: What is a roman numeral analysis of the chords from Coldplay's "God put a smile upon your face"? I'm trying to apply Roman numeral analysis to some pop songs and am a little stumped on Coldplay's "God put a smile upon your

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In some cases, Roman numerals aren't all that helpful, and this piece might be one of them.

In my opinion, Section A is best understood by considering two simultaneous actions:

The chromatic descent in the bass from E, through E? and D, to the tonic D?.
And the constant presence of the tonic D? in all four of the chords. The D? is obviously the root of D?, it's the 6 of E6 (spelled as C?), the 7 of E?7, and the maj7 (again spelled as C?) of Dmaj7.

These two aspects make it very clear that D? is tonic, and that's ultimately what drives the harmonic motion: tension and resolution to that D?.

The B Section is less clear, but there are two things to consider: B Sections often go somewhere else tonally, and here it seems to be rooted in A, which is enharmonic to ?VI (B??), a relatively common move dating back almost two centuries. Note also that the overall tonic D? is still present in every single chord, though now always spelled as C?: it's the third of Amaj7, the sixth of E6, and the fifth of F?add9.

In other words, Coldplay makes clear what the tonic is by playing it in every single chord of the song. If you try to sing a D? throughout the song, you'll see that it fits everywhere!

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I tried listening to the song and the progression in the A section is pretty non-functional which means there are going to be some ambiguities when doing the analysis.
The B section sounds like I-V-VI-I in the key of A (I'm not sure about the tensions, but if you're right then Imaj7-V6-VIadd9).
If I'm hearing it right each chord in the A section is played on the guitar by moving the open C chord shape around but leaving the open stings open, so each chord has an E and G though I think you got the basic movement down. We could interpret this section to also be in the key of A as III#9#11-V#9-bVb9-IVadd11 with the G and/or E providing the tensions on each, but I think you could make an argument for analyzing this in Db/C# since during the verse the bass is alternating between B and C# throughout. Either way there are many non-diatonic tones throughout. I like the interpretation in A since the III chord could be thought of as a sort of substitute for the I.