"Green Onions" is indisputably a classic blues number that I heard throughout my life and that opening guitar vamp has stuck with me for decades.
This song presents an interesting case study in applied harmonic rhythm as a foundation for understanding what makes the guitar vamp so identifiable. The song is in F but the guitar chord that hits at the tail end of the last beat of every measure always lands a perfect fourth above the root of whatever chord is prevailing at the downbeat of each measure. Ethan Hein describes that as blues tonality, which is true, but one of my music theory professors once said that the beauty of music theory is that you can disagree with the teacher and you "could" still be right. So ... I have an alternative explanation for how to understand those unique chord vamps the guitar is playing in the song, that should be explicable for both classical and blues fans.
The guitar vamp is so staccato and steady on the weak half of the weak end-beat of the measures we can't call this "polytonality" but that is also why I don't think of any of the chords as thirteenth chords. The second inversion chordal pattern is too persistent across the piece for that to be how to explain what's going on. But if you had the guitar vamping those chords on the weak beat of every beat of every measure then the effect would be polytonal, where the keyboard vamps along F dorian while the guitar functionally cruises along in B flat major. Cropper hitting the pure triad of whatever chord Booker lands on at the end of each measure doesn't changing the prevailing harmonic rhythm at the downbeats, but the quasi-polytonality that results from that decision of Cropper's gives "Green Onions" a quasi-bitonality of F and B flat simultaneity that defines the song.
If you want to find out just how important this dual-tonality element is to "Green Onions" try playing the chords that are "supposed" to be in the key based on the root movements of the downbeats! Where ever you see F at the downbeat play F, where ever you see B flat at the downbeat play B flat and so on. Remove that perfect fourth displacement where the guitar is consistently in the subdominant key in relationship to the minor tonic key and what do you get? You will find that "Green Onions" becomes more "Russet Potatoes"! Sure, once the opening is played through the song proceeds to F blues, which is wonderful, but the joyfully ambiguous polytonality of the introduction is what set the mood and gave us a mysterious question as to "what key is this really in? The guitarist seems to be deliberately playing in a completely different key from the rest of the band" The reason for that "can" be explained in terms of blues tonality but that isn't the "only" way to explain it. In any event, the song is a great song.
It "is" too short but that's why it was a good idea to go hear Booker T. play this song in concert. I was fortunate to hear a double feature of Booker T. and John Lee Hooker at the start of this century and I can tell you that in live performance "Green Onions" could go on for minute after glorious minute. :)