Have a look at this. This is Bach beginning a canon in inversion. The follower is a 6th below the leader:

(If you can’t see that the shapes are inversions, hold up a mirror — seriously!) Yet here, only a few bars later, the imitation seems to be at a different interval:

The follower is no longer a sixth below, but a third. How rare! And going on, something else:

(We’re looking at the lower two voices in this picture, the quarter notes.) We see the canonic imitation has shifted yet again, to the interval of a second. What is happening? Dare I say… W.T.F. Bach?

This type of composition is, I believe, completely unique. I’d love to see another example elsewhere in music. Bach writes the chorale melody four times, and in all four appearances, finds a different interval at which inverted imitation works.

The man’s capacity to combine a single shape with itself, to abstract the DNA of the smallest musical cell, to spin it, lengthen it, shrink it, to construct a world from a grain of sand; this is late Bach.

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