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When playing a piece by Bach, is there anyway to figure out what tempo he intended it to be played at? I ask because I am working on Sinfonia No. 4. I prefer a fast tempo in that piece, but everybody seems to play it very slowly. Is there a "correct" tempo that we know of?
"Everybody" in your post meaning top pro pianists or amateurs you've heard play it? The tempos chosen by top pros is more meaningful as a guide. There is no one correct tempo but most would say there is a range of appropriate tempi for most Bach pieces. Even then one can always find a good pianist who plays it at some outlier tempo. Gould was famous for quite often choosing very fast or very slow tempos.
For Bach pieces that are based on dance forms knowing what the dance looks or a typical tempo for each dance like can help with choosing a tempo. One can find videos of the various dance forms Bach uses on YouTube.
I find that often - although not always - the music itself can set its own tempo. With Bach, since he very, very rarely gave any tempo indications, the tempo set by a performer is the one that the performer feels the music dictates or that s/he is comfortable with. Looking at and reading through the music, but never having played it, the score of Sinfonia number four suggests to me a Moderato tempo. Some edited editions will give tempo suggestions, but they are not Bach's; they are more modern editors' suggestions. Bischoff, for example, suggests Andante maestoso at MM = 56 to the quarter-note, and that's a shade faster than I think I would play it. That said, becoming more familiar with the work, I might well change my mind.
I think, therefore, that you have every right to play the Sinfonia at the tempo that suits you.
The sinfonia 4 has a structure of a trio with bass line. Usually pieces by Bach will either be in a dance or suggest other forms. The way the piece is written, the theme and the time signature will give you some indications. With a 4/4 tempo, which is usually moderate , and for this piece, i would play it in a range of 55 to 60 quarters, potentially even just a little faster is an option.
But what is more important is to make it sound convincing and well played at whatever tempo you choose. There is no point playing it fast if that does not work musically.
There're a on youtube a couple of very interesting lectures on Bach by pianist Arthur Loesser. In one of them regarding sinfonias his advice is those ones with long motives may be played slowly. The ones with very short motives sound better when played faster so the constant repetition of short motive doesn't become boring. This is not any kind of strict rule, just the suggestion he makes. I hope it may help you.
I also like this recording with Janin Jansen, Maxim Rysanov and Torleif Thedeen, where they take a slightly slower tempo. The whole CD (containing the inventions, sinfonias, and the D minor partita) is wonderful!
