In music software, I wrote out the trill from Haydn Sonata in D, XVI/24, measure 48. At the suggested tempo of 120 beats per minute, 3 thirty-second notes for every 2 sixteenths still sounds much too fast (12 notes per second). So, on the recording, I was apparently not hearing the number of notes in the trill correctly.
Can you really play this movement at 120, apart from the trill? To me this seems too fast. Ideally you should just play the trill as an unmeasured trill and not in any particular ratio to the LH 16ths. But having said that, if you try to get the fingers to "think for themselves", they may well end up unwittingly synchronising themselves into a simple ratio anyway. Don't fight what they want to do. If they settle on a ratio, let them, but don't impose an arbitrary 2:1 or 3:2 ratio on them. Really 12 notes per second is not ridiculously fast, you just need to train harder! I'm no Speedy Gonzalez by any stretch of the imagination, but even I can play this trill at 2:1, provided I drop the tempo to 108 or so. That's more than 14 nps. But even 16nps should be doable with a bit of practice. How are you fingering the trill? 2-3? Try 2-4.
I"ve learned to fit in as many trill notes as possible, but the notes are so short that I can't count them.
Tempo of 120 beats per minute in Haydn Sonata I don't play in the highest sonata at 120 beats for minute, that tempo was was suggested in the music, and served as the basis for the question can someone play 16 notes per second. When I play back notation of 16 notes per second in music software, it doesn't sound like it's humanly possible to play, nor does it sound musically valid. I would stay away from attempting this speed out of concern for a serious injury.
Re: Tempo of 120 beats per minute in Haydn Sonata Don't worry. Pianos are pretty robust. Injuring them by playing fast trills is virtually unheard of.