What does the High Sabbath have to do with defining the true calendar of Scripture?

Answer: There are two High Sabbaths which occur every year.  This is when an appointed Feast Sabbath commences on a weekly seventh-day Sabbath, such as in the case of the Feast of Unleavened Bread in the spring and on the Feast of Tabernacles in the fall.  Counting from the New Moon both feasts begin on the 15^th and end on the 21^st day.  Because the Feast of Weeks (Pentecost) is not a fixed date, it will sometimes also coincide with a weekly Sabbath.

And on the fifteenth day of the same month is the Feast of Unleavened Bread to Yahuwah; seven days you must eat unleavened bread. In the first day ye shall have an holy convocation: ye shall do no servile work therein. But ye shall offer an offering made by fire unto Yahuwah seven days: in the seventh day is an holy convocation: ye shall do no servile work therein. (Leviticus 23:6-8)  

NOTE: Leviticus 23:8 states that the 7th day of the feast is also a holy convocation (which falls on the 6th day of the week since it started on the 15th, a High Sabbath).  This presents back to back Sabbaths on the 21st and 22nd days of the first month.

Speak unto the children of Israel, saying, the fifteenth day of this seventh month shall be the feast of tabernacles for seven days unto Yahuwah.  (Leviticus 23:34)

Both festivals always begin on the seventh-day Sabbath and end on the sixth day of the week, so there is no variation when they begin or end.  Contrary to popular belief it is clearly stated in Leviticus 23:34 that the Feast of Tabernacles is a seven-day feast and not an eight-day feast. Yahuwah in His wisdom makes it plain by stating in Lev. 23:36 the following eighth day is to be a holy convocation. We find in Leviticus 23:2, 3 that the seventh-day Sabbath is this holy convocation.  The fact that the eighth-day which follows the seven day Feast of Tabernacles is a holy convocation does not automatically make the Feast of Tabernacles an eight-day feast, but rather it is making a calendation distinction.  The first day of the Feast is a seventh-day Sabbath as well as the day following the seven-day Feast.  However, what it accomplishes is that it acts as Yahuwah’s checks and balances to show that the holy seventh-day Sabbaths continue intact to be legislated by the moon.  This is because the seventh-day Sabbath is the day after the seven-day Feast of Tabernacles each and every year and not just once in a while. This cannot be accomplished using the Gregorian calendar.