A comment used about Frank Zappa's music, during the early years of his career, was that "Ugly can be beautiful". This piece is not exactly an example of that principle - it's definitely not ugly - but it is harmonically quirky and none the less, still quite beautiful.
What do I mean by that? If you've studied traditional harmony, you know this piece is not traditional and yet it has a traditional ambience. The opening theme is basically E Mixolydian and dropping to a major chord on the flattened sixth, C major, is a traditional enough effect, but the quirkiness comes from then rising a minor third to a major chord a semitone below the tonic E before resolving into it. Major chords a minor third apart are quite common in rock music, but even there, not used in this much less obvious way.
The following transcription has the exact melody, but the harmony is pared down to be playable easily on a guitar. The given score is for piano, but could easily be played by two guitars. I haven't included the improv section at the end.
I had transcribed all but the arpeggio section and the improv section a long time ago but adding the arpeggio some time later, was inspired by the fact that I got lazy and downloaded a MIDI file of this piece, which turned out to have the arpeggio section completely wrong and didn't include the improv section at all. So I ended up having to make the extra effort to transcribe the arpeggio section, and it was well worth it.