tldr: Deal is in A major and opens with a pentatonic blues-style riff on the open A chord. The song is built out of I, IV, and vi chords connected by chromatic steps in between. These steps are provided by a C#7 secondary dominant V/vi chord; an Ao7 common-tone diminished seventh chord; an F# secondary dominant V/II chord; and a II chord, B, which is arguably borrowed from the Lydian mode, but which I think is a V/V chord that deceptively resolves to the IV . The chorus is a mixolydian I – bVII – IV progression. The solo is generally based in A major, but substituting in the relevant alterations over the non-diatonic chords, working in a bunch of chromatic passing tones, and switching to A mixolydian over the chorus.
Deal full analysis
Deal is in the key of A major. For the opening riff, your index finger should be on the open A chord at the 2nd fret, with your other fingers adding the riff notes off of that base. The notes are structured on a blues-style A major pentatonic scale, mixing in a b3 (C note) moving up to the natural 3 and a b7 (G note) moving down to the natural 6 (bolded below).
The gist of the intro, although it varies each time, is:
----------------------------- --------------22------------- 22------------22------------- 22----2-2-2h4-22----2-2-5p4p2 00-3h4--------00-3h4--------- -----------------------------
The main verse is A – C#7 – F#m – A – D7 – Ao7 – A – F# – B – D, and then the same thing but going into a mixolydian A – G – D chorus followed by the intro riff. I’ve bolded the non-diatonic chords. This translates to I – V/vi – vi – I – IV7 – cto7 – I – V/II – II (V/V) – IV (and a chorus of I – bVII – IV).
This song is really about the voice leading between chords, and to see what is really going on, let’s line up the individual notes, with the most significant ones bolded:
A: E A C#  C#7: F G#C#   B F#m: F# A C# A: E A C#  D7: D F# A C Ao7: D#F# A C A: E A C#  F#: F# A#C# B:  D#F# B D: D F# A
(Brackets show where I moved a note for illustrative purposes).
The verse starts with the A tonic and then moves to a non-diatonic III chord, C#7. Functionally, the C#7 is a “V7 of vi” or “V7/vi” chord — a secondary dominant that temporary tonicizes the F#m that follows it. What that means is that the V7-to-i dominant function in the key of the vi chord (F# minor) is borrowed in this key, leading from C#7 to the F#m chord. Also note that the F and G# notes are a half-step away from E and A notes of the initial A chord, which creates a leading quality away from the A even before the C#7 resolves to F#m.
Next, the F#m and A are similar chords in key, and they create a whole step movement down from the F# note to the E note of the A chord to the D note of the D7 chord. You can add a twist by making this A chord an A7, which would make it a secondary dominant of the D7 chord that follows (a V7/IV7 chord).
The D7 kicks off a chromatic voice-leading progression from D to D# to E and back down to D# and D. It is an altered IV chord (Dmaj7 would be the diatonic 7th of the IV chord), and here it served as a passing chord leading to the Ao7 chord. You don’t actually need the D7, and could just play the Ao7 twice, but note the similarity of the chords and how the D7 helps transition to it.
The Ao7 is the key chord here. Note that it is a fully diminished chord, in contrast to the half-diminished chord that pops up in each mode. A fully diminished chord is four chords in one; each of the four notes in the chord is the same distance from the next, a minor-third, so any of the notes can be the root without changing the type of chord (i.e., this exact chord can be named as Ao7, D#o7, F#o7, or Co7).
A fully diminished chord that contains the root of the I chord (here, the A note) resolves well to the I chord. This is because they share one note and there is a half-step chromatic pull between two other notes, from the #2 and #4 in the diminished 7th chord to the 3 and 5 of the tonic chord (in this case, C towards C# and D# towards E). There is a name for this — a “common-tone diminished seventh. ” This chord is sometimes designated without a Roman numeral function, as a cto7 chord, and sometimes as a #iio7 chord with an inversion showing the bass note (making this a Co7/D# chord). I’ll go with the former and Ao7/D#, shortening to just Ao7 in the examples. A couple of ways to approach it:
D7 Ao7 A -2-2-2---2-2-2------------ -1-1-1---1-1-1---2-------- -2-2-2---2-2-2---2-------- -0-0-0---1-1-1---2-------- -----------------0-------- --------------------------
D7 Ao7 A ------------------5------- -7-7-7----7-7-7---5------- -5-5-5----5-5-5---6------- -7-7-7----7-7-7---7------- -5-5-5----6-6-6---7------- ------------------5-------
After resolving back on A, there is a non-diatonic major IV chord, F#, that is a secondary dominant for the B chord that follows (a V/II) chord. Note that both by function and by charting the individual notes as we did above, making the F# chord an F#7 chord, with an E note, should sound good here too, and in fact it does.
The B itself is also non-diatonic, a major II chord. Arguably this chord is borrowed from A Lydian. But what I think is actually happening here is that it is yet another secondary dominant — a V/V chord that creates an expectation of resolving to an E chord. You can hear what this sounds like by actual playing the E chord; it totally works, and gets you back to A. But instead, the B chord deceptively resolves to the IV chord on the way back to I.
As noted above, on the third A chord the second time through, the song goes into a mixolydian chorus of A – G – D, or I – bVII – IV, followed by the opening riff of the song.
The solo has many possibilities and permutations, but the core of it really follows the important notes of the chords that we already discussed. At a high level (and where there are options, the first is the easiest and last is hardest):
- Play A major over the diatonic chords
- Over C#7, either (1) outline the notes of the C#7 chord or (2) play the F# harmonic minor from which it came.
- Over Do7 – Ao7, either (1) simplify to A major pentatonic to avoid the clash between the C# in the scale and C in the chords; (2) play a diminished arpeggio of the Ao7 chord; or (3) stay with the A major scale but substitute the C note for C#
- Over the B, either (1) play the individual notes of the B major chord as an arpeggio; (2) play the A Lydian scale from which it was borrowed; or (3) try a blues sound with B minor pentatonic or B aeolian (which has the same notes as the D major scale and leads nicely to the D chord that follows) or even B dorian (which is halfway between A Lydian and B aeolian/D major)
- Over the D chord, either (1) play the individual notes of the D major chord as an arpeggio; (2) play the D major scale (which equates to A mixolydian); (3) go back to the A major scale; or (4) try D minor pentatonic or D aeolian or D dorian.
- Over the A – G – D of the chorus, either (1) play arpeggios of those chords or (2) go to town with the A mixolydian mode.
The key to the Jerry’s solos, though, is hitting the significant notes from the analysis earlier and connecting them with chromatic passing tones. When you’re as good as he was, you play it by ear.