UPDATE: One of my astute listeners pointed out that it is in fact Jones’ review of Butler’s work in Music & Letters, and the original work by Butler is this book. Thanks for the correction!

Don’t miss the end of this episode where I play three of Bach’s earlier settings of the same tune, BWVs 700, 701, & 738!

We finish our study of this late masterpiece by reading some scholarship on the two different versions Bach made of his canonic variations on Luther’s 1539 melody. Whereas Wolff suggests both versions could be ‘authentic,’ Gregory Butler reveals that he believes the Original Edition was a mistake— one that prompted the handwritten fair copy.

As for the signature in the augmented canon— the finale in the fair copy— it is first spelled out in bar 19. See the top line, G, F#, A, G#:

These are not the same notes, but it is the same shape as B-A-C-H. The line that imitates this upper line is moving at half its speed. Therefore, it must repeat the spelling twice as slow later in the piece. See how it is joined by an independent line of counterpoint, now singing out the signature in parallel 3rds:

Two signatures in two different final movements!

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Concepts Covered:

In this episode, we explore Bach canonic variations, as well as other chorale setting of BWV 700, BWV 701, and BWV 738, and their connection to the Luther 1539 melody. We dive into Bach scholarship, focusing on insights from P. 271 and Gregory Butler’s Bach Research. You’ll also learn about Bach's original editions and the handwritten fair copy Bach created, as well as the significance of the augmented canon signature — the iconic B-A-C-H motif. We examine Bach counterpoint techniques, analyze Baroque music in detail, and explore Bach's final movements in these canonic counterpoint studies. This episode serves as a gateway to understanding Bach's late masterpieces, with special attention given to the use of Bach’s signature in these variations.

Today, as we did in episode 5 of this miniseries, we’ll examine the revisions Bach made from engraving copy to handwritten copy. This is an important view into the composer’s workshop, and unlike clear ameliorations between layers in his other works, the two versions of BWV 769 present a unique challenge in seeking the “best” version.

Changes like this (first beat, alto) are minute, yet fascinating:

(Top: engraving. Bottom: fair copy.) Bach made three revisions dealing with a similar leap of a fifth.

The most important revision in the inverted canon variation, is in this pedal line:

(Top: engraving. Bottom: fair copy.) Notice the ornament in the fair copy— we often see more ornaments in handwritten versions, but this is not consistently the case in this piece.

Heading over to the augmented canon, this revision (in the bottom line) seems to be the only one of major consequence:

(Top: engraving. Bottom: fair copy.) The need to change this canonic line stems from a revision Bach made 11 bars earlier— the lines being in augmentation with one another. Admire Bach’s brazenness as he changes what was D over B, to D over C#!

Here, as I mentioned, is a very early episode introducing the concept of Bach in revision:

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Show me a finale as densely packed with thematic material as this one. Here are the five bars — the only five bars — discussed in today’s episode. You might listen while looking at them:

Notice the finale comes in two stages, first diminution, then stretto. The signature in the final bar is noteworthy (though it should be mentioned that the letters are an addition by the editor.)

And here is a video of the Mandelbrot set fractal, as promised (with perfect background music:)

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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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Concepts Covered:

The musical canon has long been a cornerstone of Baroque music, with J.S. Bach canons exemplifying the height of Bach’s canonic art and canonic structure in Bach’s compositions. This episode explores Bach’s musical contributions, from his early compositions to his sophisticated fugue and canon techniques. We also discuss Pachelbel’s Canon in D, one of the most recognizable pieces in classical music, analyzing its compositional style, melody, and Baroque influences. Through Bach musical theory, Bach analysis and theory, and comparisons with Pachelbel’s influence, we uncover the lasting impact of these works on Bach music history and the broader canon of Baroque music masterpieces.

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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