The crazy part of [Jacob Collier’s arrangement of In The Bleak Midwinter] comes between the third and fourth verses, when he modulates from the key of E to the key of G half-sharp, which is halfway between G and G-sharp. This is a bananas thing to do!
If you don’t feel like sitting through the whole video, the bottom line is this: over the course of his “four magical chords,” Collier doesn’t just change key, he changes the entire tuning system he’s singing in. He’s able to accomplish this dazzling feat by exploiting the subtle differences between interval sizes in equal temperament and the ones in “pure” harmonic tuning. Each of the four magical chords is overall a little bit sharper than the one before, but it still sounds in tune because it also shares a tone exactly in common with the one before. David Bruce explains how this works in detail in his excellent explainer video – the crucial part is here.
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