Has anyone subjected Torah trope to Schenkerian analysis?

I was thinking that among Ashkenazim at least, it is tonal music, so it should work.

Machpah, Pashta, Munach before Zakef are all related to I, the tonic chord. It changes on Zakef to a V (or perhaps ii) and holds that through Tipcha and Etnatchta, finally coming back to I with the Sof Passuk. Revia could be considered a vi (minor sixth) and Zarka is almost certainly a V.

Has anyone with a more sophisticated understanding of music theory than I have applied these concepts to Torah, Haftarah, or other tropes?

Somewhat related to this, is that Torah trope specifically seems to abhor the fourth, using it only as a passing note in Darga and similar places. I wonder if that aversion is a result of it originally being a major pentatonic scale without a fourth (1,2,3,5,6) that only developed into what we think of as a Ionian major scale under European influence.