I would not call this tonic expansion.
Tonic expansion is a concept for classical music where key changes are essential to the musical structure.
That doesn't really happen in the music of The Stokes. So let's dispense with tonic expansion and try to approach the music on it's own terms.
We need some rough outlines of the choruses. I will only try to approximate the rhythms of two guitar parts. The letters are single notes except the guitar in NYC Cops where chords are listed.
Hard to Explain
Guitar| D C B | D C B | B A G | B A G |
Bass | G G G G | G G G G | B B B B | A A A A |
Guitar | D B | A B | E B | A B |
Bass | G G G G | G G G G | B B B B | A A A A | x2
Guitar keeps repeating the same thing...
Bass | G | G | E | E |
| D | D | E | E |
Guitar |Cmaj| / |Fmaj9| / |Cmaj| / |Fmaj9| / |
Bass | C | C | F | F | C |C (E)| F | G |
There isn't much to say harmonically about Hard to Explain. It's just a
G chord with rhythmic figuration and some passing tones the
C's in both parts. Harmonically nothing is expanded, because there's just one chord. The
B in the bass is interesting, because the chord third isn't normally played in rock music, except for arpeggiating the whole chord or walking bass, which this is not. The following
A in the bass is a passing tone and that adds a nice tension before it resolves back to
The next two use what I think is a formula in a lot of indie rock: superimpose two basic triads to make a larger extended chord. The extended chord is broken up into multiple riffs so it's never heard clearly like a block chord. The riffs sort of shift around the larger extended chord. Multi-tracking and lots of reverb help blend it all to a big shimmering sound.
Barely Legal combines
G B D and
E G B into
E G B D. All the notes of the chorus fit that
vi7 chord except the
A in the guitar - a neighbor tone - and the
A in the bass - a passing tone. At the moments we hear only tones
G B D is it a
G chord or a portion of the
vi7 chord with
E omitted? The music just shifts back and forth between the two sets of tones so I like thinking of them as just parts of the one larger set, the
vi7. Compare the chorus to the verse where we have
I IV I IV V vi V. That's pretty traditional harmony. That progression could be a hymn! Each chord is distinct. The chorus is treated differently using a shifting/superimposing of
NYC Cops combines
C E G and
F A C into
F A C E G. I voiced the guitar chords as
x33010 to approximate the recording (I'm not sure exactly what's played.) The same shifting back and forth and superimposing like Barely Legal happens here. Compare the chord treatment in the chorus to the verse. The verse mostly moves between distinct
G chords. But when the chorus arrives the
C chord is sustained when the bass goes to
F. Those parts superimpose to make a big major-ninth chord.
You could disagree with my superimposed harmony idea and say the two chords are being played separately. That's fine. With that point of view you would have two super common chord pairs: relative major/minors
I-IV. All rock music uses those. It's barely worth mentioning. Nothing special is explained by those chord labels. I think superimposed harmony is more descriptive of how the two guitar parts work together in the choruses.