tldr: Sugar Magnolia starts in A major and ends in B major. The main riff is based on an open A chord with a hammer-on IV chord, D, along with connecting notes from A major pentatonic. Most of the chords are diatonic, with a borrowed bVII chord mixed in. And the lead work uses the major scale, around the framework of the major pentatonic. There’s a quick key change to D major at “She’s got everything…” and later a permanent key change from A major to B major at “cuckoo’s crying.”
Sugar Magnolia Full Analysis
Sugar Magnolia is starts in A major. The main riff slides into an A chord chromatically from G#. From there, there’s a major pentatonic riff with a hammer-on to the IV chord, D, as a partial chord. The gist is:
G# A D A ----------------------- -1/2-2---------3--2---- -1/2-2---------2--2---- -1/2-2-----2h4-4--2---- --------/4------------- -----------------------
G# A A ----------------------- -1/2-2---------------2- -1/2-2---------------2- -1/2-2-----2-4-2-----2- -------3/4-------4-2-0- -----------------------
The bolded 3 note is a flat third sliding into a major third, which is a common bluesy addition to the major pentatonic.
The main verses (“Sugar Magnolia, blossoms blooming…) start the same way, from A to D to A, but then go one of two ways, depending on the version or even different parts of the same version. One way is A – G – E – A. The G chord is a bVII borrowed from mixolydian, but the E chord, a V chord, makes clear that we’re still in the ionian (natural major). It melds in chromatically:
G: G B D E: E G# B A: E A C# 
The diatonic vii chord would have been G#dim, which shares two of the same notes (G# B D), so the alteration is an easy substitute, works well to introduce a mixolydian sound, and as shown, can smoothly lead back to the V chord chromatically.
The other way uses a D instead of the E (A – G – D – A) and is perhaps more susceptible to a full mixolydian read, if you are playing lead over it. But the part that follows (“Saw my baby”) is straight-up A major, with both a iii and V chord that wouldn’t exist in mixolydian: A C#m F#m E D A, which is I – iii – vi – V – IV – I.
At “She’s got everything,” there’s a subtle key change to D major, with D – G – D as I – IV – I, and D – A – D as I – V- I. Then an E returns us to A major, where the E is the V chord.
There’s a nice little solo over the intro riff using the A major scale, with a lot of A major pentatonic notes used.
When we get to “Sometimes when the cuckoo’s crying,” there’s a modulation up to B major, with a I – IV pattern of B – E. Moving up a whole step is an abrupt but common way of changing keys. This part ends with a quick-moving progression I’ve heard a few ways, but along the lines of B – F# (or A) – E – D – A – E – B – A – E. I think this is sort of a variable circle of fifths pattern, depending on how you play it, as all of the chords have basic relationship to adjacent chords: F# is the V of B, B is the V of E, E is the V of A, and A is the V of D. Strictly speaking, A and D are not in key, but they are used in transition, relative to adjacent chords and not so much in the context of the B tonic.
Finally, there is a jam with B, E, and F#, the I, IV, and V in B major. The B major scale works over everything, and you can also try mixing in B mixolydian over the B and E chords (but not so much the F#, which clashes). You can also work in that minor third to major third chromaticism from the opening riff over the B chord.
- Easy hammer-on I to IV from an A-shaped chord
- Subtle key change to IV chord by pairing with bVII, which is its IV chord.
- Abrupt key change by moving tonic up one whole step.