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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Let’s delve into a third variation from Bach’s 1747 masterpiece, “Some canonic variations on the Christmas song, ‘From Heaven Above’ for the organ with two keyboards and pedal, by J.S. Bach.”

Two versions of this piece exist: the ‘fair copy’ and the ‘publication’ (Stichfassung), which present the variations in a different order. In this episode, we follow the publication, where the canon at the 7th appears as the third variation.

The previous two variations featured canons between right and left hands, while the pedals carried the slow moving chorale melody. This variation introduces something new: a canon between the pedals and left hand. On that page that looks like this:

Above those two lines, the right hand plays a quick-flowing accompaniment marked cantabile, but the chorale melody is missing…

Note the rest up top, and the downward-facing stems on all the notes. This implies a second voice is coming: the Christmas melody sung in half notes.

Together, the two voices of the right hand, combined with the canon between the pedals and the left hand, create a four-voice texture— the previous variations were in three voices. As we’ve seen in his other late canonic works, Bach will gradually increase the complexity of the canonic treatment toward the finale.

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I never knew the authentic version of the world’s most famous canon, having only known arrangements which conceal the fact that the music is indeed a canon in three voices. Here is what the ‘real’ canon looks like:

It continues for over 50 bars as a three voice canon at the unison. In my brief survey of this piece, I found one theory that suggests the 9-year-old J.S. Bach was in attendance at the first performance in history.

While the canonic treatment is clever and not worthy of our loathing— we blame its ill fate on others— Bach’s contributions to the genre outshine this example. We continue with Bach’s canonic art in the next episodes.

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Continuing our mini-series exploring Bach’s canonic variations on the Christmas song, ‘Vom Himmel hoch da komm ich her’ BWV 769, we listen to the second canon: a canon at the perfect fifth.

Here is what the initial shape looks like in the right hand:

So the same shape must be imitated down the perfect fifth. It appears like this in the left hand:

I briefly mention the difference between ‘tonal’ and ‘real’ answers. Although the majority of the imitating line appears a perfect fifth below the leader, several accidentals are changed to keep the overall tonality. Hence Bach here gives us a ‘real answer.’ (I.e. where the F# and G# appear in the left hand, find the corresponding notes in the right hand, note the resulting intervals are diminished fifths, not perfect.)

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The first variation in these late variations for organ, is a canon at the octave. The two hands, each on a separate keyboard, play the same shape, one octave apart, while the feet provide the chorale melody. It looks like this:

Those are the first three measures of 18 measures. That’s right: the shape is imitated note for note for 18 bars! If you’re having trouble seeing that the two upper lines are in fact the same melody, one octave apart, try this image:

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In this first of several related episodes, we will learn about Bach’s late contrapuntal masterpiece, the Canonic Variations on Vom Himmel hoch da komm' ich her, BWV 769.

The variations— although certainly not as familiar— should be considered alongside Bach’s other late achievements, the Goldberg Variations, The Art of Fugue, and A Musical Offering. They employ many similar ideas and highlight the composers uncanny ability to ‘squeeze water from a stone,’ making elaborate pieces with minimal material.

This first episode discusses the origins of the chorale melody and for what purpose Bach used this piece.

Drop me a note to tell me if you like this shorter episode length. Are you the type of listener who loves the hour long podcast? Or did this fit into your schedule better?

I mention the title page:

And the Wikipedia link to the chorale melody: https://en.wikipedia.org/wiki/Vom_Himmel_hoch,_da_komm_ich_her

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