Matt H. answered 12/11/14
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Hi Andrew--
The song's key is dictated by the notes that form the melody and combine to form its chords.
The basic chords in this song (with some little variations here and there for extra Coldplay-ness) are:
D# minor, B, F#, and C#
The scale whose notes run through that collection of chords is the F# scale. Its notes are:
F#, G#, A#, B, C#, D#, E#, and back to F#
"E#" is kind of a weird occurrence--we are often told that E's and B's don't have sharps, and that E# is really just an F, and while enharmonically that's true, you can't have 2 notes in a scale that have the same "first name," because the written notation would get confusing. So in this key, the note that would be played on the "F" key on the piano has to be notated as an "E sharp" because we already have a note with F in its name, which is the F#.
Anyway, since the scale that runs through these is the F# scale, the song is said to be in the key of F#. (Those notes are the same in the D# minor scale, and since the D#minor chord is also featured prominently in the song and feels kind of like a "stopping point," as does the F# chord, you could also consider the song to be in the key of D# minor. They would be written the same way, with the key signature looking the same: 6 sharps, including the weird E sharp. D# minor is considered the "relative minor" of F#.)
Not dorky enough for you yet? Consider that F# is enharmonically the same as G flat, so you could write it in that key as well. Your scale would be:
G flat, A flat, B flat, C flat, D flat E flat, F, and back to G flat.
We need to call it a "C flat"--even though it is played with the B key on a piano--for the same scale-rule reason in orange type above.
And since you could write the key as G flat, you could also consider it to be in the relative minor, which would be E flat minor--equivalent to D# minor.. G flat or E flat minor are both notated with 6 flats in the key signature, and E flat minor is considered the "relative minor" of G flat.
ANYWAY, I hope this helps. Note that if you buy the sheet music for this, it may very well be written in a different key. But if you plunk along with the recording on a standard-tuned guitar or keyboard, the key information above is accurate.
All best,
Matt in NY