Paranoid Android – Radiohead

tldr: Paranoid Android has three parts plus a coda based on the second part. Each part explores two keys/tonal centers and contains some ambiguity by design.

  • Part I has a repeating progression that seems to start in C minor, dorian mode, but then either changes to G minor or reveals that the key was G minor all along (in which case the opening Cm was the iv chord). Two notes of a Cm and then Gm are held down while a walking bass line converts those chords into other related chords. Each phrase ends with a G dorian progression, represented by a Gm6/Eø chord. Part I ends by transitioning to an E7 dominant chord that leads to an Am riff (V7 to i) that starts the next section.
  • Part II opens in the key of A minor and goes back and forth with its relative major key, C major. The A minor portion uses the harmonic minor scale and a riff equating to Am and G#b5 chords, the latter of which operates a substitute for an E7 chord (i to V7). The C major portion is based around a I – bVI – bVII progression of C – Ab – Bb that borrows the latter two chords from the parallel minor key, C minor. When the distortion kicks in, the A minor part bends its concluding D note to D# (making the implied chord a G#), and the C major part switches to power chords, which makes the whole thing take on a C minor feel. The lead over the riff uses the C minor pentatonic, then, over the power chords, switches between C major pentatonic, C minor pentatonic, and the C whole tone scale. The section ends on a chromatic chord walk-down of C – B – Bb – A – F.
  • Part III has a repeating, slow progression that starts with a chromatic progression in C minor and changes to a diatonic progression in D minor. The C minor portion is based in a chromatic movement along the bass notes, from C to B to Bb to A (the chords being Cm, G/B, Gm/Bb, A). The A chord is the V chord for the next key, D minor, and leads to a diatonic progression down the D minor scale with the roots/bass notes of the chords Dm – Dm7/C – Bb – F/A – Gm – F – E. The major E chord is a secondary dominant V/V leading to an A chord, which then resolves deceptively back to Cm instead of Dm to start the progression again. The final time though, the E chord is repeated twice, leading to the Am that opens the next section (that is, serving as a V chord to change the key back to A minor).
  • The coda returns to the distorted portion of Part II and its ambiguity between A minor and C major/minor. The lead over the riff focuses on the C and D# notes, suggesting C minor, and the lead over the power chords uses C dorian, which likewise suggests C minor. The song ends with a chromatic downward progression of C – B – Bb – Ab.

Part I

Part I of Paranoid Android is built around Cm and Gm chord shapes and a walking bass line that adds and replaces different notes in those chords. There is ambiguity in the key based on the similarities between the C minor and G minor keys, which normally differ by one note (Ab vs. A), and have the same notes when C minor is in the dorian mode (which raises its Ab to A).

When the song begins, it seems to be in C dorian, with partial chords built around a Cm-chord core (specifically, its minor 3rd and 5th) that are altered by a walking base line:

  Cm   Cm7/Bb F9  Cm6/A Cm7/Bb
------------------------------
---8-----8-----8-----8---8----
-----8-----8-----8---8---8----
------------------------------
------0------8-----0----------
-8-----6---------------6---6-5

However, the song then resolves to a Gm chord, indicating that perhaps the Cm was the iv chord of G minor all along. The key is now G minor, and the Gm chord is itself then altered into its related major chord, the III chord, by the walking bass line:

 Gm   Bbmaj7/	A  Bb
--------------------
---3-------3-----3--
-----3-----3-----3--
--------------------
---------0-----1----
-3------------------

Then, a natural 6 note is added — E instead of the Eb note of G natural minor — reflecting that we are in G dorian:

Gm6  Asus4 Eø  Asus4
-------------------
-3----3----3-3---3-
-3----2----0-0---2-
-2----2----2-2---2-
-------------------
-------------------

(there is room to disagree about how I named these partial chords — in particular, Gm6 and Eø, which have the exact same notes)

The Eb note previously appeared only in the Cm portion. If we have always been in the key of G minor, this reflects a change from G natural minor to G dorian. If the Cm part is viewed as being in the key of C minor, dorian mode, then the Eb note only ever appeared in the first key, and Part I can be characterized as simply alternating between C dorian and G dorian. I’m inclined toward this latter view.

Finally, there’s a transition of arpeggios of Gm6 – Dm9 – E7, again consisting of two notes held throughout while other individual notes walk around (in bold):

 Gm6 Dm9  E7 Gm6 Dm9  E7
--0---0---0---0---0---0--
--3---3---3---3---3---3--
--3---2---1---3---2---1--
----------2---2-------2--
--------------1----------
--3---1---0-------1---0--

(play notes individually, not as chords). Note that the second Gm6 is voiced a little differently in the bass than the first.

The concluding E7 chord is non-diatonic (the difference in the E7 being a major 3rd, G#, instead of G) and serves as a dominant for the key of A minor, where the song moves to begin Part II. However, it doesn’t resolve there the first time through; there’s a deceptive resolution back to Cm for more of Part I.

*Too much detail alert: The E7 to Cm is a good deceptive resolution. Dominant chords a minor third apart are related to one another through a shared diminished chord, and E7 is a minor third (three frets) away from G7. (The relatedness is that E7 is one note different from Fo7; G7 is one note different from G#o7; and those two diminished chords have identical notes). Because of this similarity, E7 can substitute for G7, which is the dominant that leads back to Cm.

Part II

Part II opens in A minor, with a distinctive riff that includes a minor third and major 7, signifying the use of the A harmonic minor scale. However, the song then shifts to its relative major key, C major, and goes back and forth between the two keys.

The opening riff in A minor goes something like this:

 Am   G#b5   Am    G#b5
------------------------------
------------------------------
------------------------------
------------------------------
---3-----3-5---3---5-3h5p3----
555-5-444---555-5-4-----------

The first chord represented by these notes is Am. The second is a G#b5 chord (a major G# triad with a flattened 5, alternatively viewed as a #4). While its notes are all from the A harmonic minor scale, it isn’t the typical diatonic vii chord — that would be G#dim, which has a minor third instead of the major third in G#b5. You could view it as just an altered major version of that chord, but to me a better interpretation is that the G#b5 chord is a substitute for the V chord, E7, as it contains the important guide tones (the 3rd and 7th) of that dominant chord:

G#b5:   G# C  D
E7:   E G# B  D

After this riff several times, there is a C chord that changes the key to C major. The key change is a smooth one both because (1) C major is the relative major of A harmonic minor and (2) not only are the C and D notes of G#b5 included in the C major scale, but its G#/Ab note features prominently here as a borrowed note from the related minor key, C minor.

Specifically, the C major progression uses two major chords — the bVI and VII chords, Ab and Bb — borrowed from C minor. The pattern here is essentially C – Ab – Bb repeated. Layered on top from other instruments, I also hear some other notes mixed in, notably an F note that sounds nice added to the Ab as an Ab6 chord (4×6564). Adding a 6 to the Bb chord sounds good too (6×8786).

The song then returns to the A minor riff through a chromatic C – B – Bb downward chord movement.

When the distortion kicks in, there are two changes. First, in the A minor part, the G#b5 portion of the riff adds a bend up from the D note to D#, turning the implied chord into a G# chord instead of G#b5. This makes the A minor key more ambiguous, as G# has already been established here (within the key of C major) as a borrowed bVI chord from C minor. And the lead over this part appears to use C minor pentatonic, with a heavy focus on the C note. If we view this part as suggesting a key change to C minor, the A note would be a C dorian natural 6th, and the G# note (enharmonically, and Ab note) would be the regular flat 6 of C minor, so the riff would be sort of going back and forth between those two notes and modes.

The second change is that the former C major part switches from triads to power chords, which makes the chords themselves neither major or minor. Because the other chords were borrowed from C minor, and the C5 tonic now is non-specific as to whether it is major or minor, there is ambiguity as to whether we are in C major or C minor. The chord pattern also changes to something like this, adding in a quick B5 passing chord:

 C5 Ab5 Bb5  B5  C5... 
------------------------------
------------------------------
------------------------------
-10\-6---8---9---10\----------
-10\-6---8---9---10\-{repeat}-
--8\-4---6---7----8\----------

The first solo really takes off here. First, over the C5s, there’s a little two-note riff from C major, and over the Ab5 to Bb5, a similar two-note riff from C minor, which makes sense as you switch to chords borrowed from C minor:

    C5         Ab5 to Bb5
---------------------------
-8-10-b12-8---9-11-b13-9---
---------------------------
---------------------------
---------------------------
---------------------------

Then something really interesting happens the second time through starting over the Ab5 chord:

  Ab5   Bb5   G7
------------------------
--7h9---5h7---3p0-------
------------------------
------------------------
------------------------
------------------------

The notes, in order, are F# – G#, E – F#, and D – B. At first look, they didn’t make a lot of sense to me — in particular, dissonant E and F# notes over a Bb5 chord that has an F in it. What I think is happening is that the lead uses the C whole tone scale here up until the last note (the pulloff to 0 over the G7 chord, which works because that B note is in G7). The whole tone scale is a six-note scale consisting of every other note of the twelve overall notes. There are only two possible versions (one that has C and one that has C#).

Here’s the logic that I think is behind the lead work. The underlying chord progression primarily consists of three major chords that have roots a whole tone apart — C, Bb, and Ab. So the lead plays along the whole tone scale that includes those roots — C, D, E, F#, G# (Ab), A# (Bb) — notwithstanding that other notes in those chords are not included in that scale. You can hear the dissonance from the conficts with those other notes, which makes it sound weird and awesome.

Part II then ends with a chromatic walk down from an A chord to an F chord, which is the IV chord in C major.

Part III

Part III opens with a key change from C major to C minor. This section is characterized by two descending chord progressions in two different keys. The first, in C minor, descends through chromatic voice leading. The second, in D minor, descends through diatonic voice leading.

First, Cm – G/B – Gm/Bb – A. The chromatic voice-leading line proceeds in half-steps along the bass notes — C, B, Bb, A. The Cm and Gm chords (the i and v) are from the natural minor scale. The G/B is a major V chord (inverted with the B note in the bass) from C harmonic minor. The A is non-diatonic and serves as a dominant for the Dm chord that opens the next progression (A being the V chord of the key of D). Even though the A chord is somewhat foreign to C minor, it follows naturally in this chromatic progression because the A and C# of the A chord are a half-step down from the Bb and D of the preceding Gm chord.

So, there’s a change to the key of D minor from that A chord to Dm (V to i). Then, after another A chord, the diatonic descent through the Dm scale begins: Dm – Dm7/C – Bb – F/A – Gm – F – E – A (or i – i7 – bVI – III – iv – III – V/V – V). The descending D minor scale in the bass notes is bolded below:

Dm:               D  F  A
Dm7/C:         C  D  F  A [] 
Bb:          Bb   D  F
F/A:        A  C     F  [][] E
Gm:       G  Bb   D
F:      F   A  C
E:     E   G# B
A:     E    A   C#  []

(brackets where note moved to bass)

Note also how similar these chords are; until the E chord, they are all Dm chord variants, related-chord substitutes for Dm (Bb and F), or substitutes for those substitutes (Gm for Bb). This consistency, I think, puts the emphasis on the descending bass line, which is what changes one chord into another, not unlike what we saw in Part I of the song.

Although the E bass note is part of the descending pattern, a major E chord is non-diatonic (the diatonic ii chord would be D diminished). It is instead a secondary dominant V/V chord that leads to an A chord that concludes this section. And, although the A chord is also a V chord implying a return to Dm (V to I), there is instead a deceptive resolution back to Cm, which begins the pattern anew in the key of C minor. Compare how A to Cm works nicely as a deceptive resolution through half-steps in the opposite direction as the expected resolution to Dm:

A:    A  C#  E
Dm:   A    D  F  []

vs.

A:    A  C#  E 
Cm:     C   Eb  G

Instead of the C# and E each moving up a half-step, they go down a half-step to return to the opening Cm chord.

The final pass through this progression ends on two E chords. E, as just discussed, is the V chord in the key of A minor. And, instead of serving as a secondary dominant for A this time, the E is used as a primary dominant changing keys to A minor in the coda.

Coda

The coda brings us back to the riffs and progressions of Part II. Over the riff, the lead seems to focus on bends involving the C and D# (Eb) notes, which again suggests that the riff may be in C minor/dorian by this point instead of A minor.

Over the C5 power-chord part, the lead to me appears to be based in C dorian even though the chords are borrowed from C natural minor, which creates some interesting dissonance with an A note over the G#5 power chord.

Finally, there’s a chromatic chord walk-down of C – B – Bb – Ab to end the song.

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