Trying to work this one out.
From what I can gather it is in B Mixolydian, but the chords are A, B, D, E, which as far as I know do not fit any scale.
Apart from by ear, how do I know what notes to pick for each individual chord?
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Welcome back, Brian!
Mixolydian has a flat 7th scale degree.
B Mixolydian is therefore:
B, C#, D#, E, F#, G#, A, B
Harmonised it gives these chords:
B → (or B7) → I
C#m → (or C#m7) → ii
D#dim → (or D#m7b5) → iii
E → (or Emaj7) → IV
F#m → (or F#m7) → v
G#m → (or G#m7) → vi
A → (or Amaj7) → bVII
Note, these are the same chords you would find in the key of E major. Look at it series, B Mixolydian is the 5th mode of E major (Ionian).
You have the I bouncing down to the bVII and back again:
B → A → B → A etc.
In the refrain you have bIII (a borrowed chord) to bVII to IV to I:
D → A → E → B repeating
If you consider that B Mixolydian has E major as its parent major scale, the D chord = bIII is borrowed from the parallel key of E Minor (Aeolian).
More here:
And here: