Pyramid song
Pyramid song by Radiohead is a memorable and interesting chord sequence, in a song which feels freighted with shifts in emotion. But from a harmonic point of view, what is going on?
Initial root sequence
Graphically tracing at first just the roots of the chords in harmony space (while playing and listening to the full chords) we have:
F# G A G F# F# E G F#
The Rest or ‘Home ‘ chord appears subjectively to be the F#.
Moving the key window around visually to find places where this sequence of roots could fit the diatonic scale, there are only two such positions – one with the F# in the phrygian spot (middle of the ‘east coast” of the key window) and one with the F# in the locrian spot (top of the ‘east coast” of the key window).
So at first sight, this could be in F# phrygian or F# Locrian.
Initial chord qualities
Now tracing the full chords, the first two chords are a major chord followed by a major chord whose root is a semitone higher. But playing with key window positions demonstrates that this sequence of two chords fits no diatonic key naturally.
Leaving aside the quality (chord shape) of the F#, the first five chords are moving in a way that is characteristic of the phrygian mode. (By contrast, in the very rare Locrian mode, only the G chord would have the right quality - so we can discount this.)
Flamenco feel
Guitarists may recognise the first five chords as very close to a typical flamenco sequence (related to a flamenco cadence). This falls easily under the fingers on a guitar by moving an E shape on the inner strings up and down and using the outer strings as drones.
Picardian modes
But we still haven’t come up with any good reason for why the first chord quality in this piece might be major rather than minor.
Harmony Space extends the idea of a picardian mode to all minor modes. A picardian mode is one where the home or I chord would normally by the shape of the diatonic scale be minor, but it is altered by fiat to major (especially at the end of pieces – a ‘happy ending’). This is found extensively in renaissance music and also in recent popular music. Surveying recent popular music, the picardian mode can be found in distinguishable ways all the minor modes (minor, aeolian, dorian and phrygian) and so Harmony space reflects this.
An emotional shift
Thus, a candidate perspective for making sense of 8 of the 9 different chords in pyramid song is that they are in the picardian phrygian mode. At the 6th chord, after revisiting the initial F# major chord, the root is played again as a minor chord, matching the uninflected phrygian mode. This gives an evocative emotional shift.
Details
Now there are just three details to account for. On the A chord, what is the inverted sixth chord doing there? This is straightforward – it’s an inverted pedal or drone note referring back to the pitch of the phygian centre.
What is going on with the E major add 9?
Two apparent puzzles here: why the add 9 quality, and why on a major rather than minor chord base? A major quality at this location does not even fit the phrygian mode. The first part of this is straightforward – the ninth is another inverted pedal note reinforcing the (Phrygian) home pitch. But why the major quality?
One candidate reading
One interpretation is that there has been a momentary modal modulation (or borrowing). The closest candidate modal modulations are (a) changes to a relative mode (where the key window doesn’t move, but the home pitch and location inside the key window changes) and (b) changes to parallel mode where the home pitch does not change, but the key window moves, causing the location of the home note relative to the shifted key window to be altered. Given the inverted pedal reinforcing the existing home pitch, we can provisionally discount a relative modulation. Only three parallel modes could account for the shape of the E - the parallel aeolian, dorian and mixolydian. Of these, the least move is to the aeolian. also the direction of travel of the sequence here is distinctively aeolian. This mode fits both the E major add9 and the preceding F# minor. So the claim is, it may be musically useful to interpret this as a momentary modulation to the parallel aeolian.
Thumbnail Summary
• Picardian phrygian shuttle modulates at bottom to parallel aeolian.
• Modulation yields thrilling blend of aeolian and phrgian cadence
• Inverted pedal keeps unity
Criticisms of this interpretation
Immediately after these two chords there is a short flamenco cadence G major F# major, reverting back to the picardian Phrygian mode. The root of the G in this cadence does not even occur in the F# aeolian mode. So the putative momentary modulation is only brief. So is there any musical value to this interpretation? Can it help explain the emotional shift felt in that part of the song.
Pragmatic practical testing of the hypothesis
If it really makes sense to assert that there has been a modulation to the parallel aeolian, then speculative variations of the piece that extend the putative aeolian section should make sense musically. To my ear, this does work, for example using an aeolian I VII VI V movement at this point. This seems to want that the V is inflected to a dominant, identifying the mode as minor rather than aeolian. The dominant would give the option of a neat V I cadence folding back to the former phrygian home.
Tracking emotional shifts?
A picardian twist to the Phrygian mode might be associated with an assertive masculine energy, though very tempered in this particular song. Pivoting on the home chord to the minor tends to precipitate sadder more accepting mood. Drifting into an Aeolian shuttle often reflects sad helpless moods, but here the mood is pulled back with a slightly more assertive picardian phrygian cadence. Your interpretation may vary. Songs should never be painted by numbers. But exploring how a good one works, then putting that totally to one side and writing your own can be rewarding.