The tonus perigrinus has a pedigree which reaches back to the Temple, Historically used in the Church with the psalm In exitu Israel, it seems that this is a carry-over from Jewish worship, in which it was also used with this psalm. There are isolated Jewish communities in Yemen and other places which to this day sing this psalm to this tone. While not traditionally used with Magnificat or other canticles, it would be appropriate if you want a somewhat 'authentic' '1st century Palestine' tone.
As for the canticles in Hebrew or Aramaic, you must needs look elsewhere for that.
I didn't know of the pedigree of the tonus peregrinus, so I'm grateful for that information. I knew it was connected to the psalm In exitu Israel, because this psalm is frequently part of Vespers, and this tone is frequently in use when the psalm is.
On the question of Hebrew or Aramaic, I guess the question probably comes down to this: as a part of the formal worship of the Jew, wouldn't it be in Hebrew, rather than in the "vernacular"?
Why not look into a Syriac translation from one ot our oriental rites. That would be sure to have an ancient provenance. I seriously doubt that there would be a Hebrew version of Magnificat or the other New Testament canticles!
I have a little book called The Daily Offices with Hebrew, Greek and Latin Supplements compiled for private recitation by Boyce M Bennett Jr, The General Theological Seminary, 1977 (Episcopal, New York) which I much enjoyed using and it indeed had Magnificat in Hebrew. Being Episcopal it had an extensive list of canticles such as Gloria in excelsis, Phos hilaron and many of those OT and NT canticles used along with psalms in Liturgy of the Hours. I also want to point out that Tonus Peregrinus got used as the melody to sing Magnificat in the Lutheran Reformation where it continues in the current ELCA-ELCIC Worship book. As such there are some organ settings by JSBach (Meine Seele erhebt den Herren) as well as several movements of his choral Magnificat that feature the melody.
The Magnificat is of course a close parallel to 1 Sam 2:1ff. I wonder whether that gets chanted in synagogues. There are plenty of recordings of current Jewish cantors chants such as these. And there are grandiose claims made for a recording here. To my untutored ears there is a strong similarity between most of the monophonic chanting, whether Jewish, Maronite, or Greek. In contrast to the Old Solesmes, they all treat complex neumes as 'ornaments' (sorry, being untutored I do not know the correct term). OTOH the range/ambitus varies.
There is New Testament translated to (classical biblical) Hebrew and I have it, but I won't post text of the canticles for purposes of something I consider liturgical abuse.
The Society for Distributing Hebrew Scriptures has downloadable copies of the NT in Hebrew here. The text has been recently revised, and I imagine is in modern Hebrew.
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