Bach takes this interval in one hand, the cascade motive as it’s been until now in the other,

and combines them. (The notes of the diminished third are bridged by an intervening one, but the interval’s presence is no less overt for that.)

In the annals of great creative conjunctions— Newton’s yoking of apples and planets, Donne’s likening of separated lovers to the arms of a draughtsman’s compass, Picasso’s smuggling of African masks into European art— this fusion of uncanny interval and straightforward motive deserves an entry of honor. The energy this fusion releases, moreover, would be the envy of a star’s, resulting as it does in one of the most powerful modulations in the history of music.

To understand how Bach effects this modulation, we need to look at the forces at work in a diminished third. The lower note of this interval strongly tends a half step upward,

while it’s upper note strongly tends a half step downward: