MiMachorat HaShabbat/2

MiMachorat HaShabbat

Exegetical Approaches

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Sunday

The word Shabbat refers to the seventh day of the week (שבת בראשית), and the Omer offering is always brought on the following day.  This position subdivides regarding to which Saturday the verses refer:

Within Chag HaMatzot

The Omer is sacrificed on the morrow of the first Saturday which falls within or immediately preceding the holiday of Chag HaMatzot.

Sources:Perhaps the BoethusiansMegillat Taanit, Scholion 8 NisanMishna Menachot 10:3Tosefta Rosh HaShanah 1:15Tosefta Menachot 10:23,¹ the SamaritansVayikra 23About Yefet b. Eli the Karaite, the KaraitesDaniel AlKumisi Vayikra 23:15-16Karaite opponents in R. Saadia Gaon Sefer HaHavchanahSalmon b. Yerucham Milchamot Hashem Shaar 10Yefet b. Eli Vayikra 23Levi b. Yefet Sefer Hamitzvot 2 p. 404Karaite opponents in the Kuzari 3:41

Connection to Chag MaMatzot – Since the verses regarding the Omer follow the discussion of Chag HaMatzot, all these commentators assume that the time marker "מִמׇּחֳרַת הַשַּׁבָּת" must relate to the previously mentioned holiday, and that there is chronological overlap between the two. However, they disagree regarding whether it is the Sunday of bringing the Omer or the Shabbat marked in the verse which must fall within the festival.

• Sunday – The Karaites assume that it is the Omer offering itself (the day which is "מִמׇּחֳרַת הַשַּׁבָּת") which must overlap with Chag HaMatzot. Thus, the Omer offering could be brought as early as the 15th of Nisan,² but never after the 21st.
• Shabbat – The Samaritans, in contrast, maintain that the Shabbat itself must fall within the holiday.  As such, one would never bring the Omer offering before the 16th, but depending on when Shabbat were to fall, one might bring it as late as the 22nd of Nisan, after the conclusion of the festival.

Evaluation of meaning of Shabbat – This understanding of Shabbat as the seventh day of the week would seem to be the simple meaning of the word, as supported by multiple verses in Torah.³

Various mentions of Shabbat – The Karaites⁴ point out that one of the advantages of this approach is that it is consistent in understanding the word "Shabbat" in all three of its occurrences in Vayikra 23:15-16 as referring to the seventh day of the week.⁵

How would one know that the Shabbat is within Chag HaMatzot? One of the main questions raised by the opponents of this position is how one is supposed to know from the verses to which Shabbat is referred,⁶ as it could be any Shabbat of the year!  Aharon b. Levi the Karaite replies that the placement of the verses connects it to Chag HaMatzot. As mentioned above, this position assumes that there is an overlap in time between the unit of verses speaking of the holiday and those speaking of the Omer offering⁷ and the latter's dating is thus naturally informed by the former.⁸

Lack of date for Shavuot – The Karaites⁹ point to another advantage of this approach; it easily explains why Shavuot, unlike other holidays, is not dated in the Torah. According to them, Shavuot actually has no fixed date, only a set day of the week, and in any given year it might fall out anywhere between the 5th and 11th of Sivan.¹⁰

Significance of Sunday? A disadvantage of this position is that the Torah's normal mode of marking time is to date events to their lunar calendrical date or by an agricultural season, not by the day of the week in which they fall. Moreover, this approach must further explain what is significant about a Sunday specifically that Hashem would decide that the Omeroffering (and thus Shavuot) need fall out on that day of the week.

• Two days of rest – In the Scholion to Megillat Taanit, a Boethusian tells R. Yochanan b. Zakkai that Hashem wanted the nation to rest for two consecutive days on Shavuot, which otherwise would be a short one day holiday.¹¹
• Prevent Sabbath desecration – Salmon b. Yerucham the Karaite suggests instead that Shavuot was set on Sunday to ensure that the holiday never fell on Shabbat which would be problematic for bringing a Shelamim offering.

"וַיֹּאכְלוּ מֵעֲבוּר הָאָרֶץ מִמׇּחֳרַת הַפֶּסַח"

• The Karaites¹² assert that the year the Israelites entered the land, Chag HaPesach fell on a Shabbat, and the Omer offering was brought on the next day ‎‏(‎"‏‎‏מִמׇּחֳרַת הַפֶּסַח‎"),¹³‎‏ the 15th of Nisan, allowing the nation to eat of the new harvest on that very day. The passage in Yehoshua, thus, could support their understanding of "מִמׇּחֳרַת הַשַּׁבָּת".
• Since the Samaritans do not accept Sefer Yehoshua as part of their canon they are not bothered by any contradictions from it.¹⁴

"תִּסְפׇּר לָךְ מֵהָחֵל חֶרְמֵשׁ בַּקָּמָה" – Aharon b. Yosef suggests that this time marker is equivalent to that of "מִמׇּחֳרַת הַשַּׁבָּת", with both referring to the day on which the Omer is offered.  He compares the phrase to that in Divrei HaYamim II 31:10, "מֵהָחֵל הַתְּרוּמָה לָבִיא בֵית י"י" suggesting that both point to a day when a sacrifice is brought to the Mikdash.

Motivations – This reading might in part be motivated by a desire to prevent the possibility of the day of the Omer sacrifice falling on a Shabbat, necessitating reaping on Shabbat.¹⁵  Setting a fixed day of the week eliminated the need to ever have to transgress the regular laws of Shabbat.¹⁶

After Chag HaMatzot

The Omer offering is brought on the day following the first Shabbat Bereshit after the festival of Chag HaMatzot.

Sources:Qumran Scrolls4Q321 Fragment 4 Column 54Q325 Fragment 1 Column 2About the Qumran Scrolls

Meaning and mentions of Shabbat – As above, the understanding that Shabbat refers to the seventh day of the week is supported by many verses throughout Tanakh.  This interpretation also allows one to explain all three appearances of the word in the same manner.

How would one know that the Shabbat is after Chag HaMatzot? According to this approach, the verses which speak of the Omer offering follow chronologically from those that precede them. As such, it is natural to assume that the Shabbat referred to is the one that falls right after Chag HaMatzot and not within it.

Dating of "מִמׇּחֳרַת הַשַּׁבָּת" – Unlike the above approach, due to the unique calendar of the Dead Sea sect¹⁷ whose year is divisible by seven, the Omer offering was always brought not only on a set day of the week but also on a set date of the month, the 26th of Nisan.¹⁸ As such, according to their calendar,¹⁹ Shavuot always falls on the 15th of Sivan.²⁰

Lack of date for Shavuot – Since the Qumran sect does assert that the holiday of Shavuot has a set date²¹ it is surprising that the Torah never mentions one.  They might reply that it was simply unnecessary since the law requires one to count from the Omer offering until the holiday.²²

"וַיֹּאכְלוּ מֵעֲבוּר הָאָרֶץ מִמׇּחֳרַת הַפֶּסַח" – This verse in Yehoshua is difficult for this approach as it implies that the Israelites ate from the new wheat on the 15th or 16th of Nisan, while, according to Qumran, this should have been prohibited until the 26th of Nisan when the Omer was brought.  They might reply that the verse is not speaking of eating of the new produce but rather the old.²³

Significance of Sunday? As above, this approach might suggest that really there was no inherent significance to the day, but Hashem specifically chose a Sunday for both the bringing of the Omer and Shavuot so as to eliminate any need for desecration of Shabbat (in reaping or the sacrificing of Shelamim offerings).

After the First Harvest

The Omer is brought on the first Sunday following the initial harvest of the season.

Sources:Mashwi al-'Akbari the KaraiteVayikra 23 pp. 118-119About R. David Zvi Hoffmann,²⁴ Samaritan Savoim sectVayikra 23About R. David Zvi Hoffmann

Disconnect from Chag HaMatzot – This position disconnects the Omer offering and count from Chag HaMatzot entirely.²⁵  It suggests that the new heading of verse 9, "וַיְדַבֵּר י"י אֶל מֹשֶׁה לֵּאמֹר" breaks the verses into two distinct units, leaving no reason why the dating of the Omer should be related to the verses speaking of Chag HaMatzot.²⁶

"תִּסְפׇּר לָךְ מֵהָחֵל חֶרְמֵשׁ בַּקָּמָה" – According to this approach the time markers in Vayikra and Devarim complement each other.  The former ("מִמׇּחֳרַת הַשַּׁבָּת") teaches which day of the week the Omer is to be brought²⁷ while the latter ("הָחֵל חֶרְמֵשׁ בַּקָּמָה") explains when this day falls out during the year.²⁸

Meaning and mentions of Shabbat – As above, one of the advantages of this approach is the ability to uphold the simple interpretation of the word Shabbat as the seventh day of the week in all its appearances in the passage.

Dating of "מִמׇּחֳרַת הַשַּׁבָּת" – This position, like the first approach above, assumes that there is no set date for the Omer offering.  It asserts that the date is totally dependent on nature and can fall before, during, or after Chag HaMatzot.

Lack of Date for Shavuot – Since the date of the Omer offering varies from year to year based on the agricultural climate, it is easily understood why the Torah could not write a set date for Shavuot; it does not have one.

"וַיֹּאכְלוּ מֵעֲבוּר הָאָרֶץ מִמׇּחֳרַת הַפֶּסַח" – This position could maintain that the year the nation entered the land the first harvest was early and the first Sunday afterwards coincided with "מִמׇּחֳרַת הַפֶּסַח", when they brought the Omer and ate from the new grains.

Significance to Sunday – This position, even more than the others in this category, must explain why Hashem would think it necessary to choose a specific day of the week to bring the Omer.  If the dating is so variable due to the changes in nature from one year to the next, why not allow the day of the week to be variable as well?²⁹  They might agree with the suggestion above that the choice was related to ensuring that Shabbat never be violated.

Day After Yom Tov

The term Shabbat is another way of referring to Yom Tov. The Omer offering is brought on the day after the Yom Tov of Chag HaMatzot.  This approach divides based on which Yom Tov is referred to:

First Yom Tov

The Omer offering follows the first Yom Tov of the festival and falls out on the 16th of Nisan.

Sources:PhiloThe Special Laws II:XXIX:162About Philo, JosephusAntiquities of the Jews 3:10:5-6About Josephus, Megillat TaanitScholion 8 NissanAbout Megillat Taanit, MishnaMenachot 10:3About the Mishna, ToseftaRosh HaShanah 1:15Menachot 10:23About Tosefta Menachot, Sifra VayikraEmor 10:10:5Emor 10:12:1-5About the Sifra Vayikra, BavliMenachot 65b-66aAbout the Bavli, the TargumimTargum Neofiti Vayikra 23:16Targum Onkelos Vayikra 23:11Targum Onkelos Vayikra 23:15-16Targum Pseudo-Jonathan Vayikra 23:11Targum Pseudo-Jonathan Vayikra 23:15-16,³⁰ R. SaadiaTafsir Vayikra 23:11Tafsir Vayikra 23:15-16Commentary Bereshit 2:2Sefer HaHavchanahAbout R. Saadia Gaon, RashiVayikra 23:11Vayikra 23:15About R. Shelomo Yitzchaki, Lekach TovVayikra 23:3About R. Toviah b. Eliezer, Ibn EzraVayikra 23:11About R. Avraham ibn Ezra and many others.

Meaning of Shabbat – The Karaites question whether the meaning Yom Tov is a valid definition of the word Shabbat.³¹

• The Scholion to Megillat Taanit, Lekach Tov and Ibn Ezra³² respond that many other holidays are called a "Shabbaton", pointing to Rosh HaShanah, Yom HaKippurim and Sukkot as examples.³³  From these one can learn that the word Shabbaton, and hence, Shabbat, is not limited in meaning to a specific day of the week, but can refer to any Yom Tov.³⁴
• Other commentators attempt to maintain the Rabbinate dating of the Omer sacrifice as the 16th, but offer other definitions for the word Shabbat.  Ramban proposes that it means "week", as it does in the rest of the passage.  The bringing of the Omer begins a new week (for purposes of the future counting) and thus starts at the end of the week ending on the 15th.³⁵

Why use a word with a secondary meaning? R. D"Z Hoffmann points out that the alternatives would have been ambiguous.  The term "ממחרת הפסח" could refer to either the fifteenth or sixteenth of the month³⁶ and the term "ממחרת החג" would likely be understood as referring to the 22nd of Nisan, the day after the entire festival.³⁷

Various mentions of Shabbat – This position maintains that while the initial appearance of the word Shabbat ("וּסְפַרְתֶּם לָכֶם מִמׇּחֳרַת הַשַּׁבָּת") means Yom Tov; in the later phrases, "שֶׁבַע שַׁבָּתוֹת" and "עַד מִמׇּחֳרַת הַשַּׁבָּת הַשְּׁבִיעִת" it means week.³⁸ The Karaites³⁹ point to this inconsistency as a disadvantage of this approach. R. Saadia and Ibn Ezra rebut that this is an example of normal variation and literary artistry throughout Tanakh. Often, even within one verse, the text might play with words, using the same root for different understandings.⁴⁰

Lack of date for Shavuot – R. Saadia asserts that no date is given for Shavuot not because it varies from year to year, but simply because it was unnecessary.  Once the Torah set when to begin the count of fifty days, anyone could calculate when the festival falls.⁴¹

"וַיֹּאכְלוּ מֵעֲבוּר הָאָרֶץ מִמׇּחֳרַת הַפֶּסַח" – These commentators disagree regarding the dating of "מִמׇּחֳרַת הַפֶּסַח" and thus how this verse works with the date of bringing the Omer:

• Fifteenth of Nisan – According to Ibn Ezra "מִמׇּחֳרַת הַפֶּסַח" refers to the fifteenth of Nisan,⁴² when eating of the new wheat was still prohibited.  To solve the problem, he suggests⁴³ that the verse speaks of eating from the old grain.⁴⁴ An opinion in Yerushalmi Challah 2:1 alternatively asserts that the prohibition of "new wheat" only took effect after the conquest.⁴⁵
• Sixteenth of Nisan – Other exegetes⁴⁶ maintain that "מִמׇּחֳרַת הַפֶּסַח" is the 16th of Nisan.  Since the Pesach sacrifice is eaten on the evening of the fifteenth, the next new day is the 16th. This is equivalent to "‏"‏מִמׇּחֳרַת הַשַּׁבָּת‏‎⁴⁷ when the Omer is brought and the new grain is permitted.⁴⁸

"תִּסְפׇּר לָךְ מֵהָחֵל חֶרְמֵשׁ בַּקָּמָה" – This position asserts that the new harvest begins on the 16th of Nisan.  The different time markers in Vayikra and Devarim are just two expressions of the same idea.

Polemical Motivations

• Transgressing of Shabbat – As opposed to the Sectarians, the Sages were not bothered by the potential transgressing of Shabbat were the Day of the Waving of the Omer to fall on it.  As such, they were more concerned with setting a monthly date rather than a day of the week for the offering.
• Shavuot and Matan Torah – It is possible that part of the Rabbinate disagreement with the Karaites related to their desire to connect Shavuot with the revelation at Sinai.  Since this was associated with the sixth of Sivan, they had an incentive to date Shavuot then.

Who Counts? If the date of the bringing of the Omer and Shavuot were variable, the fifty day count would have a practical purpose and one would assume that the calculations be done not by individuals but by the courts, as is done for the Jubilee year.  Since the Sages hold that Shavuot has a set date, though, they assume the count is not purely utilitarian but assume that it must have inherent religious value. As such, they maintain that every individual must count and not just the court.

Last Yom Tov

The Omer is sacrificed on the 22nd of Nisan, the day following the last day of Chag HaMatzot.

Sources:PeshittaVayikra 23:11About the Peshitta, some Ethiopian Jews⁴⁹

Why the Second Yom Tov – These sources read the passage regarding the Omer as following chronologically from the previous passage⁵⁰ regarding Chag HaMatzot and thus naturally assume that its dating should follow it.

Meaning of Shabbat – This position, as above, might point to other holidays which are referred to as a Shabbaton to support the possibility that a secondary meaning of the word "Shabbat" is Yom Tov.

Various mentions of Shabbat – According to this position only the first mention of Shabbat refers to Yom Tov, while the others mean "week". As above, the variation might be simply attributed to the Torah's literary artistry.

Lack of date for Shavuot – According to this approach, Shavuot always falls out on the 12th of Sivan.  As above, one can explain that the Torah nonetheless leaves out the date since the fifty day count makes it superfluous.

"וַיֹּאכְלוּ מֵעֲבוּר הָאָרֶץ מִמׇּחֳרַת הַפֶּסַח" – This position might explain that Pesach in this verse refers to the entire seven day holiday and not just the day that the Pesach sacrifice was brought.  If so, the "morrow of the Pesach" is the 22nd of Nisan, when the Omer is brought and new grain is permitted.  No where in Tanakh, though, is the week long festival referred to as Pesach, making this a difficult read.

"תִּסְפׇּר לָךְ מֵהָחֵל חֶרְמֵשׁ בַּקָּמָה"

Morrow of a Cessation

The word Shabbat refers to something which ceased, and the Omer offering is brought on the day following this event.

Sources:HaKetav VeHaKabbalahVayikra 23:11About R. Yaakov Mecklenburg #1, some modern scholars⁵¹

What ceased?

• Leavened bread – According to HaKetav VeHaKabbalah⁵² the 15th of Nisan is referred to as a Shabbat since it is a day in which one is obligated to desist from leavened bread.
• The manna – Lichtenschtadt and I. Kislev assert that the Torah is referring to the future⁵³ cessation of the manna,⁵⁴ which took place on the 15th of Nisan in the year of the nation's arrival in Israel.⁵⁵ 

Meaning of Shabbat – There is much evidence to support the idea that the root שבת refers to stopping.  Its very first occurrence in Torah (Bereshit 2:3) speaks of Hashem ceasing his creative work.  In noun form, too, many verses can uphold this meaning.  See, for example, Shemot 15:23, 24, Shemot20:9, Shemot 31:15, and Vayikra 23:3.⁵⁶

Why refer to the fifteenth in this manner?

• Essence of day – According to HaKetav VeHaKabbalah, the entire essence of the first day of Yom Tov is the cessation from leavened bread.  This was especially true during the year of the Exodus when leavened bread was only prohibited for that one day.  HaKetav VeHaKabbalah does not explain, though, why it is only here that the first Yom Tov is so called.
• Recall the manna – According to I. Kislev the Torah purposefully wants to connect the bringing of the Omer and the cessation of the manna.  In fact, the entire ritual comes, in part, to commemorate the miracle and the subsequent transition from supernatural providence to natural living.  Giving a calendrical date would have obscured the connection.  In addition, at this point it was not yet known what specific date the people were to enter the land and stop eating manna.

Connections between the Omer and the Manna

• By dating one event to the other, the Torah connects them.
• The specific measure of an omer's worth of the harvest recalls the omer's worth of manna that was allotted to each Israelite each day.
• While the harvest focuses on man's natural food supply, the manna represents Hashem's supernatural source of sustenance.  The cessation of the latter is what led to man's harvesting.

Why commemorate the cessation of the manna? Throughout the forty years in the desert the manna served as a constant reminder of God's providence.  Its absence on Shabbat and the provision of a double portion the day before reinforced the nation's dependence on God.  Upon entry to the land and the transition to natural providence with the cessation of the manna, the likelihood that the nation would forget its reliance on God grew.  Thus, at the moment of harvest, when man is most likely to attribute his success to himself, the Torah commands to bring the Omer sacrifice, and remember the messages of the manna..

Lack of date for Shavuot – It is possible that at the time of the giving of the command, the exact entry date into the land (and the related ceasing of supernatural sustenance) was unknown.  Thus no set date could be given for either the bringing of the Omer or Shavuot.

"וַיֹּאכְלוּ מֵעֲבוּר הָאָרֶץ מִמׇּחֳרַת הַפֶּסַח"

Various mentions of Shabbat – According to this approach the other mentions of the word Shabbat are understood differently than the first and mean week.

¹ This position is known through the many rabbinic sources which aim to refute it. These sources all have the Boethusians mark both the day of bringing the Omer and Shavuot on "the day after Shabbat Bereshit", but it is not clear if this refers to the Shabbat Bereshit within Chag HaMatzot or afterwards.

² This would happen any year in which the fourteenth of Nisan coincides with Shabbat.

³ See, for example: Shemot 20:7,10, Shemot 31:14-15 and Devarim 5:12-15.  However, it should be noted that in many of its appearances in Torah, the word "Shabbat" might not connote a proper noun, the name of a day of the week, but might more generally be pointing to a day in which something ceased.  See, for example, its usage in Shemot 15:25-25 or Vayikra 23:3, and the opinion below which takes this understanding in Vayikra 23:15 as well.  See, though, Salmon b. Yerucham and Aharon b. Yosef who argue that the definitive "ה" in the beginning of the word "הַשַּׁבָּת" suggests that it is a defined day, known from beforehand as the special day of the week, Shabbat.

⁴ See Alkumisi and Salmon b. Yerucham and the position that R. Saadia Gaon is responding to in his ספר הבחנה.  One of the main arguments of the Karaites against the Rabbinate approach was the latter's inconsistency in understanding the word Shabbat in each of its appearances in the unit.

⁵ Nonetheless, R. D"Z Hoffmann points out that the additional adjective "תְּמִימֹת" ("complete") at the end of the phrase "שֶׁבַע שַׁבָּתוֹת תְּמִימֹת תִּהְיֶינָה" is somewhat difficult for this approach, as it is unclear what it adds if the word "שַׁבָּתוֹת" simply means Saturdays. He notes that the Karaite Aharon b. Eliyah answers that the verse comes to say that the Shabbatot include the days of the week before them.  R. D"Z Hoffman rightly points out that such an explanation effectively suggests that the word Shabbatot in this verse means week (and not Saturday), for only a week can be complete in all its days.

⁶ See, for example, the question of R. Yose in Sifra Emor 10:12:1-5 and Bavli Menachot 65b-66a and the discussion of R. Saadia as quoted in the commentary of Yefet the Karaite. See also Rashi and RambanVayikra 23:11About R. Moshe b. Nachman who point to this question as being the strongest of those raised in the gemara. The very fact that so many sects accepted the idea that the word Shabbat referred to a day of the week but nonetheless disagree regarding when that Shabbat fell, highlights the problem.

⁷ Though the latter follows the former in the text, the two speak of the same time period.  Since the rituals are distinct, though, each is relayed separately, with its own passage and unique heading despite the chronological overlap.  The Rabbinates read the chronology of the verses in the same way, but the Qumarn sect do not.

⁸ Though one might argue that this still leaves ambiguity if the Shabbat referred to falls in the middle of Chag HaMatzot or afterwards, Salmon b Yerucham the Kaarite argues that this is as much of a problem for the Rabbinates. According to them too it is unclear if "the day following the Shabbat" refers to the first or second Yom Tov of the holiday.  See also Yefet who argues similarly.

⁹ See, for instance, Alkumisi, Salmon b. Yerucham and Levi b. Yefet.  See also those against whom R. Saadia Gaon is reacting in his ספר ההבחנה.

¹⁰ According to the Samaritans the date is also variable but ranges between 6-12 Sivan instead.  [See above that the Karaites and Samaritans disagreed about whether one began counting on the first Sunday of Chag HaMatzot if that fell out on the 15th of Nisan.]  Such flexible dating serves to sever the direct connection between Shavuot and the giving of the Torah.  As neither the Samaritans nor the Karaites assume that the revelation at Sinai occurred on 6 Sivan, they had no incentive to set Shavuot on that date.  [The Karaite R. Aharon b. Yosef, in his comments to Shemot 18:29, asserts that the date of revelation is 3 Sivan, while the Samaritans commemorate it on the 46th day of the Omer.  However, since the Samaritans celebrate Shavuot for a full week, beginning on the Monday of the last week of the Omer, they too end up connecting revelation and the holiday.]

¹¹ It is not clear if this reflects a serious explanation or if it is fabricated conversation used to mock the Boethusian position.

¹² See Alkumisi and Salmon b. Yerucham.  Aharon b. Yosef further points out that according to the Rabbinate position, in contrast, the verse in Yehoshua suggests that the Israelites sinned in eating from the new harvest before the day of bringing the Omer!  See below how the sages understand the verse.

¹³ Pesach is understood to be the fourteenth of Nisan, the day the Pesach offering was brought.  This fits with the usage and dating of the term in Bemidbar 33:3.

¹⁴ As they maintain that one can never bring the Omer before the sixteenth of the month, they cannot explain the verse as do the Karaites.

¹⁵ See Tosefta Meanchot 10:23 which suggests that the Boethusians opposed the date for this reason. See also Salmon b. Yerucham's similar argument above regarding the desire to eliminate any problems bringing the Shelamim offering if Shavuot were to fall on Shabbat.

¹⁶ This discomfort was not shared by the Rabbinates who suggest in several cases that another law might supersede the laws of Shabbat.

¹⁷ The Torah does not lay forth rules as to how one should set up a calendar and different sects chose different methods.  While the sages opted to make a combination lunar-solar calendar, the Qumran sect preferred  a solar one of 364 days and 52 weeks.  As this is divisible by seven, all monthly dates consistently fall out on the same day of the week.  New months were not determined by the moon but set to be 30 days each, with every third month being 31.
The sect set יום רביעי as the first day of its year, perhaps because on this day of creation the luminaries were established to be "לְאֹתֹת וּלְמוֹעֲדִים וּלְיָמִים וְשָׁנִים".  As such, both the first of Nisan and the 15th of Nisan fall out on a Wednesday, and the day following Shabbat Bereshit after Chag HaMatzot is always the 26th of Nisan.

¹⁸ Others who adopt this approach but do not abide by the Dead Sea sect calendar would say that the date is variable and could fall anywhere between the 22nd and 28th of Nisan, making Shavuot fall anywhere between the 12th and 18th of Sivan.

¹⁹ Since they maintain that Nisan and Iyyar always have thirty days, a count of fifty days from the 26th of Nisan would end with the 15th of Sivan.

²⁰ Compare with Jubilees1:1-315:1-416:16-1844:1-6About Jubilees which also sets the holiday on the fifteenth of the month, the day which it understands to be the revelation at Sinai.  As is its wont, Jubilees roots this date with earlier events associated to the Patriarchs, suggesting that the Covenant between the Pieces, Avraham's circumcision and the birth of Yitzchak all occurred on this date as well.  As such, from early on the date was related to covenant making.
Qumran might also associate the date with the revelation at Sinai, in which case, despite their different starting point for the fifty day count, they agree with Rabbinates that Shavuot is "חג מתן תורה". [This would be another point of difference between this position and that of the Karaites above.]

²¹ See above point.

²² Compare this response with the similar one of the Rabbis below.

²³ See Ibn Ezra in the name of R. Saadia who raises this possibility below.

²⁴ See R.. D"Z Hoffmann who mentions this approach and the discussion in Y. Erder, "אבלי ציון הקראים ומגילות קומראן" (Tel Aviv, 2004): 184-187.

²⁵ R. D"Z Hoffmann argues against such a disconnect.  As evidence, he points out that in the list of festivals in Bemidbar 28-29, the Omer is never mentioned.  If one suggests that it is subsumed within the holiday of Pesach this is not problematic, but if one wants to maintain that the two holidays each stand on their own, it should have been counted distinctly.

²⁶ Mashwi al-'Akbari and his followers support their position by pointing out that had the Omer been tied to Chag HaMatzot, when listing the sacrifices of the day the verse should have included the words "מלבד הנפת העומר". On other festival days, the verses list not just the sacrifices unique to the day but others that might need to be brought on that day as well.  See, for example, Bemidbar 29:1-6,  where after the special Rosh HaShanah offerings are listed, the verse adds "מִלְּבַד עֹלַת הַחֹדֶשׁ וּמִנְחָתָהּ".
One might respond that, unlike Bemidbar 28-29, Vayikra 23 is not trying to give a comprehensive listing of all the sacrifices of the day and thus, also does not say "מִלְּבַד עֹלַת הַבֹּקֶר אֲשֶׁר לְעֹלַת הַתָּמִיד" despite this being sacrificed on Chag HaMatzot as well.

²⁷ From Vayikra alone, as the Rabbinates point out, one might indeed not know which Shabbat is referred to.  It is only by looking at both sources together that a complete picture can be drawn.

²⁸ The description of the Omer as "רֵאשִׁית קְצִירְכֶם" further supports the connection to the season of "הָחֵל חֶרְמֵשׁ בַּקָּמָה".

²⁹ See R. David Zvi Hoffmann who brings this argument.

³⁰ Targum Onkelos does not specify which Yom Tov is referred to, but probably agrees with the Rabbinate approach that the verse is speaking of the first one.

³¹ See Salmon b. Yerucham's claim: "אתה עתה צריך להביא ראיה ברורה
כי השבת יום טוב כאשר תדברה"

³² See also the Rambam.

³³ Though Pesach and Chag HaMatzot are never explicitly identified as a Shabbat or Shabbaton, R. D"Z Hoffmann asserts that the usage by the holidays mentioned can serve as a prototype for all others as well.

³⁴ R. Saadia points out that the word itself really means to cease, so any day or time period in which there is a ceasing from work can be so called.  Cf. the opinion below which elaborates on this etymology but does not go as far as to say that the word Shabbat can really substitute for the word Yom Tov..

³⁵ This is not a simple nor fluid reading of the verses, despite the advantage of maintaining a consistent understanding of the word Shabbat.

³⁶ Since the Pesach is sacrificed on the fourteenth and eaten in the evening, the morrow could be interpreted as either the fifteenth or the sixteenth.

³⁷ R. Hoffmann adds that had the text instead written a lunar date, that would have severed the connection to Pesach, which is highlighted in the formulation "the morrow of..."

³⁸ See the examples brought by Lekach TovVayikra 23:16About R. Toviah b. Eliezer to prove that this is a valid understanding of the word as well.

³⁹ See Alkumisi and Salmon b. Yerucham above.

⁴⁰ Amongst R. Saadia's many examples, see Vayikra 14:41, "אֶת הַבַּיִת יַקְצִעַ מִבַּיִת" and  Yonah 3:7, "מִטַּעַם הַמֶּלֶךְ וּגְדֹלָיו לֵאמֹר הָאָדָם וְהַבְּהֵמָה הַבָּקָר וְהַצֹּאן אַל יִטְעֲמוּ מְאוּמָה".  Ibn Ezra adds the play on words in Shofetim 10:4,"יְהִי לוֹ שְׁלֹשִׁים בָּנִים רֹכְבִים עַל שְׁלֹשִׁים עֲיָרִים וּשְׁלֹשִׁים עֲיָרִים לָהֶם".

⁴¹ He compares it to the holiday of Shemini Azeret which is similarly not dated in the Torah, but rather marked as the "eighth day".  In both cases the Torah links a second holiday to a previous one and dates it from there.

⁴² As the Pesach was sacrificed on the fourteenth, the next day is the fifteenth. This fits with the phrase's usage in Bemidbar 33:3.

⁴³ He says this in the name of R. Saadia.

⁴⁴ In support, he proposes that the the language "מֵעֲבוּר הָאָרֶץ" might hints that the food eaten was from the past year (השנה שעברה).  This contrasts with the language of the next verse which states that the rest of the year the Israelites ate from "תְּבוּאַת אֶרֶץ כְּנַעַן", from the root "בוא", meaning the coming year's produce.

⁴⁵ In his article, "והאכילנו את המן ונתן לנו את השבת", Megadim 16 (1992): 43-55, I. Kislev points to a difficulty in both variations of this approach. If the nation simply ate from the old grain, why is the verse emphasizing this? Moreover, the language of "מַצּוֹת וְקָלוּי" recalls the prohibition in Vayikra 23 "וְלֶחֶם וְקָלִי וְכַרְמֶל לֹא תֹאכְלוּ עַד עֶצֶם הַיּוֹם הַזֶּה" suggesting that in Yehoshua, too, it refers to the new grain.  Against Ibn Ezra, he adds a practical question: how would the nation have had access to old grain which presumably was owned by the enemy Canaanites?  Ibn Ezra suggests that the people ate of their own food which they brought from the other side of the Jordan, but this does not match the verse's phraseology that they ate "מֵעֲבוּר הָאָרֶץ"

⁴⁶ See R. Saadia as brought by Ibn Ezra, Lekach Tov, Rambam, and R. Yitzchak in Tosafot Kiddushin 37b.

⁴⁷ The Rambam suggests that since Sefer Yehoshua chose to mark the day with the term "מִמׇּחֳרַת הַפֶּסַח" rather than "מִמׇּחֳרַת הַשַּׁבָּת" this proves that the Omer sacrifice need not be brought on the morrow of Shabbat Bereshit, but instead on the 16th of the month.

⁴⁸ Ibn Ezra argues that this position is difficult from the verse in Bemidbar 33:3 which identifies "מִמׇּחֳרַת הַפֶּסַח" with the 15th, R. Yitzchak  in Tosafot Kiddushin 37b dismisses the problem by asserting that "לשון התורה לחוד ולשון נביאים לחוד ולשון חכמים לחוד"; one cannot compare the usage of language in the Torah with that in the prophets.

⁴⁹ R. D"Z Hoffmann points to their custom in his commentary, p. 125.

⁵⁰ The approach of the Rabbinates above assumes instead that the passages overlap chronologically and return to the day after the first Yom Tov.

⁵¹ See the opinion of Lichtenschtadt, brought by R. D"Z Hofmann p. 140 n. 95,  A. Ron, "ממחרת השבת", Megadim 16 (1992): 37-43, and I. Kislev, "והאכילנו את המן ונתן לנו את השבת", Megadim 16 (1992): 43-55.

⁵² A. Ron elaborates on the approach in the article cited above.

⁵³ R. D"Z Hoffmann argues that at this point in the narrative there was not yet a decree of forty years in the desert, and the people would likely have entered the land in the fall. If so, it would be an illogical choice of season to celebrate the beginning of the harvest! Kislev attempts to prove that, despite its textual placement, this law was given only after the decree. More simply, one can suggest that Hashem wrote the command knowing what the future held (and that in reality the nation would enter the land in the Spring) even if the nation did not.

⁵⁴ See Rashi and Shadal on Shemot 16:26 who both suggest that even the proper noun Shabbat (the seventh day of the week) is related to the cessation of the manna.  The first appearance of the word as a noun comes in the story of the manna, in reference to the fact that on the seventh day of the week the manna was not to fall.

⁵⁵ This position understands that when Yehoshua 5:12 states that the manna ceased on the "morrow", it is referring to the day mentioned in the previous verse, "the morrow of the Pesach", which is the fifteenth of Nisan. [One could, instead have said that it refers to the day after the day mentioned in the previous verse which would be the sixteenth.]

⁵⁶ A. Ron in the article cited above attempts to distinguish between instances where the Torah writes "יום השבת" which he suggests refers to a day of the week, and those in which the word "שבת" appears alone and refers to a condition of rest or ceasing but not a particular day.  Thus in Vayikra 23, it does not mean Shabbat Bereshit but can refer to any day in which something ceased.