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The song Tornado of Souls by Megadeth is in the key of Bm. The solo plays over a progression of power chords that goes B5 - G5 - E5 - F#5 - A5. Over the E5, the solo first plays an Em arpeggio but then changes to E major. What's the theory behind this? I don't think they meant it as a dorian thing, but I could be wrong.

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It's a trick used in music. It's called using the parallel key. Chords (and notes) from E major can and are used as alternates to E minor and its chords/notes. Since the chords used are known as 5s, with no major or minor third, solo notes can be from major and/or minjor, since there's nothing to clash.

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