I1)

  This guitar part is loosely in E major, with a borrowed II chord, and a brief
  modulation to D major.

      ii    V    IV   II     iv of D   I of D
    F#m/C#  B    A   F#/C#   Gm/D      D

  This section is roughly E mixolydian. I believe the guitar is playing power chords
  but it may just be octaves sometimes. The bass and guitars here sound a bit
  improvised, moving independently but transforming these simple power chords into
  more complex harmonies (right):
  
    E      D5/G  E5/A  A5/B  => (Gadd9  Aadd9  B7sus)

    E      D5/B  E5/C  F5/D  => (Bm7    CM7    Dm7)

    C/G    Bb5/C C/F   F5/Eb => (C7sus  F      F7)

    C      Bb5/G C5/F  D5    => (Gm7    FM7    D)

    E      D5/G  E5/A  A5/B  => (Gadd9  Aadd9  B7sus)

I2)

  At 0:22 a blast of bluesy 7th chords in E, with a temporary dissonant C7#9 chord
  (distortion makes this chord hard to identify). These bar lengths are ad-libbed
  (31 beats total) and sometimes the chord changes on an eight note:

    8          6      7       10
    E7         A7     C7#9    F#m7

  The guitar falls out and some simple melodies outline E and A chords.

V)

  This section is in D dorian, but playfully borrows A and D from mixolydian. The
  Cm7 is a bit like a Neapolitan Eb chord (there's a real one later). These "add13"
  and "add11" are just B notes. Probably played as 5th fret of the G string and
  open B string.

    Dm7add13              Cm7         A7     D7add13     Dm7add13  G7add11
    Hey mister hey mister out of this picture.       I'm only the  sister.

  Now a long string of secondary dominant resolutions. This section lacks a strong
  tonal center, but roughly starts out in E dorian:

    V/V    V            i
    F#11   B11          Em7
    Royal- ty I learned I will become

  Now shifts to G major, though it doesn't fully resolve:

    V/V                     v/V              V7
    A7                      Am7              D13
    queen of the cast-offs. I will thrice refuse.

  This D13 is a real 13th [D F# A C E G B] (across multiple guitars), not just a D7
  with added 13th. I think the F# is only in the vocal.

V2) (same progression)

  At 1:27 the bass plays out of sync with the guitars in a wonderful way. Following
  a bar of Dm, the guitars play Cm7 and A7 over a full bar, but the bass seems to
  hold the Dm and cram the last two chords into the last 2 beats:

  guitars:    Dm7                  Cm7           A7
  bass:       D           D        D        Eb E C     A
           Oh lover oh lover,      where is the  thun- der?
  
  So the bass ends up playing D and E natural under Cm7, and C natural under A7.
  Maybe a mistake (?), but sounds amazing, as if those last 3 bass notes are 3
  different chords.

B) (1:56)

    F#m/C#  B  A  F#/C#  Gm/D  D

  Here the verse progression transposed up a whole step with some small
  variations. Before the B chord we have a real F Neapolitan.

    Em7        FM7  B  E7        Em7   A7

    G#11  C#11         F#m       B7  Bm7  E7

E)

  To end we get the intro guitar, not tuned up, but rather *down* a whole step.
  I think this is done for two reasons: So the bridge's E7 can lead into the Em
  (this major to minor change is almost thematic to the song), and so that we're
  spit out in the key of the verses.:

    Em/B   A   G  E/B   Fm/C  C    Dm

I)

  See B2 section below. Starts in Eb major, ends in E major.

  A vocal melody is interrupted by a A-G-G bassline, making it sound like
  A7 harmony, but this is a trick. As the bass continues alone we start to
  hear this as what it is: 2-1-1 in G major. The guitars come in with G
  chords to confirm.

V)

  The verses starts in G mixolydian, with bass as a pedal. You can see the
  pattern they're building in the progression:

    G  C/G
    G  F/G  C/G
    G  C/G  F/G  C/G
    G       C/G  F/G  C/G
    G

  A bit of the pattern is then repeated in Eb mixolydian:

    Eb           Db   Ab
    Eb

V2) (with vocals)
B1)

  A lot happens in these 4 chords. The Bb is the V of Eb (shifting from
  mixolydian to ionian). The Db teases that we're back in Eb mixo, but
  instead of leading to Ab, we get harmonic planing down to a C major. The
  melody still has Eb, giving it a jazzy sharp 9 sound, and makes the
  following F chord sound like it functions as the V of Bb. So really the
  C is the V/V of Bb.

    V           VIIb    V/V (of Bb) V
    Bb          Db/Ab   C           F

  A full resolution to Bb is skipped in favor of 2 thrilling modulations:

    I      I
    Db     Eb  (We get a couple nice pentatonic lines here)

B2)

  We start in Eb major, slipping in a borrowed iv chord:

    I      iv          I
    Eb     Abm/Cb /Ab  Eb/Bb 

  The borrowed Abm is used to modulate to Gb major:

    ii   V        IV         V         V7      I
    Abm7 Dbadd9   Cbadd9/Eb  Db        Db7/Cb  Gb/Bb

  A i (Gbm) is used to modulate to E major:

    ii        I        ii   I  V7          I  iv       I
    Gbm/A     E/G#     E/F# E  B7sus/E     E  Am6/E    E

End)

  The G#m chords are dotted with brief A chords then we resolve to E:

    iii            V  I
    G#m7   A  x4   B  E

    v/II    II
    C#m7    F#7add11