Also bear in mind that in the solo violin piece there's no (possibly bored) bass line player chugging along underneath what's going on above. The violinist needs to create that bass line. At the same time, though, the bass line (by virtue of being played on a non-bass instrument and in a non-bass register) becomes something more thematic and complicated. That ambiguity/duality needs room to express itself.
There are places where the harmonic rhythm clearly speeds up, and yet slowing the tempo down to compensate would make no sense. Yes, there are many places where one could argue either way whether the harmony is actually changing or whether Bach is incorporating passing tones, neighbour notes, etc; but there are places where the harmony is completely unambiguous. A couple of examples: the last bar of the variation starting in bar 121, full of hemi-demi-semi-quavers and leaping string crossings, clearly changes harmony on every crotchet. It's not a good place to slow up as it leads back to what at first seems to be a reiteration of the opening, but in fact turns out to be
another place where the harmony changes on every crotchet. Too much slowing down at these points would get turgid, and also bring the piece to a stop when in fact it then blooms into D-major. Later in the piece, in the variation starting bar 241, the harmony moves on
every quaver. I don't think there's anything like that going on in either of the chorale chaconnes.
I also agree with Ian about the "harmonic implications of the melody." In the first beat of the second bar of your comparison, Ollie, there's an amazing high B-flat absent in the chorale. Yes, it's just an upper neighbour of the following consonant A, but to pass it by in a hurry without giving it the breadth to clash against the C-sharp in the lower line (held in the ear, not the bow) would be a shame. Same with the F-against-B clash in the first beat of bar 3. But not only are these harmonic clashes and touches interesting - those passing notes give the whole of the upper line a sinuous shape that the other does not have, and that takes a certain breathing space to make the most of.
Also keep in mind how it takes a
bit of time to spread chords on a violin. Some modern violinists imagine that those 4-note chords ought to be played as near to simultaneously as possible. Those of us in the hysterical world think more akin to how harpsichordists might spread chords, how you can vary the timing and overlap of the spread to emphasise different voices, etc. A fast tempo allows much, much less scope for such things. In particular the three variations starting at bar 141 would lose much scope for showing that ambiguity/duality between harmonic rhythm and melodic line, not to mention passing which voice does what amongst themselves.
I'm not saying it's technically impossible to play this piece at a faster speed - I'm sure with enough practise one could get ones fingers around it - but how much would be lost, would go racing by without the chance to register or to exhibit the subtle differences Bach puts into each variation. Many variations seem grouped into categories of similar or developing ideas, but each one is different - most of the time the end of each variation contains the seed of the next - and hurrying through gives neither the player nor the listener a chance to register such things. Maybe it would be exciting, but is it possible or desirable to sustain mere excitement over such a vast piece? Surely an emotional journey such as the chaconne should have more to offer than just rhythmic momentum and excitement?
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Just saw your latest post, Ollie. I'm not quite sure what you mean by the "status quo" with this piece. I've never heard two people play it the same way. I'm pretty sure I've heard a very wide range of tempi as well. But I can't say I have much desire to hear it at crotchet=anything-faster-than-100, no more than I do to hear it at crotchet=anything-slower-than-50. Anything outside these rather wide parameters seems gimmicky to me. I'd be interested to be convinced otherwise, but skeptical that it would be possible.
Also, just because the opening is bare, that doesn't mean one ought to take the tempo from that. The opening of the Mozart clarinet concerto could have a very nice swing at half-bar=92, but would you want to play the rest of it like that?