrelevant to the moon or to the sun - they are independent. The first day of the month may fall on any day, just as 'June 1st' can be any day of the week. We don't start the WEEKS over at the start of a month. If it's Tuesday, it's Tuesday still, no matter what the month's date might be.