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I recently came across a recording of Bach's Partita for Violin No. 2, the fifth movement (the Chaconne), and upon researching it further, I learnt that it is often praised as a very important composition.

From Wikipedia:

Yehudi Menuhin called the Chaconne "the greatest structure for solo violin that exists".

Violinist Joshua Bell has said the Chaconne is "not just one of the greatest pieces of music ever written, but one of the greatest achievements of any man in history. It's a spiritually powerful piece, emotionally powerful, structurally perfect." He played the piece busking in L'Enfant Plaza for The Washington Post.

However, while listening to it myself, sure, I'd agree that the intense double-stopping and polyphonic nature of the piece would certainly deserve some praise (more so for the performer than the composer, I'd imagine), I fail to see why the composition is so highly regarded.

Could someone shed some light on this?

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I think Mr. Bell is a little over the top. But the Chaconne is an impressive compositional achievement. Consider the challenge: you want to write a chaconne - that is, a dance piece built over a repeating bass line - but you are writing for a single instrument, not an ensemble with bass and treble instruments. That instrument normally plays just a single note at a time; two notes at once is possible, but you have to be quite careful which two; three or four require extremely careful planning, and are exponentially harder to write and play, just as juggling plates gets exponentially harder as you add each plate.

And, you are not satisfied to write a "simple" dance piece. It will be a chaconne, and use chaconne rhythms, but will be a thoroughly contrapuntal piece. Thus in between the carefully chosen double stops, you'll use compound melodies (single melodies that imply multiple independent voices) to set up contrapuntal tension.

But that's not hard enough. You will write dozens of variations, shifting figuration, patterns, contrapuntal devices, key and tempo for each one, and then grouping the variations into satisfying emotional arcs that rise and fall. The final result will be danceable, singable, and playable at the same time. It will satisfy violinists (because it is really hard and shows off their skill) and listeners (because it sounds like "real music," not a violin etude).

I'm impressed...

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