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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Imagine composing an ornate melody, then stretching it out so it moves twice as slow, and somehow when you layer the stretched version onto the original, they match up beautifully: One shape, two different speeds. This is what Bach has done in this canon (but he also made sure that the consequence of both lines also blends into the harmonic implications of the chorale melody, which must also past through both lines…)

Let’s see what our augmented canon looks like on the page. Here is the opening of the ‘quick’ line:

And now see the same shape, moving in augmentation:

Those images are from the print, which as I mentioned is in open-score, and particularly difficult to read. The left hand is on the 2nd and 4th lines, the pedal sandwiched between them on line 3, and, did I mentioned? Four different clefs. Have a look:

We’ve seen this type of composition before on the podcast. Here is the episode from Season One about the augmentation canon (as well as in inversion) from the Art of Fugue:

Stay tuned for the final variation!

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The subject of the last several episodes has been Bach’s canonic variations on a Christmas tune by Martin Luther himself. A major inquiry into this work is its existence in two versions: engraved and handwritten. The published version (for reasons explained in the episode) doesn’t fully solve the canonic lines, as seen here:

Notice how the notes of the bottom line don’t continue after the fifth note!

See two other canons, each with the comes omitted:

Variatio 2 omits the follower after only three notes, while the last image shows the second voice dropping out after two full bars.

Because of such condensed notation, a copy working out the solutions would be necessary for anyone wishing to play the work; Bach himself made one— and couldn’t stop himself from making very minor changes. Those intriguing revisions are the subject of this episode.

P.S. In the episode I mention that for time’s sake, I cut three revisions from our comparative study of the canon at the 7th. For reference, they are found below. The staves show the pedals and left hand, engraving copy on top, followed by the handwritten copy:

Bar 7:

Bar 13:

Bar 22:

P.P.S. I received a notification that the featured recording of Stravinsky conducting his own arrangement is banned in certain countries in which I have listeners. Pardon me if the sound drops out at the end of the episode! If this happens, you’ll have to look the piece up on your own: it can be found searching Stravinsky’s music under the title “Choral-Variationen” (or “Chorale Variations” in other languages) with either W83, K087, or BH-2629 as the catalogue number.

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