DOES THE NEW COVENANT EXIST, OR IT IS THE SAME “SCRIPTURE”?
CAN NEW TESTAMENT HAVE OWN NEW FESTIVALS?

1. Nisan 14 is the Day of Atonement of the Mankind and the Day of the New Covenant. As such it is much more important than Pesah (Passover) itself. Have in mind, it is the single eve of a festival which is especially mentioned by G-d in Torah, not as any other eve of a festival.
2. Nisan 16 is the Day of Resurrection. Naturally, there are no G-d's ordained festivals of the New Covenant in Torah. This is the reason why the Adventists speak of One Sacred text of the Bible only, not about any "New" vs "Old" Testaments, usually pointing out to Paul's 2 Tim 3:16: "All Scripture is given by inspiration of G-d, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness" – should we understand that Paul speaks of his own letters as of the "Scripture"? When neither Acts (not to say about today known Gospels) still had not been written, known and recognised, nor was Paul so shameless to present his own circulars as Holy Scriptures: he spoke about Torah (Acts 15:21) only! G-d' Covenant does not mean ("Old" vs. "New") Scripture, but any real Covenant concluded beween G-d and His people chosen for Coming Mashiah and Salvation. Series of Covenants followed concluded through Abraham, Moses and Messiah J-shua on Golgotha's Cross (cf. New Covenant first mentioned Jer 31:31). 
Should Messianic believers commemorate main  events of the New Covenant (Nativity, Atonement, Resurrection), or not? Nisan 14 is a commemoration of the Atonement, however it was Resurrection only which showed that the Atonement had really taken place and that the New Covenant had started. No hint to any festival on Nisan 16 is seen in the Bible except connection with the end of the Quietude of the Sabbath Grave (Matth 28:1).
Even more! What is the sense to celebrate Resurrection on Nisan 16 if this Jewish lunar-solar date fells on the first day of the week (when the Lord resurrected) only in minor occurances? It is not important whether the adventists uderstand that the meaning of the Sabbatism is entrance from the temporary Rest of the seventh day of the week into eternal Rest (Hebr 9:4) of the eschatological Eighth day of the Creation, shown by the Resurrection after the Sabbath Rest. This is what the adventists do really negate: a connection of the temporary Rest with the eschatological eternal Rest as aim of the temoral rest. This is what the Resurrection reveals on the first / Eighth day of the week: the fulfilment of the creation. Therefore, the Resurrection should be celebrated on the break of the next day after the Paschal Shabbat, but this should always be "Sunday", of course! In what a way then, if Nisan 16 can be „Sunday" in minor occurances only?
3. However Passover as commemoration of the Exode was not an isolated festival in the Jewish calendar. It was connected with Pentecost (Shavuot) as one continuing celebration, the finalizing of which should be counted: 
- through 49 days of the Omer (‘sheaf’ and a measure of barley), 
- starting from consecrating in Temple a barley sheaf of the first harvest, 
- "on the morrow after the [first] Sabbath" of Pesah (Lev 23:11).
On the 50th day the festival of Shavot takes place when two loaves baked of the first wheat are sacrificed.
Dates of all Jewish festivals are pointed out in Torah, except one of the three main festivals, which is is Shavuot!
No problem to count 49 days from the morrow after the first Sabbath, however the word ðabbât ‘quietude’ has two main meanings: a festive rest’, ‘the seventh day of the week’ ("Saturday"). If one counts from this day of the week, then Shavuot becomes an exception among all festivals because its (Jewish) calendar day will not be fixed as a day of the month, but it will be the first day of the week ("Sunday") any time!
4. Last not least, what does the Festival of Shavuot mean, or commemorate? It is obvious from the text of Torah, it is a thanksgiving harvest festival, or in pre-Mosaic terms, a Semitic agricultural feast. It has been connected with Pesah ca. in the 13th c. only, as a commemoration of the goal of the Exode from Egypt: receiving of the Law at Mount Sinai. This is very logical and really provides deep sense to the festival, since first fruits of the liberation are seen in the Covenant between G-d and Israel. Thus Shavuot is Festival of the Covenant in Abrahamic sense. However is this not the same with the New Covenant? The birth of Ecclesia with sending the Holy Spirit to it is equally a festival of the New Covenant in turn. Thus Shavuot is Commemoration of Covenants, the Day of Covenant. The birth of Ecclesia with sending the Holy Spirit to it is equally a festival of the New Covenant in turn. Then a link to Golgotha Sacrifice is clear: Y-shuah Mashiah Congregation receives the Holy Spirit and becomes the Body of Christ as a result of the Golgotha Covenant confirmed by Resurrection. Is it not a feast of Resurrection then? –
It is, if one counts the Omer as actual Shabbats, not as a festive Pesah rest on the second day (Nisan 16) of the festival, i.e. not as weeks, because it always happens on the first day of the week ("Sunday") only.
What are gounds to count Omer in such a way? – Even a greater one than in traditional rabbinical Judaism, which counts weeks in order the festival be only on a fixed month's day, i.e. on Sivan 6. Enough to say that the Caraites, who have never accepted traditional concept of the Oral Torah, as well as ancient Essenes, celebrate Shavout having counted the Omer with 7 Sahabbats (seventh days of the week), and this is always the first day of the week ("Sunday") in turn. The practice of the Essenes is the oldest. One refers to it on the basis of the apocriphal Book of Jubilees found within Qumran Dead Sea Scrolls. This conforms to the earliest comprehension of the post-Judean Christian fathers in turn.
Therefore, the best conclusion for Messianic Jews could be not to follow the adventists in denying festivals of the New Covenant, but to celebrate the Resurrection together with the feast of Coming of the Holy Spirit to the Church, i.e. always on the first day of the week ("Sunday"), and this is also right according to the Jewish tradition in which Pesah–Shavuot is one continuing festival of Liberation and the Covenant.

PS According to the Gospels, Y-shua was crucified on Nisan 14 as a Lamb of G-d, however a poblem arises how His Last Supper could be a Paskhal (better: Pashal, Passhal, not German/Yiddish ch!) Seder in this case. The Paskhal Seder takes place on Nisan 14/15 after the Sunset. However in order to facilitate preparations for the feast, the Paskhal Seder could be allowed to arrange a day earlier provided the first day of Passover was a Sabbath day of the week. One problem more is usually touched upon, which is three days and nights in the midst of Earth, as foreshadowed in the book of Jonah. However the Jews did not even have a special word for one day-night then: any event which took place within the term of three days-nights was rendered as having occurred during three days and nights (cf. 1 Sam 30:12–13). 
On his highly informative site Hebrew for Chistians (Holidays) John J.Parsons states that Y-shua resurrected on Nisan 17. This is done basing on a premise that Y-shua was in Grave 3 full day-nights. John J. Parsons mentions different meanings of the word Hebr. Ðabbât and argues that Sabbath as the first day of Pesah (Nisan 15) was on Friday that year, but Sabbath as the last day of the week was Nisan 16 after that. He also regards calculation of the Omer from the Sabbath day of the week (always producing the Sunday of Shavuot, i.e. the first day of the week) to be erroneous as coming from “corrupted Sadducees”. 
However a calculation by modern converter http://www.abdicate.net/cal.aspx/cal.aspx shows NO Nisan 15 occurring on Friday between Jewish years 3779 and 3796, i.e. between the years 19 and 36 of the Julian calendar. 
However Nisan 15 WAS ON weekly SABBATH four times over a span of 3779–3796 = 19–36: 
אon April 4, 19 (had Y-shua been born in year 6 BCE, He should have been only 25 years old then), 
ב –
on March 23, 26 (had He been born in year 6 BCE, He should have been 38 years old then, but if born in 4 BCE, He should have been 36 years old, what is closest to the Gospel narrative), 
גon April 4, 33 (even elder!), and 
ד
on March 31, 36 finally, when no Pesah of the Gospel could be because of the age of Y-shua not corresponding to the Biblical narrative anyway.
Thus one can admit that the mankind was redeemed on March 22, 26, 
but the Salvator resurrected on March 24, 26.
 
Now if one is eager to know the actual Birthday
, it is a twoness
March 22/24, a Mystical Birthday of Mankind, what is also the same one of Y-shua as a Son of Man. 
As for the Sadducees, their Omer calculation corresponds to the Book of Jubilees discovered in Qumran among scrolls coming from Essenes, as just said above.

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