The Karaite Jews have it correct and Pharisaic Rabbinical Judaism has it wrong.
Shavout is always on a Sunday because of Leviticus 23:16, since that is the only way for the fiftieth day to fall on the morrow after the Sabbath.
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Yes, I believe after Jesus was resurrected the rabbis changed the omer counting from the day after the weekly Sabbath to "counting" from Nisan 16, which in fact requires no counting at all, Pentecost is always on Sivan 6. They did this to deny that Jesus fulfilled the wave offering as the firstfruits.
And you shall count for yourselves from the day after the Sabbath, from the day that you brought the sheaf of the wave offering, seven Sabbaths shall be completed. Count fifty days to the day after the seventh Sabbath, then you shall offer a new grain offering to the LORD. (Leviticus 23:15-16)
The word for completed is
tamiym which means complete or whole. A whole Sabbath is referring to a week, day one through day seven. This is done seven times and the next day is Pentecost.
Luke says in Acts, "When the Day of Pentecost had fully come..." (Acts 2:1).
The term "fully come" is the Greek
symplēroō which means to be fulfilled. So the days had to be counted to know when they were fulfilled, meaning the day was not automatically Sivan 6.
Jesus was resurrected on the first day of the "week" which began the count toward Pentecost.
Now on the first day of the week, very early in the morning, they, and certain other women with them, came to the tomb bringing the spices which they had prepared. (Luke 24:1)
The word "week" is
sabbaton, which is plural because Jesus was resurrected on the first days of the weeks, the seven weeks leading to Pentecost.
sabbaton - Of Hebrew origin [H7676]; the Sabbath (that is, Shabbath), or day of weekly repose from secular avocations (also the observance or institution itself); by extension a se'nnight, that is, the interval between two Sabbaths; likewise the plural in all the above applications: - sabbath (day), week.
In the OT Pentecost is referred to as the Feast of Weeks.
And you shall observe the Feast of Weeks, of the firstfruits of wheat harvest and the Feast of Ingathering at the year’s end.
(Exodus 34:22)
The word for "weeks" is
shabuwa`which refers to a set of seven, in this case a set of seven weeks which is a set of seven days.