Close, but "David's line" is the Royal Family of the Hebrew Nation. The pedigree of Jesus as a royal descendant of David is given in Matthew 1:1-17 — the "begats." Luke has a genealogy in Chapter 3 of his Gospel, but in reverse order and with many different names.

As far as I can tell, the earliest recording of this song was the Alan Lomax recording of Bessie Jones singing "Turkle Dove" on April 11, 1960:

https://archive.culturalequity.org/field-work/southern-us-1959-and-1960/st-simons-island-iii-460/turkle-dove-done-drooped-his-wings

Here is the Lomax recording of his interview of Bessie Jones about the song:

https://archive.culturalequity.org/field-work/southern-us-1959-and-1960/st-simons-island-iii-460/interview-bessie-jones-about-turkle

At the beginning, it sounds like she's saying that "sasalado on salasari" is musical notation sung by angels.