I mentioned J.S. Bach and Beethoven specifically in the question, but if there was a general trend I would be interested in other composers from 18-th and eary 19-th century also. I got interested in this issue because of Belgian clavichordist Wim Winters and his YouTube channel AuthenticSound, where the topic is frequently discussed. As far as I can tell there are two main theories about early music tempi. In the "mainstream" view historical (early 19-th century) metronome numbers are interpreted the same as today. However, this often results in a tempo so fast it's physically unplayable, which is problematic. The alternative "double beat" view interprets historical metronome numbers as effectively two times slower. This in turn often results in a tempo which is shockingly slow to a modern audience. The "double beat" theory was proposed in 1974 by Erich Schwandt and more recently elaborated by Lorenz Gadient ("Sekunde, Takt und Pendelschlag", https://www.jstor.org/stable/25162336), but many authors that hold the mainstream view, such as Klaus Miehling in his book "Das Tempo in der Musik von Barock und Vorklassik", argue against the "double beat" theory.
I am not a musicologist nor a historian, so it's hard for me to make sense of all this. Especially since the topic itself seems to be quite controversial and confusing, with even the experts understanding the same primary sources in exactly the opposite way. On the other hand I find it kind of fascinating that there seems to be so much disagreement about a seemingly straightforward issue. I thought that maybe somebody on AskHistorians could be able to inject some clarity into all this :)
Concert cellist and Bach specialist here :) Never thought I’d be qualified to answer something in this sub, but here goes!
We don’t know the actual speed at which Bach’s music was played. In the cello suites, we use some clues to try and guess at what the groove is. Things like meter (time signature), the relative length of notes (16th notes vs. whole notes, for example), the title of the movement (courante, for example, translates roughly “running dance”), and perhaps most importantly the rate of harmonic motion are all good clues.
The last clue I mentioned, harmonic motion, is the rate at which there is tension and resolution felt as a result of harmony and dissonance. You can intuit what is an appropriate speed based on what speed will keep the listener’s attention (i.e. not too slow) and won’t let important or interesting details go by too quickly.
Usually modern performances are all at similar speeds because music is somewhat of an oral tradition, learned kind of like a language where you mimic what others before you have said. It is rare to find a performer who will think outside the box and take the score at face value. Glenn Gould was one such brave performer. I really love his 1981 recording of Bach’s Goldberg Variations.
If you want to learn more about the different theories about what things might have sounded like when they were composed, you may be interested in a sector of the classical music population that specializes in what is called historical performance. There you may find people who geek out in search of clues like what the dance moves of the day were and how they relate to music.
Other considerations might be the technical capacities of the instruments of the day. Could you play as quickly with a baroque bow and gut strings as you can on a modern violin? You can also consider the venue. If the pieces were meant to be played in a cathedral, do you need more time for the resonances to fade before moving onto a new harmony?
Great question, OP, and one that I wish more musicians would ask themselves! I was tickled once to learn that I had chosen such a radically different tempo for a well known piece by Bach that the listener didn’t recognize what piece I was playing. I think if more people asked the question you’re asking, we’d see a lot more diversity in interpretations as we all make our best guesses at connecting the dots.
I hope someone will chime in and give you some info on Beethoven and can elaborate on Bach. I’ll be following with interest!
I can help add to Beethoven. We aren't certain, but there are a few theories.
Beethoven was one of the earlier composers to use a metronome, but we aren't sure if it was working correctly or not. Tempos that are unplayable may have been a result of a poorly made metronome. Johann Nepomuk Mälzel, the creator of Beethoven's metronome, was known for creating musical automata, but may have stole many of his inventions from colleagues. We do know that the idea from the metronome came from another inventor, Dietrich Winkel. Winkel created the double pendulum, which Mälzel repurposed into the classical metronome that we know and love today.
Beethoven was upset with the imprecision in the typical tempo markings. Andante may imply walking, but we don't all walk at the same pace. Having an explicit verifiable marking at the beginning of his score was the key to the specificity he wanted. Unfortunately, as you've noted, those markings are frequently much faster than even some of the most talented musicians can play. The Hammerklavier sonata's marking of 138 beats per minute for the half-note was considered unplayable in the early 19th-century, and professional musicians still dial it back a few clicks in performance today.
We don't know why this marking is so fast. Beethoven's eyesight may have been failing. His metronome may have been unstable. He does mention that it broke in at least one letter. Mälzel's markings could have been inconsistent. The publisher could have made a simple error engraving the score. Beethoven's original metronome has been found, but the bottom weight was missing. Without it, we can't tell how accurate the machine was. Anecdotally, a conductor once explained to me that instruments in the Romantic era were developed to be heavier with a thicker sound, and that on period instruments the tempi are achievable.
I know this isn't a definitive answer, but fortunately, as modern day musicians we get to decide how fast we want to play a piece regardless of how Beethoven would feel. You can find recordings of his music at his original tempi, slower, on period instruments, on electronic synthesizers, and everywhere in between. Getting to choose your favorite recording is a great gift of technology, and one of the reasons that performing the music exactly as the composer would have imagined is not always the most important part of a performance.
Noorduin, Marten. 2017. “Re-Examining Czerny’s and Moscheles’s Metronome Marks for Beethoven’s Piano Sonatas.” Nineteenth-Century Music Review, 1–27. https://doi.org/10.1017/S1479409817000027.
Stadlen, Peter. 1967. “Beethoven and the Metronome, I.” Music & Letters 48 (4): 330–49.
Forsén, Sture, Harry B. Gray, L. K. Olof Lindgren, and Shirley B. Gray. 2013. “Was Something Wrong with Beethoven’s Metronome?” Notices of the American Mathematical Society 60 (09): 1146. https://doi.org/10.1090/noti1044.