Reflections on the Bach Chaconne: variation technique

I haven't written about the Chaconne by Bach for a while, but I have been continuing to work on it, though I did miss over a month due to moving houses. Today I want to talk about what is probably the most salient aspect of the piece: it is a set of variations on a theme eight measures long, though the second four measures are nearly identical to the first four. Call it a theme of 4X2 measures. After this theme there are thirty-one variations the last of which is a slightly varied repeat of the theme. The theme is a version of the old chaconne chord progression that I talked about in this post.

What is so interesting, to both composers and listeners, about a theme and variations? I guess it is because it faces head-on the basic problem of composition, that of unity and variety. Arnold Schoenberg in his text for composers, Fundamentals of Music Composition, devotes a whole chapter to theme and variations. His models in this text are almost all from Beethoven, but, of course, Beethoven looked to Bach for some of his models. Schoenberg says "A simple theme will consist of closely related motive-forms, in preference to distant ones. Structurally, the theme should show definite subdivision and clear phrasing." (op. cit. p.167-8)

In order to make my points as succinctly as possible, I am just going to look at the first four measures of the theme (as I said, the second four are nearly the same). I'm also going to use examples from my edition of the piece to save time. Here is the beginning. As you can see, the phrase begins on the second beat of the measure and ends on the first. (You can click all these images to enlarge.)

What I am going to do is take a slice through the piece, picking out subsequent variations and placing them alongside this one so you can instantly compare how he varies the theme. Notice how the variations now start on the downbeat. The first few use a chromatic descending bass line and dotted rhythms:

Then flowing eighth notes:

A sequence using that chromatic descent and dividing the melody between treble and bass:

Next a rhapsodic variation with the melody spanning two octaves:

After a few similar variations that introduce some G minor harmonies, there is a lovely lyric variation using a descending sequence:

Then this sequence is itself given a variation:

And yet another variation on the same sequence, this time with a stretto effect:

And still another variation using the same sequence, but this time with 32nd notes:

[There are different colors in the score because my music software shows different voices in different colors.]

I could go on, but this is probably enough for today. A lot of variations by other composers are of the "division" type that tend to simply divide up the melody into smaller and smaller notes and frankly, they can be rather boring for the listener. The great masters of the variation, of whom Bach and Beethoven stand at the top of the list, are far more creative. They take a sharp focus on different aspects of the theme. There is one G minor harmony in Bach's original theme, but he expands the passage work in several variations to use this harmony. Also, he takes the implied harmonic sequence in the first two measures. D, C, Bb, A, and uses it in a variety of different ways. He has variations in shorter note values followed by ones in longer note values. He gets an astonishing amount of musical ideas out of a very tiny theme. The variety comes in the harmony, but also in the melody and especially in the rhythm.

I wonder, when Bach set out to compose this afterthought to the Violin Partita No. 2 if he saw that it was going to turn out to be such an enormous movement, the longest single instrumental movement in the whole Baroque era?

Here is Segovia's performance with the sheet music.