This piece was originally written in E Dorian, so FZ probably created it in open position on the guitar.
The Lumpy Gravy performance was speeeded up, raising the pitch a minor third, so it ended up in G Dorian. A clue to my guitar theory is in section C, which is, harmonically: Gm, Fm, A♭m, Gm, but the bass line is G, C, A♭, G, which in the original would have been chords Em, Dm, Fm, Em, played with bass notes E, A, F, E, where the low D is not available on a guitar tuned normally.
I like this theory because it sits well with my own feelings about serendipity. The number of times I've been frustrated with the limitations of the guitar only to come up with something that sounds better than what I was originally trying to achieve.
Some months ago I decided to try and play this on the bari sax and the really neat thing there is that I'm playing it in E Dorian, but because bari sax is E♭ transposing, it comes out in G Dorian, just like on Lumpy Gravy. Another rush of serendipity in relation to this tune for me. I love the way it sounds on the bari sax in this register and E Dorian is very nice to play on a saxophone.
If I wanted it to sound in E Dorian on bari sax, I'd have to play it in either C♯ or D♭ Dorian, which are (a) trickier to play, (b) messier to notate and critically, (c) the low G♯ or A♭ required, does not exist on the E♭ transposing saxophones. I play it on the alto sax in E Dorian as well, which is also E♭ transposing, but sounds an octave higher than the bari sax.
My transcription is in G Dorian, to fit the Lumpy Gravy sound. The G dorian scale is A, B♭, C, D, E, F, the intervals being, major second, minor third, perfect fourth, perfect fifth, major sixth and minor seventh. The key signature is G minor, so a natural is needed to get the major sixth. Although the basic scale of this tune is G Dorian, which gives much of its character, significant chromaticism is used.
Firstly, the flattened sixth, E♭, harmonised by E♭ major in the A theme, which is also used in the B theme. Secondly, the flattened second, A♭, harmonised with A♭ major. Thirdly the sharpened (natural applied to B♭) third, B, harmonised by G major in the B theme. Fourthly, the flattened second, A♭, in the bass and the flattened fifth, D♭ and flattened sixth, E♭ in the melody harmonised by A♭ minor, in the C theme, which is also supported in mood by the use of F minor, which also has the flattened second, A♭.
The basic structure of the piece is A A B A C B A. In my score, just in case you get lost following the repeat markers, which were organised to produce the briefest notation, the sequence is A E1 A E1 B1 A E1 C C C C B2 A E2 E2 E2 E2 E2 E2 E2. On Lumpy Gravy, the sixth repeat of E2 is chopped in half and segues into the following section.