While the Karaites are not the true inheritors of the Boethusian tradition, a famous Karaite has written a good article on the subject. I will paste it here and provide a source:
The Pharisees argued that Shavuot is to be counted from the first day
of the Feast of Unleavened Bread, which they designated a “Sabbath.”
According to the Pharisees, “morrow of the Sabbath” means the “morrow
of the 1st day of Unleavened Bread.” The ancient Pharisees and their
modern day successor the Orthodox rabbis begin the 50-day count to
Shavuot on the second day of Unleavened Bread, which is always the
16th day of the First Hebrew Month. As a result, the Pharisee Shavuot
always fell out in ancient times from the 5th to the 7th day of the
Third Hebrew Month (Sivan). After the destruction of the Temple, the
Pharisees became the predominant surviving faction among the Jewish
leadership and their interpretation is followed by most Jews until
this very day. In 359 CE, the Pharisee leader Hillel II established a
pre-calculated calendar and ever since the Pharisee Shavuot has always
been observed on the 6th of Sivan.
The Essenes who wrote the Dead Sea Scrolls began the 50-day count to
Shavuot on a different Sabbath from the Pharisees. In their reckoning,
the Omer offering was to be brought on the morrow of the weekly
Sabbath, in modern terms: “Sunday.” The Essenes began their count on
the Sunday after the seven-days of the Feast of Unleavened Bread. As a
result, they always began their count on the 26th day of the First
Hebrew Month. The Essenes had a 364-day solar calendar, which began
every year on a Wednesday and had fixed lengths for each month. Based
on the Essene calendar, Shavuot always fell out on the 15th day of the
Third Hebrew Month. The Essenes are presumed to have been wiped out
when the Romans invaded Judea in 66-74 CE and only their documents
survive today.
The third faction, the Sadducees, agreed with the Essenes that Shavuot
must be counted from a weekly Sabbath, but disagreed as to which one.
The Sadducees believed the 50-day count must begin on the weekly
Sabbath that falls out during the seven-days of the Feast of
Unleavened Bread. According to their reckoning, the counting towards
Shavuot could begin anywhere from the 15th to the 21st day of the
month, depending on what day of the week the Feast of Unleavened Bread
began. If Unleavened Bread began on a Sunday, the count would begin on
the 15th day of the month. If Unleavened Bread began on a Saturday,
the count would begin on the 16th day of the month, and so on. Based
on this counting, Shavuot could fall out from the 4th to the 12th of
the Third Hebrew Month. Karaite Jews have accepted the Sadducee
reckoning as the only one to be consistent with the plain meaning of
the biblical text.
The bigger problem with the Pharisee interpretation of “Sabbath” is
when it comes to the end of the 50-day count. Leviticus 23:16 says,
“Until the morrow of the seventh Sabbath shall you count fifty days.”
The 1st day day of the Feast of Unleavened Bread could theoretically
be called “Sabbath,” even though the Hebrew Bible never uses this
terminology. However, the 49th day of the Pharisee counting is not a
Sabbath, unless it happens to fall out on a weekly Sabbath - the 7th
day of the week. Consequently, the Pharisee Shavuot is rarely the
“morrow of the Seventh Sabbath” as required by Leviticus 23:16. About
once every seven years, the Pharisee Shavuot does happen to fall out
on the “morrow of the seventh Sabbath.” For example, in the year 2018
the Feast of Unleavened Bread begins in the Pharisee reckoning at
sunset on Friday March 30. In that year, the Pharisee counting begins
on Sunday April 1, 2018 and ends 50 days later on the “morrow of the
seventh Sabbath,” Sunday May 20, 2018. However, this is the exception
to the rule. In most years, Shavuot according to the Pharisee
reckoning is actually the morrow of seventh Monday, the morrow of
seventh Tuesday, etc. The only way for Shavuot to consistently be the
“morrow of the seventh Sabbath” is for the counting to begin on the
morrow of a weekly Sabbath, in modern terms on a “Sunday.” Of course,
Scripture did not call this a “Sunday,” because that term did not
exist in ancient Hebrew. The ancient Hebrew term for Sunday morning is
“morrow of the Sabbath.”
An important verse that confirms the timing of Shavuot appears in the
Book of Joshua:
“And they ate of the produce of the land on the morrow of the Passover, unleavened and parched grain on this very day. And the Manna
ceased on the morrow when they ate of the produce of the land...”
-Joshua 5:11
This verse describes the events surrounding the cessation of the
Manna, shortly after the Children of Israel entered the Land of
Canaan. To understand this the significance of this verse, we must go
back to the Book of the Leviticus, where the Israelites were forbidden
to eat of the new crops of the Land of Israel until the day of the
Omer offering:
"And bread and parched grain and ripe grain you shall not eat until this very day, until you bring the sacrifice of your God; it
shall be an eternal statute for your generations in all your
habitations." Leviticus 23:14
When Joshua 5:11 describes the eating of “unleavened bread and parched
grain... on this very day" it is using almost the precise wording of
Leviticus 23:14 “and bread and parched grain... you will not eat until
this very day.” The new produce of the land was forbidden until the
Omer offering was brought. Joshua 5:11 is saying that when the
Israelites entered the Land for the first time, they observed this
commandment and waited until the terms of Leviticus 23:14 were
fulfilled. In other words, they waited for the Omer offering before
eating the grain of Israel. This has been widely recognized by Jewish
Bible commentators throughout history, such as the 11th Century rabbi
Rashi who explains on Joshua 5:11, “morrow of the Passover is the day
of the waving of the omer.”
Joshua 5:11 is saying that the first Omer offering in the Land of
Israel was brought on the “morrow of the Passover.” Immediately after
this, the Children of Israel were permitted to eat of the new crops of
the Land. For the first time, the Israelites pulled out their sickles
and ate of the good bounty of their new homeland.
To understand the phrase “morrow of the Passover” we need to define
two terms: “morrow” and “Passover.” The Hebrew word for “morrow” is
mi-mocharat which refers to “the morning after.” In the phrase “morrow
of the Sabbath” it describes Sunday morning, the morning after the
24-hour Sabbath.
Today we commonly refer to the Feast of Unleavened Bread as
“Passover.” However, in the Hebrew Bible, the term “Passover” (Pesach)
always refers to the Pascal sacrifice. The “morrow of the Passover” is
the morning after the Passover sacrifice. The sacrifice was
slaughtered at twilight at the end of the 14th day of the First Hebrew
Month (Nissan) and eaten on the evening that began the 15th day of the
First Hebrew Month (see Exodus 12:18; Deuteronomy 16:4). The morrow of
the Passover is therefore the morning of the 15th day of the First
Hebrew Month.
Confirmation of the meaning of the phrase “morrow of the Passover” can
be found in a verse in the Book of Numbers:
“And they traveled from Ramesses in the first month on the fifteenth of the month; on the morrow of the Passover the Children of
Israel went out with a high hand in the eyes of all Egypt.” - Numbers
33:3
This verse describes the day of the Exodus from Egypt as both the 15th
of the First Hebrew Month and as the “morrow of the Passover.”
What all this means is that the first Omer offering in Israel took
place on the 15th day of the First Hebrew Month. The first year that
the Israelites entered Canaan, the 14th of the First Hebrew Month must
have fallen out on a Sabbath so that the 15th of that month was a
Sunday. In that year, the “morrow of the Passover” happened to also be
the “morrow of the Sabbath,” what we call “Sunday morning.” This
proves the Pharisee interpretation of Leviticus 23:15 to be wrong.
According to the Pharisees, the Omer offering could only be brought on
the morning of the 16th of the First Hebrew Month, but in the year
that the Israelites entered Canaan, they brought the sacrifice one day
earlier.
The great 12th Century rabbinical Bible commentator Ibn Ezra mentions
a “Roman sage” who brought Joshua 5:11 as proof for the Pharisee
interpretation. According to this Roman rabbi, Joshua 5:11 is no less
than the silver bullet, the irrefutable proof for the Pharisee
position. This Roman rabbi argued that since Passover begins on the
15th of the First Hebrew Month (Nissan), the “morrow of the Passover”
must be the 16th. This is exactly when the Pharisees believe the Omer
offering is supposed to be brought, on the 16th of the First Hebrew
Month. If the Israelites brought the Omer on the 16th day of the First
Hebrew Month in the year they entered the Land of Israel, argues the
Roman rabbi, it proves that the Pharisees are correct in beginning the
50-day count to Shavuot on the 16th.
According to Ibn Ezra, bringing up Joshua 5:11 was a disaster for the
Pharisee position:
“[The Roman Rabbi] did not know that it cost him his life, for the Passover is on the fourteenth and its morrow is the fifteenth, and so
it is written, “And they traveled from Ramesses in the first month,
etc.” (Numbers 33:3). Eating parched grain is forbidden until the
waving of the Omer.”
Desperate to salvage the situation, Ibn Ezra proposes a novel
re-interpretation of Joshua 5:11. Previous rabbis understood this
verse to describe the Israelites eating the new grain of the Land of
Israel, which only becomes permissible each year after the Omer
offering is brought (Leviticus 23:14). The time between harvest and
the Omer offering might be anywhere for a few hours to a couple of
weeks. During this interim period, the new grain must be stored and
only old grain may be eaten, that is, grain from a previous year’s
harvest. Since the Israelites were new in the Land of Israel, they did
not have any grain from previous years. They had been wandering in the
desert eating Manna for 40 years. As soon as they entered the Land,
they harvested the grain they found growing in the fields of Jericho.
They then waved the Omer, the first sheaf of the harvest, making all
their new harvest permissible to eat and began the 50-day count to
Shavuot.
From Ibn Ezra’s perspective, the Israelites did this one day too
early, on the morning of the 15th day of the First Hebrew Month.
According to the Pharisees, the Omer must always be brought on the
16th day of the First Hebrew Month. Ibn Ezra’s ingenious solution to
this embarrassing biblical fact of history is to add the word “old” to
Joshua 5:11. If the Israelites ate “old grain,” that is, grain
harvested in a previous year, then the verse has nothing to do with
the Omer offering or the 50-day count to Shavuot.
Ibn Ezra’s new interpretation was highly influential, more than most
people realize. When Christian scholars started translating the Bible
into English, they went to Jewish rabbis to learn the Hebrew language.
When it came to Joshua 5:11, the rabbis told the Christian translators
to add the word “old” to the verse. More precisely, they told them
that the word “grain,” in Hebrew avur, actually means “old grain.” As
a result, Ibn Ezra’s novel interpretation is reflected in the most
famous English translation of all time, the King James Version:
And they did eat of the old corn of the land on the morrow after the passover, unleavened cakes, and parched corn in the selfsame day.
Joshua 5:11 –King James Version
Most translations do not employ the Ibn Ezra translation trick of
adding the word “old.” This is true for both Christian and Jewish
translations. Here are a few examples:
“On the day after the passover, on that very day, they ate the produce of the land, unleavened cakes and parched grain.” New Revised
Standard Version
The day after the Passover, that very day, they ate some of the produce of the land: unleavened bread and roasted grain.” New
International Version
“And they did eat of the produce of the land on the morrow after the passover, unleavened cakes and parched corn, in the selfsame day.”
Jewish Publication Society 1917
“On the day after the passover offering, on that very day, they ate of the produce of the country, unleavened bread and parched
grain.” Jewish Publication Society 1985
“And they ate of the grain of the land on the morrow of the Passover, unleavened cakes and parched grain on this very day.”
Judaica Press
These translations were made by people who read Hebrew and they knew
that the word “old” was simply not there. The Christian translators of
the King James Version, on the other hand, did not know this and took
someone else’s word for it.
Ibn Ezra himself must have known that adding “old” to the verse was
not the correct linguistic interpretation. In his introduction to his
commentary on the Torah, Ibn Ezra declares that the rules of language
and grammar must be bent to fit rabbinical interpretation when it
affects practical religious observance. Adding the word “old” to
Joshua 5:11 is a clear example of bending the rules of the language.
Ibn Ezra reveals his true understanding when he points out in response
to the Roman rabbi, “Eating parched grain is forbidden until the
waving of the Omer.” He only mentions the “parched grain” from Joshua
5:11 and not the “unleavened bread” because he knows it disproves the
very thing the Pharisees wanted to prove.
“Parched grain,” in Hebrew kali, refers to nearly ripe grain that is
still slightly moist. The farmers would harvest this moist grain early
and parch it in fire to make it crunchy and delicious. Parched grain
could only come from a freshly harvested crop, not from old grain!
Joshua 5:11 says the Israelites ate “parched grain” on the morrow of
the Passover, on the morning of the 15th day of the First Hebrew
Month. The “unleavened bread” could theoretically have come from the
old grain, as Ibn Ezra suggested, but the parched grain had to be new
grain. Year-old moist grain would go bad, so parched grain could only
be “new” grain from that year’s harvest. This new crop would be
forbidden to eat until the waving of the Omer, which took place on the
“morrow of the Passover,” which Ibn Ezra knew from Numbers 33:3 was
the morning of the 15th day of the month. That first year in the Land
of Israel, the Israelites ate the new grain and began the 50-day count
to Shavuot on the 15th of the First Hebrew Month. This was one day too
early for the rabbinical reckoning, which is why Ibn Ezra says that
bringing Joshua 5:11 into the discussion of the timing of Shavuot cost
the Roman rabbi his life - figuratively speaking, of course.
One technical point to consider is that the word “morrow” is the
operative term in the phrase the “morrow of the Sabbath.” Joshua 5:11
makes it clear that the “morrow” has to be during the seven days of
the Feast of Unleavened Bread. The Sabbath itself might actually
precede these seven days, as it did that first year the Israelites
entered the Land of Israel.
In ancient times, the Pharisee Shavuot would coincide with the
Biblical Shavuot about once every seven years. This would happen
whenever the First Hebrew Month began with the sighting of the new
moon on a Friday night. In years such as these, the 16th day of the
month would be both the second day of the Feast of Unleavened Bread
and the morrow of the weekly Shabbat. The modern rabbinical calendar
established by Hillel II in 359 CE calculates the beginning of the
month using the dark moon, making this a less common scenario.