As historical researchers know (and the Jewish Encyclopedia), the Jews use to observe the Sabbaths according to the Lunar weeks and not according the solar weeks. This means there is 49 weeks of rotation in a year. And they observed these weeks from Sabbath to Sabbath. These courses observed their courses unbroken in order. This is not to say they didn't observe at some points as certainly they couldn't but when they resumed they resumed in the order they would be at - had the rotation always been in place. This would be the same with Sabbaticals and Jubilees. The Day of Atonement would be 9/30 in 4 B.C.E having started the evening before.
It is important to note that the Jews, observed the New Moons, their first day of the week was the 2nd Day of the Month when the Crescent would be observed. Therefore, the Sabbaths were the 8th, 15th, 22nd, and the 29th of the month. You won't find the weekly sabbaths on other days. These corresponded with the phases of the moon.
Therefore, knowing this you will see that a Sabbath can fall on any day of the solar week.
Also, knowing this you will realize that the Feasts of Unleavened Bread is ALWAYS a High Sabbath as it always falls on the Weekly Sabbath day.
Now knowing this you can count the sabbaths correctly to Pentecost because it is NOT 50 consecutive days. But the count begins on the 16th day of the first Lunar Month and is counted by Weekly Sabbaths onto 7 weeks and then 1 days is added. This will always bring you to the 9th day of the 3rd month. You may wonder then why we count it? Because we are being taught to count down the Jubilees. Remember, that man only gets 120 Jubilees (Genesis 6:3).
Hippolytus shows this in his commentary on the Psalms.
“Let us inquire, further, why there are one hundred and fifty psalms. That the number fifty is sacred, is manifest from the days of the celebrated festival of Pentecost, which indicates release from labors, and (the possession of) joy. For which reason neither fasting nor bending the knee is decreed for those days. For this is a symbol of the great assembly that is reserved for future times. Of which times there was a shadow in the land of Israel in the year called among the Hebrews “Jobel” (Jubilee) which is the fiftieth year in number, and brings with it liberty for the slave, and release from debt, and the like. …Thus, then, it was also meet that the hymns to God on account of the destruction of enemies, and in thanksgiving for the goodness of God, should contain not simply one set of fifty, but three such, for the name of Father, and Son, and Holy Spirit. The number fifty, moreover, contains seven sevens, or a Sabbath of Sabbaths; and also over and above these full Sabbaths, a new beginning, in the eight, of a really new rest that remains above the Sabbaths.”
So now, you can see that the Pentecost shows us to count down Jubilees. But how many days you may say it is from Pentecost to the Day of Atonement when the Jubilee is sounded? - 120.
These are lunar months and each has on average 29.5 days. So from the 9th day of the 3rd month to the end of the month we have 21 days. For months 4-6 we have (29.5 * 3 = 88.5 days) and for the 7th month till the 10 day (Day of Atonement) we have 10.5 days.
Do the math 21 + 88.5 + 10.5 = 120 days.
Now the 60th Jubilee was when the Temple of Solomon was dedicated. If we go from that 9th day of the 3rd month and go 60 days we land on the 10th of the 5th month. That is the day in which the Temple was destroyed.
All these mysteries are for the wise to understand.
Dan_12:10 Many shall be purified, and made white, and tried; but the wicked shall do wickedly: and none of the wicked shall understand; but the wise shall understand.